Seismic fragility and cost-benefit analysis of a conventional bridge with retrofit implements

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Highlights

  • A conventional bridge was considered, and the as-built performance of the bridge was compared to the retrofitted ones, including seismic isolations and buckling restrained brace.

  • By using nonlinear time history analysis and Opensees, fragility analysis was conducted for each model based on two criteria (column curvature ductility and abutment seat displacement).

  • In the paper, the significance of seismic retrofit implements in terms economically was considered, and the cost-benefit analysis was utilized.

Abstract

Fragility analysis is a well-known tool to evaluate the impact of different retrofit measures on damage probability of structures. In this study, the performances of a conventional multi-span continuous (MSC) concrete girder bridge reinforced with different seismic control devices were investigated. The original bridge is supported by both elastomeric bearings and exterior shear keys. For other retrofitting solutions, lead rubber bearings (LRB), friction pendulum systems (FPS), and buckling-restrained braces (BRB) were considered and compared to the original structure of the bridge in terms of seismic performances and economical costs. To analyze the seismic performances, the fragility curves based on the probabilistic seismic demand model were extracted under various near-field and far-field ground motions. Additionally, cost-benefit analyses were performed to determine the benefit of using each of the devices economically. The results indicated that both LRB and FPS significantly reduced the damage probability of substructure, while FPS provided the bridge with high vulnerability in abutment seat at slight and moderate levels of damage. Also, the installation of BRB seismically was an efficient solution and decreased the damage probability of the bridge system. Based on the results of fragility and cost-benefit analysis, LRB was found to be a beneficial implement for the studied bridge.

Introduction

Bridges are simple structures which play a vital role in the transport network. This simplicity in the structure of the bridges has been originated from their low degree of indeterminacy. Therefore, the stability of each structural member is a significant parameter since any damage in these parts can cause direct and indirect costs and ultimately lead to the collapse of a whole system as a severe consequence. In recent decades, several devices have been introduced and commonly utilized as retrofit implements to prevent failure in bridges such as shear keys, braces, and seismic isolation systems. Using seismic isolation is a practical solution that reduces the impacts of seismic consequences on new and retrofitting projects of the bridges and structures. A large number of bridges around the world have been equipped with isolation systems as a powerful earthquake resistant method. These implements separate bridge superstructures from the horizontal components of ground motions, and the deformation happens in the isolators instead of the substructure elements. Also, they increase the natural period of the bridge with their flexibility and damping to deviate the dominant frequency of earthquake inputs [1,2]. Seismic isolator systems have been classified in one of two main categories; one of them is the category containing elastomeric material. Lead rubber bearing (LRB) is the most common and well-known among them, which is made of rubber and a lead core that provides great flexibility and supplemental damping in case of an earthquake.

Another seismic isolation category is sliding components that the Friction pendulum system (FPS) is the famous one among them. FPS is spherical bearing with the spherical sliding interface and able to take very large axial loads. It can be designed to have long periods of vibration with considerable capacity for lateral displacement. The friction between sliders interfaces in the bearing can play the energy dissipater role while restoring force is produced by the self-centering action of the structure sliding on the concave spherical surface under the weight of the bridge.

Both of LRB and FPS have their own characteristics that past studies investigated and compared completely. In addition to these conventional devices, some modified systems were proposed and their performance was studied. The results of these studies showed that these systems can optimize the performance of the isolation system (For more information see Refs. [1,[3], [4], [5], [6], [7], [8]]).

Another implement to reduce responses of bridges under earthquakes is implementing energy dissipation braces such as buckling-restrained braces (BRB). BRB as a device with hysteretic behavior consists of two main parts. The internal part is a steel core that transfers the axial loading. The outer part is related to the encasing system and has a preventive role in the buckling of the core. Preventing the buckling of the inner core of BRB makes the compression yielding occur in the core and consequently decreases the seismic responses through energy absorption. BRB has been widely applied to the buildings; however, there are few investigations about BRB in bridges [9,10].

All of these implements have different performances and effects on structures. In order to monitor the impacts of these devices on bridges, fragility curves have been used as the most common tools in recent decades. These curves demonstrate the conditional probability of failure caused by various levels of ground motions [11]. Limited studies have been reported on utilizing fragility curves to distinguish the effectiveness of supporting bridge by retrofit devices.

Padgett et al. [12] evaluated some retrofit implements such as shear keys (SK), elastomeric bearings (EB), seat extenders, restrainer cables, and steel jackets in a retrofitted multi-span continuous concrete girder bridge class based on fragility curves. In another study by Padgett et al. [13], in addition to fragility curves, costs of bridges, and seismic hazard curves of locations were considered to find the most cost-effective system. According to the estimated cost-benefit ratio, they concluded that the best retrofit measure depends on the zone, due to different damage states and diversification of the local seismic hazard. Zhang and Huo investigated the effectiveness and optimum design parameters of isolation devices such as EB, LRB, and FPS for highway bridges [11]. They extracted fragility curves based on both probabilistic seismic demand and incremental dynamic analyses. Siqueira et al. replaced typical elastomeric bearings with natural rubber seismic isolators to mitigate the seismic risk of highway bridges in Quebec [14]. Based on fragility analysis, they found that the seismic isolation was more effective in decreasing the damage in columns and foundations. The impact of different rubber isolations such as natural rubber bearings, high-damping rubber bearings, and LRBs on fragility curves of a highway bridge was evaluated by Hedayati Dezfuli and Alam [15]. They found that the bridge considered by natural rubber bearings was the most vulnerable system compared to the other systems, while high-damping rubber bearing was the one that mitigated the damage and risks more than two other ones for its higher energy dissipation capacity. Lee and Nguyen examined LRBs in a continuous steel box girder bridge and extracted the fragility curves with and without isolation conditions [16]. Their results based on columns displacement ductility acknowledged the ability of LRBs in limiting of earthquakes damage. Xiang and Alam conducted a study on the effectiveness of three different braces named BRB, viscous damper braces, and piston-based self-centering braces. They performed fragility analysis for near and far-field earthquakes to assess the performance of the implements [17].

The probabilistic methods and fragility curves were used to evaluate the vulnerability of the whole system and components of the old and newly designed skewed multi-frame concrete box-girder bridges by Abbasi and Moustafa [18]. Also, they examined the two mitigation strategies such as restrainer cables and SKs. In another study, Xiang and Alam used fragility curves to compare the impacts of yielding steel cables, viscous dampers, friction dampers, and superelastic shape memory alloy cables in an isolated bridge. They indicated that superelastic shape memory alloy cable is the most effective in limiting all considered damage states. Also, other devices improved the performance of the bridge too [19].

Due to the history of the vulnerability of bridges, and also the necessity of endless serviceability of them after a natural event such as earthquakes, it is vital to conserve the bridges from serious damage [20]. For this study, a multi-span continuous concrete girder bridge, which is one of the most common types of conventional highway bridges in today's infrastructures, was selected as a case study. The as-built bridge includes EB with external SK. Based on the specifications of EBs, the allowable displacement of these bearings cannot provide sufficient ductility and freely movement due to their material properties and the inability of dissipating energy. Based on these reasons there is a need to examine other retrofit implements with the ability of high damping and more allowable deformation under earthquakes. Although the costs of these devices are significant for running projects, research has shown that these implements are able to preclude plenty of infrastructures from collapsing or even serious damage. Thus, it is important for researchers to review the necessity and efficiency of these systems. For this purpose in this study, other models, which each of them contained one of the three control devices including LRB, FPS, and BRB adjacent to the original condition of the selected bridge, were considered. Furthermore, fragility analyses were conducted to compare the relative effectiveness and functionality of these retrofit tools based on various ground motion records. Finally, the cost-benefit analysis was used to economically compare different models.

Section snippets

Bridge and modelling

The selected bridge is a typical four-span, three-column bents bridge which is currently located in Isfahan province of central Iran, (see Fig. 1). It has a continuous concrete deck containing 11.8 m wide, 0.2 m thick supported on 5 girders spaced at 2.3 m (see Fig. 2(a)). The bridge consists of a 1.65 m by 1 m cap beam and 7 m and 8 m high, 1.2 m diameter columns. Each column is reinforced by longitudinal bars and spirals. Also, piers are supported by the strip footings, and the column bent

Fragility analysis results of components and systems

Fig. 10(a)-(d) illustrates a sample of PSDM for the column curvature ductility results of the four bridge models and the value of linear regression parameters. Each of the depicted spot in Fig. 10(a)–(d) demonstrates a result of nonlinear time history analysis. Using regression parameters, fragility curves referred to primary components (curvature of columns and abutments seat displacement) were developed and presented in this section across slight, moderate, extensive, and complete limit

Conclusions

The main objective of this paper is to evaluate and compare the performance of an as-built MSC concrete girder bridge supported by EB and SK with three other retrofitted models. The considered retrofit devices include LRB, FPS, and BRB with the as-built form of the bridge. For this purpose, three-dimensional analytical models were utilized and exposed to various earthquake records. Based on the outcomes of PSDMs, fragility curves of two primary components and the whole system of the bridge

Declaration of competing interest

Maryam Montazeri, Gholamreza Ghodrati Amiri, and Pejman Namiranian declare that they have no conflict of interest.

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