Reliability of 3D multi-span bridges isolated with FPS devices

This paper investigates the seismic reliability of 3D multi-span bridges equipped with friction pendulum isolation system (FPS) isolators. Using a probabilistic approach, non-linear time history analyses in Opensees are carried out on a 3D 5-span retrofitted bridge located in central Italy. The FPS isolators are modeled varying the isolation period and assuming sliding velocity-dependent friction coefficients together with seismic inputs as relevant aleatory uncertainties. The seismic reliability of the isolation system is evaluated using fragility curves and convolution integrals, providing insights into the probability exceeding critical damage states within a 50-year time period. These findings highlight the importance of incorporating 3D effects into the seismic design of isolated bridges.

Currently, one of the most effective strategies for improving the seismic performance of bridges is the adoption of seismic isolation techniques.

The primary function of isolation systems is to reduce the seismic inertia forces acting on the deck and subsequently transmitted to the substructure by increasing the isolation period (Ghobarah and Ali, 1988), (Jangid, 2004). Various isolation devices have been developed, including high or low damping elastomeric bearings, lead-rubber bearings and sliding bearings (Constantinou et al., 2007), (Rele et al., 2021).

Among them, friction pendulum system (FPS) bearings offer distinct advantages, such as decoupling the isolation period from the deck mass and providing energy dissipation through friction between the concave surface and the slider (Tongaonkar et al., 2003), (Zayas et al., 1990). Several studies have specifically analyzed the seismic response of FPS-isolated bridges. For instance, the seismic performance of a three-span continuous deck highway bridge equipped with double concave friction pendulum devices was investigated in Kim and Yun (2007). In Kunde and Jangid (2006), different mathematical models were evaluated to simulate the response of bridges subjected to real earthquake ground motions, highlighting the accuracy of simplified modeling approaches in capturing the flexibility of piers and decks.

The impact of modeling parameters, including geometric and material properties of both the bridge and isolators, was explored in Eröz and DesRoches (2013) through three-dimensional numerical models of multi-span steel girder bridges with FPS devices. Furthermore, the effectiveness of variable FPS isolators of three-span continuous deck bridges under near-fault ground motions was assessed in Panchal et al. (2021). Reliability-based design abacuses for FPS devices in multi-span continuous bridges were developed in Castaldo et al. (2022), providing valuable design insights. In addition, advanced numerical models, such as those employed in Buckle et al. (2006), have demonstrated the importance of incorporating multiple degrees of freedom to accurately represent the response of multi-span bridges under spatially varying ground motion.

This aspect is particularly relevant when assessing the influence of SVEGM, as seismic waves propagate differently along the bridge supports due to variations in amplitude, frequency content and arrival time (Lupoi et al., 2005), (Sextos et al., 2009), (Shinozuka et al., 2000). The present work examines the seismic response of conventional highway reinforced concrete (RC) bridges equipped with FP isolators. A 5-span simply supported bridge located near L’Aquila, Italy, serves as the case study.

3D non-linear time-history analyses are conducted using OpenSees software (McKenna et al., 2010), with the friction coefficient treated as a random variable following a standard normal distribution. Two different radii of curvature, corresponding to different isolation periods, are also examined. To assess the seismic response of the bridge across varying intensity levels, incremental dynamic analyses (IDA) are performed, providing statistical insights into the response of the bridge piers. Then, seismic fragility curves are derived, considering different damage limit states. The seismic reliability of the bridge piers and FP bearings is then evaluated over a 50-year time frame, based on the seismic hazard curves for L’Aquila. Finally, reliability curves are developed for pier drifts, indicating the seismic performance of the structure.

Three-dimensional modeling of the bridge

Description of the case study

The case study is an existing straight simply supported RC bridge, built in 1979 and located in central Italy, near the border of the Marche and Abruzzo regions. The design peak ground acceleration at the site, corresponding to a return period for the life safety limit state, as defined by Italian guidelines (MIT, 2018), is 0.3g. The superstructure extends over a total length of 163m and consists of five simply supported spans, each averaging 32m in length. The deck has a total width of 12.5m and comprises RC I-girders, connected by a 27cm RC slab. The substructure includes unreinforced elastomeric bearings (70x50x2 cm) positioned on each girder, a pier cap with a hollow rectangular cross-section measuring 11m in width, and four RC piers of varying heights: H1 = 9.75 m, H2 = 13.4 m, H3 = 12.35 m and H4 =
10.22 m.

Each pier has a circular cross-section with a diameter of 2.6 m, a concrete compressive strength of 29.1 MPa, and a longitudinal reinforcement ratio of 1.6%, with steel bars having a yield strength of 420 MPa. The transverse reinforcement consists of hoops with a clear spacing of 44 cm, leading to a total transverse steel ratio of 0.055%. At both ends, the bridge is supported by seat-type abutments with no skew angle, each containing five elastomeric bearings placed on the abutment stem wall. The abutments are 12m wide and 3.5m high. Both the piers and abutments are founded on pile systems.

Given the geometrical and mechanical characteristics of the bridge, along with the lack of seismic detailing and inadequate confinement from the transverse reinforcement, it is assumed that a retrofit intervention has been implemented. The structure has been equipped with FPS bearings to replace the original elastomeric bearings. These devices maintain the same number and spacing as the original bearings, both at the abutments and on the pier caps.

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Numerical modeling

A three-dimensional non-linear finite element (FE) model of the isolated bridge has been developed using Opensees (McKenna et al., 2010). Figure 1 illustrates the numerical model and the adopted approach for representing the main bridge components. The superstructure is expected to behave elastically under seismic loading; therefore, the deck is modeled using five elastic beam-column elements per span. Each element is assigned the relevant section properties, material characteristics and mass density per unit length, contributing to the lumped mass matrix.

Material nonlinearity is incorporated exclusively in the RC piers and FPS devices. Each pier is modeled using two Euler-Bernoulli fiber-section, force-based beam-column elements. The fiber-section model includes confined and unconfined concrete fibers. To capture geometrical nonlinearity, P-Delta effects are included in the pier elements. The behavior of the concrete fibers is defined using the Concrete02 material model in Opensees, which implements the uniaxial Kent-Scott-Park with added tensile strength and linear tension softening. For unconfined concrete, the mean compressive strength is set with a corresponding strain of 2 ‰.

Regarding the confined concrete, an amplification factor of 1.023, as proposed by Mander et al. (1988), is adopted to account for confinement effects on the concrete stress-strain response. Due to the large clear spacing between the transverse reinforcement, the resulting confinement effect is minimal in the fiber-section model. The steel fibers follow a uniaxial stress-strain law (Steel02) to represent both the longitudinal and transverse reinforcement. The ultimate strain is limited at 0.1 using the MinMax material in Opensees.

The modeling approach for the abutments follows the recommendations provided in the Caltrans guidelines (Caltrans, 2019). Their contribution to the overall bridge stiffness is considered in both the longitudinal and transverse directions. In the longitudinal direction, the abutment stiffness is influenced by the passive earth pressure resulting from embankment- backwall interaction and pile-soil interaction. Conversely, in the active direction, the resistance is provided only by the pile-soil interaction. In the transverse direction, stiffness contributions arise from the combined effect of backfill-wingwall interaction and pile-soil interaction.

Regarding the isolation system, the original elastomeric bearings have been replaced by FPS devices: five at the pier cap and abutment. These isolators are implemented using the SingleFrictionPendulumBearing element available in Opensees.

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