**1. Introduction**

Over the past decades, curved continuous girder bridges have been widely used in transportation networks that featuregeometric restrictions and constraints on site space, such as complicated interchanges and river crossings. However, curved bridges are vulnerable to earthquakes. Research in previous studies showed that curved bridges could sustain severe damage due to the coupling between bending and torsional forces or the displacement caused by complex vibrations [1–3]. The combination of their horizontal curvature and the irregularity of their adjacent segments means that curved bridges feature complex dynamic characteristics, which cause non-uniform collisions along the contact surface [4,5]. In addition, large pounding forces during collisions can amplify the relative displacement, which may lead to girder unseating and the collapse of the bridge. Chiyu Jiao et al. [6] conducted a shake table experiment on a 1/25-scale curved bridge model to investigate the influence of collision between adjacent girders on the seismic response of bridges. It was found that the collision was non-uniform along the contact surface, and the girder-to-girder collision could induce significantly large in-plane rotation of the adjacent bridges, which could substantially increase the global displacement demands of the bridges.

Damage to curved bridges is mainly due to pounding between girders or between girders and the abutment, aswas commonly observed during past major earthquakes [7]. Damage reports oncurved bridges during the 1995 Hyogo-Ken Nanbu earthquake in Japan indicated that pounding can lead to local damage and the collapse of bridge decks [8].

**Citation:** Li, Z.; Kang, S.; You, C. Seismic Mitigation of Curved Continuous Girder Bridge Considering Collision Effect. *Symmetry* **2022**, *14*, 129. https://doi.org/10.3390/ sym14010129

Academic Editor: Jan Awrejcewicz

Received: 10 December 2021 Accepted: 6 January 2022 Published: 11 January 2022

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The failure of girder ends and bearing damage due to the pounding of adjacent simplysupported spans were reported after the 2001 Bhuj earthquake in Gujarat, India [9].The collapse of curved bridges, such as Baihua bridge, wasreported as a consequence of the 2008 Wenchuan earthquake. It was noted that the collapse only occurred in one of the curved segments of the 18span bridge while the other straight segments remained in location [10]. The destruction of bridges was also observed in the 2010 Chile earthquake and in the 2011 Christchurch earthquake [11,12]; most of the bridge damage, including the phenomenon of unseating, was caused by collisions between adjacent structures, especially the damage to curved bridges.

Reports from past major earthquakes and research findings from analytical and experimental researches highlight the seismic vulnerability of curved bridges and the seismic pounding impact on bridges. Therefore, seismic mitigation and collision prevention measures on curved Bridges have been highly valued in academic and engineering circles.

A variety of seismicmitigationtechnologieshave been proposed for bridges, including seismic isolation bearing, passive energy dissipation devices, tuned damper, and semiactive damping devices. Seismic isolation devices, such as rubber or lead rubber bearings, have been used to reduce seismic forces [13–16]. However, the use of lead rubber bearings can lead to large displacements, which consequently increase the possibility of pounding between adjacent segments or even unseating damage. In order to mitigate possible pounding and unseating damage, some researchers recommended the installation of rubber shock absorbers and restrainers. A few researchers have investigated the effectiveness of using steel restrainers [17–21] or Shape Memory Alloy (SMA) [22] and rubber bumpers together to mitigate pounding and unseating damage between adjacent decks. Felix [17] performeda comparative analysis of curved viaducts with cablerestrainers and different isolation bearings, and pointed out that cablerestrainers could reduce the probability of girder unseating. Raheem [19] conducted numerical studies on an isolated bridge with cablerestrainers and a natural rubber shock absorber. It was found that the use of rubber shock absorbers at the expansion gaps can significantly reduce the pounding forces, since the absorbers can reduce the impact stiffness and the cablerestrainers can effectively prevent girder unseating. Chiyu Jiao [21] performed a shake table experiment on a curved bridge model with a pounding buffer zone made of a natural rubber pad or aluminum foam at the expansion joint location to mitigate the pounding effect. The results show that the buffer zones of rubber and aluminum can effectively reduce seismic impact forces, and hence alleviate the localized damage. Meanwhile, the application of viscous dampers or viscoelastic dampers to bridges has received significant attention in recent years [23–26]. Due to the large resistance force and energy dissipation capacity, viscous dampers offer wide application prospects [27]. The main advantage of viscous dampers is that they are only activated during earthquakes, and theyshow no resistance force under slow relative segmen<sup>t</sup> movement.

Although there are some studieson seismic mitigation and unseating prevention, relatively few studies of curved continuous girder bridges have comprehensively considered the measures of seismic energy dissipation and pounding or unseating prevention together. In order to improve the seismic performance of curved girder bridges, it is necessary to carry out further research on the reasonable combination of seismicmitigationtechnologies and pounding mitigation measures together. For this purpose, this paper presents acomparative numerical analysis of the impact of different combinations of unseating restrainer with different isolation bearings or dampers on the dynamic response of the curved continuous girder bridge to seismic shock. Based on the principle of energy dissipation combined with constraints, this paper optimizes the combination of unseating restrainers and damping devices to form three seismic mitigation strategies for the curved continuous girder bridge. Athree-dimensional non-linear model of anentire bridge structural system is established; the model includes adjacent bridge superstructures with different sizes and the presence of expansion joints, as well as considering the unbalanced distribution of pounding forces across the contact surface and the nonlinear characteristics of bearings and

dampers. Furthermore, the seismic response of the bridge structural systems is studied by dynamic nonlinear analysis. This study sheds some light on the benefits and limitations of restraining devices and damping or isolation devices when acting in combination. The results presented could assist bridge engineers in selecting damping devices to effectively mitigate damage tothis type of bridge structure.
