**1. Introduction**

The long-span deck-type concrete-filled steel tube (CFST) arch bridge has good terrain adaptability, while being economical and providing high levels of structural stiffness [1–6]. It is suitable for building in the mountainous area of southwest China. It is also one of the most cost-competitive bridge types in the 300-to-600-meter-span range. However, China is a country subject to frequent earthquakes, especially in the south-west region. All the earthquakes in recent years have caused severe losses.

Under the effects of earthquakes, the inertial force of a deck-type CFST arch bridge is mainly concentrated in the upper part, and excessive inertial force of the upper structure directly leads to the shear failure of the bearings between the upper and lower structures. The placement of an isolation device between the upper and lower structures can reduce the inertial force of the upper structure, which not only overcomes the problem of the insufficient shear resistance of the bearings, but also achieves the purpose of protecting the lower structure. The technique of base isolation originated in the 1960s and 1970s [7–9]. Its main purpose is to introduce a flexible bottom layer into the structure, so that the structure can be isolated from the ground motion induced by the earthquake, thus protecting the superstructure from earthquake damage. In the 1960s, Li Li, a Chinese scholar, proposed and studied the idea and method of using a sand layer and a rubber layer for isolation [10]. At the same time, Kelly, an American scholar, proposed the use of laminated rubber bearings as a method of isolation [11]. Later, Ali and others used the finite element method to conduct numerical simulations and calculated and evaluated the damping effect of lead–rubber bearings applied to long-span cable-stayed bridges [12]. Since then, foundation-isolation

**Citation:** Ye, D.; Tong, Y.; Gan, L.; Tang, Z.; Zhang, R. Improvement in the Seismic Performance of a Super-Long-Span Concrete-Filled Steel-Tube-Arch Bridge. *Buildings* **2023**, *13*, 1811. https://doi.org/ 10.3390/buildings13071811

#### Academic Editor: John Mander

Received: 9 June 2023 Revised: 27 June 2023 Accepted: 12 July 2023 Published: 16 July 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

technology has developed rapidly; isolation technology has matured, the design theory has been refined, and the application of isolation technology has become increasingly widespread [13]. The friction-pendulum bearing (FPB) is a promising new type of seismic isolation device, which converts seismic energy into heat energy through friction-energy dissipation. Its unique circular sliding surface gives it a self-resetting function [14–16]; in recent years, research into this feature has increased. Many scholars [17–27] studied the seismic responses of FPBs applied to beam bridges and cable-stayed bridges, among others. The economical and structural efficiency of FPBs for the retrofitting of continuous beam bridges in the State of Illinois was studied by Dicleli et al. [17]. Almazán et al. [18] presented a physical model for frictional pendulum isolators (FPS) that was ready to be implemented in most commercial software, and the physical model was validated by studying the earthquake response of a continuous beam bridge. Murat et al. [19,20] proposed a new model for the FPS and examined the effects of modeling parameters on the response of a three-dimensional multi-span continuous (MSC) steel-girder-bridge model seismically isolated with the FPS. Jun Gao et al. [22] assessed the damping performance of frictional pendulum bearings in long-span cable-stayed bridge bearings. Zhiqiang Li et al. [23] explored vibration mitigation and isolation for a long-span cable-stayed bridge with doublearch pylons based on FPBs. Jing Li et al. [24] studied the parametric optimization of vibration mitigation and isolation scheme for a railway cable-stayed bridge. A global non-linear time-history analysis of the Benicia–Martinez Bridge, which is a long-span truss bridge, was conducted using ADINA by Mutobe et al. [25]. Ingham [26] presented a non-linear time-history analysis undertaken in support of the seismic retrofitting of the bridge, and the work included the installation of friction-pendulum-isolation bearings. Marin-Artieda et al. [27] proposed an XY-FPB that consisted of two perpendicular steel rails with opposing concave surfaces and a connector and applied it to a truss bridge. At present, isolation technology is mainly applied to the seismic resistance of medium- and small-span continuous beam bridges, cable-stayed bridges, and truss bridges in areas of high seismic intensity. However, the application of isolation technology in long-span CFST arch bridges requires further research.

The transverse connecting system of the main arch is a vulnerable component; because of the high level of stiffness of the lateral connection system, there a large internal force response and buckling instability occur under earthquake conditions [28,29]. Of the existing seismic performance-improvement technologies, buckling-restrained brace (BRB) may be the only type that can effectively address the buckling instability of the transverse connection system of the main arch [30–37]. However, compared with buildings, the super-long-span CFST arch bridge has the characteristics of large internal force and small displacement. As a displacement-type energy-dissipation device, the BRB is applied to a super-long-span CFST arch bridge, and it is very likely that the energy-dissipation effect is lower than the expected effect, making it necessary to find another way in which to improve the seismic performance of the transverse connection system of the main arch.

The cable-hoisting-and-inclined-pulling-and-fastening method (CHIPFM) is the most commonly used method of construction for long-span CFST arch bridges. The associated construction process is as follows. First, a temporary buckle tower and cable tower are built before the installation of the arch rib. At the same time, the arch rib is divided according to the hoisting capacity of the cable-hoisting system (CHS). Next, the CHS is used to hoist the arch rib to the designated position section by section for cantilever assembly. At the same time, each arch-rib section is buckled onto the buckle tower with the help of an anchor cable until the arch rib is closed. Finally, the CHS is removed. The stayed buckle cable (SBC) is the main item of equipment in the CHS. It is often used in such work; it is only a temporary facility, and it is removed after construction. The CHIPFM has been vigorously promoted and used in the construction of large-span DCFST arch bridges because of its mature construction technology, fast construction speed, convenient transportation of materials, strong spanning ability, and applicability to canyons and rivers with complex terrain and harsh environments [38–41]. Scholars have conducted significant

research into the CHIPFM, to good effect [42–44]. The existing research mainly focuses on the calculation of the cable forces of SBCs and construction control [42–45]. However, relevant research on the impact of SBCs on the seismic performance of arch bridges has not been performed. As a temporary measure in the CHIPFM, SBCs complete missions after the arch rib is closed and cannot be reused, resulting in a waste of resources. Since SBCs show the characteristics of convenient installation, easy replacement after earthquake damage, and reasonable arrangement to increase the transverse stiffness of arch bridges, they can be retained after the completion of bridge construction to improve the transverse seismic performance of super-large-span arch bridges, providing a new way of improving the seismic performances of these bridges.

The existing research still lacks evidence that can guide the seismic-performanceimprovement design of super-long-span CFST arch bridges. Therefore, this research took a super-long-span CFST arch bridge with a total length of 788 m as the object on which to perform a non-linear time-history analysis and a seismic-checking calculation according to its seismic response, so as to reveal the seismic weak points of the arch bridge. The seismic performance of the arch bridge was improved through FPBs and SBCs, making it possible to propose a more suitable seismic-performance-improvement technology for super-long-span concrete-filled steel-tube arch bridges. Finally, the seismic-performanceimprovement effects of the FPBs, SBCs, and combination schemes were compared, and the optimal scheme was established.

#### **2. Seismic-Response Analysis of Original Model**

## *2.1. Project Overview and Modeling Method*

The background bridge is a prestressed-concrete continuous rigid-frame bridge with a CFST arch bridge, with a length of 788 m. The construction-drawing model of the arch bridge was taken as the research object to improve its seismic performance. The main bridge is a CFST arch bridge with a span of 500 m, and the rise-span ratio is 1/4.76. The arch axis adopts a catenary, with an arch-axis coefficient of m = 2.0, and the bridge deck is horizontally arranged, with four lines of railway track. The main arch ring adopts a CFST transverse dumbbell-shaped four-limb truss-basket arch, with two arch ribs on the left and right. The main beam of the main bridge adopts 10 × 40.8-m steel-box continuous beams arranged on left and right sections. Spherical steel bearings are used to support the main beam. The left and right approaches are (51 + 66 + 66)-meter prestressed-concrete continuous rigid-frame bridges. The piers are variable-cross-section reinforced-concreteframe piers, which show an inverted V shape when viewed horizontally.

The dynamic calculation model established by bridge-finite-element software is shown in Figure 1. The CFST arch rib was established by the double-element method. Apart from the spherical steel bearings, which feature elastic connection elements, the other components of the bridge were submitted to a beam-element-simulation analysis. The finite element-calculation mesh contained 2780 beam elements, and the number of nodes was 1442. According to the design data, the bridge site is on bedrock, so the interaction between the foundation and the structure did not need to be considered [44]. In the model, the pier bottom and arch foot of the approach bridge were set as the consolidation-constraint boundary.

The main pier and main beam of the approach bridge adopt consolidation, while the tops of each pier (column) of the whole bridge adopt four bearings. Specifically, the longitudinal movable bearings of model TJQZ-10000 were used at the approach-bridge side of columns 1 # and 10 #, and the fixed bearings of model TJQZ-7000 were used at the main bridge side. The vault adopted the fixed bearings of model TJQZ-12500. The tops of columns 2–10 # used the longitudinal movable bearings of model TJQZ-12500. As the bearings were arranged transversely and symmetrically, the layout plan of the main bridge bearings along the longitudinal direction of the bridge is shown in Figure 2.

**Figure 1.** Finite element calculation model.

**Figure 2.** Layout plan of main bridge bearings (unit: m).

The bridge site of the project is a mountain-canyon landform, with high mountains and deep valleys, steep slopes, and a V-shaped river valley. The ground elevation on both banks of the river valley is 2700–4700 m, and the maximum elevation difference exceeds 2000 m. The topographic map of the site is shown in Figure 3. The intention of the project was to use CHIPFM to construct arch ribs.

**Figure 3.** Topographic map of project site.

According to the seismic-safety-assessment report, the seismic fortification intensity of the bridge site is 7 degrees, the basic acceleration is 0.15 g, the site's characteristic period is 0.65 s, and the site is classified as Class I. Through the seismic analysis, the bridge was still in the elastic stage under Level-I earthquake excitation (E1), the internal force of the section passed the checking calculation, and the transverse seismic performance of the arch bridge was worse than the longitudinal seismic performance. Therefore, this paper focuses on the transverse seismic performance under Level-II earthquake excitation (E2) of the arch bridge. Three artificial seismic waves with a 50-year exceedance probability of 2% provided in the bridge's site-safety-assessment report were used for the non-linear timehistory analysis. The peak accelerations of the three waves were 0.23 g, 0.21 g, and 0.27 g, respectively, after considering the terrain effect. In the non-linear time-history analysis, the transverse + vertical input mode was adopted for the ground motion, without considering the influence of the longitudinal earthquake excitation. The vertical ground-motion input was obtained by reducing the transverse seismic wave, and the reduction coefficient was 0.65. The acceleration-time-history curves of the three artificial seismic waves are shown in Figure 4. To ensure the clarity of the discussion, the envelope values of the calculated results of the three waves are discussed later.

**Figure 4.** Time-history curve of seismic-wave acceleration.
