Effect of Subsequent Subgrade on Seismic Response of the High-Speed Railway Track–Bridge System

Abstract

As an important part of the boundary conditions on both sides of the high-speed railway track–bridge system, the seismic response of the subgrade structure is different from that of the bridge structure. This difference has become increasingly significant with the widespread adoption of continuous welded rail technology in bridge construction. Therefore, investigating the seismic response of the bridge system, with a specific focus on the longitudinal constraint effects of the subsequent subgrade track structure, is of paramount importance. Utilizing finite element software, two distinct bridge models are developed: one incorporating the subsequent subgrade track structure and another excluding it. Through nonlinear time history analysis under varying seismic intensities, it is demonstrated that the longitudinal constraint of the subsequent subgrade track structure mitigates the longitudinal displacements and internal forces in critical components of the high-speed railway track–bridge system. Concurrently, acknowledging the heightened complexity and cost associated with post-earthquake repairs of the bridge structure compared to subgrade structure, this study uses a risk transfer connecting beam device. This device can redirect seismic damage from bridge structure to subgrade structure, thereby potentially reducing post-seismic repair expenses for the bridge.

1. Introduction

Due to the extensive use of continuous welded rail technology in the construction of high-speed railway bridges, the track structure is gradually extended from the bridge structure to the subgrade structure [1,2]. Although the continuous track structure allows for smoother train travel on high-speed railway bridges, during major natural disasters such as earthquakes, the continuity of the track structure can be disrupted due to variations in structural integrity. During an earthquake, the seismic displacement response of the track structure above the bridge is more pronounced than that of the track structure above the subgrade. Consequently, as the only longitudinal connecting element in the high-speed railway continuous beam bridge, the track structure partially constrains the seismic displacement response of the bridge structure. This interaction results in a certain degree of coupling between the seismic responses of the bridge structure and the subgrade structure [3]. Moreover, this extension of the track structure to the subgrade–bridge transition section results in substantial internal force and deformation. This phenomenon demonstrates that a portion of the seismic inertia force of the bridge structure can be transferred to the flexible subgrade structure through the longitudinally continuous track structure, thereby achieving energy dissipation in the subgrade–bridge transition section, i.e., the longitudinal constraint effect of the subsequent subgrade track structure (SSTS) [4]. This effect helps to balance the differences in seismic response not only between bridge and bridge, but also between bridges and the subgrade. Nevertheless, the design of continuous beam bridges recommended by the current Chinese seismic design code does not consider the longitudinal confinement effect of the SSTS, leading to a potential underutilization of this effect and possible adverse impacts on bridge design.

In order to obtain more accurate results from the seismic response analysis of bridge structures, many scholars have analyzed the railway track–bridge system considering the subgrade [5]. Hu et al. created a coupling system encompassing a train, track, and subgrade, revealing that the bridge–subgrade transition section experiences peak dynamic stress and displacement [6]. Wei et al. examine the seismic vulnerability of HSR bridges with track constraints, emphasizing the importance of track–bridge interaction in seismic response analysis [7]. Yan et al. employed a 100 m finite element model for the subgrade track outside the bridge, aiming to minimize boundary condition impacts [8]. Montenegro et al. modeled track extensions at viaduct ends for accurate transition zone representation [9]. Liu extended the subgrade length to 150 m as per DS899 and UIC774-3 codes to negate boundary condition influences [10]. Jiang et al. discovered that there is a critical track length at which the subgrade structure significantly impacts the dynamics of high-speed railway simply supported beam bridges [11]. Zhang et al., considering longitudinal constraint and beam-track interaction, found that the range of subgrade constraint on the bridge is only partially related to the subgrade itself [12]. Yan et al. developed a high-speed railway simply supported beam bridge–subgrade model and conducted an in-depth study and analysis of the damage patterns of key bridge components [13].

Based on prior investigations, the subgrade–track constraint effect influences the seismic response of bridge structure during seismic events [14,15,16]. Nevertheless, the focus of existing studies predominantly centers on multi-span, simply supported beam bridges, with comparatively scant attention given to continuous beam bridges. In the finite element analysis of multi-span, simply supported beam bridges, these structures exhibit characteristics of repetition and symmetry. This has led some researchers to prioritize model simplification and computational efficiency, often at the expense of a thorough examination of the longitudinal constraint effect of the SSTS on the seismic response in continuous girder bridges. Therefore, conducting a detailed study on the impact of SSTS’s longitudinal constraint effect on the seismic responses of high-speed railway track–bridge system (HSRTBS), particularly in the context of continuous beam bridges, holds substantial practical engineering value.

Building upon existing research, this study focuses on the high-speed railway track–bridge system (HSRTBS) with CRTSII ballastless track structure, considering the longitudinal constraint effect of the subsequent subgrade track structure (SSTS). The specific research content and chapter arrangement are as follows: The Section 1 introduces the research background of the longitudinal constraint effect of the SSTS, outlines current issues and challenges, and presents the research content of this study. The Section 2 describes the research object and its engineering background. The Section 3 details the establishment of two bridge models using the finite element software SAP2000: a bridge model considering the subsequent subgrade track structure (BMCS) and a bridge model without the subsequent subgrade track structure (BMWS). These models form the foundation for nonlinear time history analysis under varying seismic intensities. The Section 4 discusses the seismic input method and calculation conditions. The Section 5 analyzes the longitudinal constraint effect of the SSTS on each critical component of the HSRTBS by comparing the seismic responses of the two models. The Section 6 introduces the risk-transferring connecting beam device used in this study, designed to shift seismic risk from the bridge structure to the subgrade structure. The findings of this study are intended to provide valuable insights for the effective redistribution of seismic forces in bridge structures, enhancing their overall resilience and safety.

2. Engineering Background

To analyze the longitudinal confinement effect of the SSTS on each critical component in the HSRTBS, a 48 m + 80 m + 48 m dual-lane continuous beam bridge is selected as the engineering context in this study [17,18]. The four-span simply supported beam approach bridge and the subgrade structure are considered on each side of the continuous beam bridge, and the upper part is paved with CRTSII ballastless track structure. These elements collectively constitute the high-speed railway track–bridge system, whose overall layout, specific pier configurations, and bearing arrangements are shown in Figure 1.

The continuous beam bridge in this design features a main beam structured as a single-box, single-compartment box beam. Notably, both the height and cross-section of this main beam vary along its length, and it is cast from C50 concrete. For the bridge’s support, the piers are constructed using C30 reinforced concrete, shaped into rectangular forms. The deck height of the center pier is 3.85 m, and the deck height of side pier is 6.65 m. These piers display a gradation in height, arranged from left to right as 16 m, 14 m, 14 m, and 16 m, respectively. The center pier is arranged with 20 piles of 1.5 m diameter as group pile foundation, and the side pier is arranged with 16 piles of 1.25 m diameter as group pile foundation. Mirroring this design, the main beam of the simply supported beam bridge also adopts a single-box, single-compartment box girder structure. The specifics of its height and cross-section are detailed in Figure 1b. The pier design of the simply supported beam bridge is consistent with that of the continuous beam bridge, and its piers height are 16 m. Meanwhile, 12 piles with a diameter of 1.0 m are arranged under the square platform as a group pile foundation. The entire upper portion of the bridge is paved with the base plate made of C35 concrete and the track plate made of C55 concrete. Between the main beam and the base plate is filled with a two-fabric, one-membrane sliding layer of material. Moreover, the track plate is connected to the base plate by a CA mortar layer. The CHN60 rails are fixed and restrained to the track plate by WJ-8C type fasteners. The design of the bearings of the whole bridge is based on spherical steel bearings [7], which are arranged as shown in Figure 1c.

3. Finite Element Model

In this study, two bridge models were established using the SAP2000 finite element software, as shown in Figure 2. Figure 2a shows the bridge model considering the longitudinal constraint effect of the SSTS in the 130 m length section, referred to as BMCS. Figure 2b shows the bridge model without considering the longitudinal constraint effect of SSTS, referred to as BMWS.

The piers and foundations of bridges are critical components of bridge substructures, playing a vital role in ensuring the safety and stability of the entire structure [19,20]. Their primary function is to support the bridge span structure and transfer the deck loads to the foundation [21]. The substructures, including rectangular piers and circular piles, are simulated using nonlinear beam-column elements with discrete fiber sections that encompass cover concrete, core concrete, and reinforcement steel. (Figure 3) The side piers of a continuous beam bridge and the piers of a simply supported beam bridge are simulated using beam units at 0.8 m intervals. In contrast, the central pier of a continuous girder bridge is simulated using beam units at 1 m intervals. Additionally, this study takes into account the influence of the pile–soil effect. The interaction between the piles and soil at the base of the foundation is simulated using zero-length units (Figure 3), which are essentially fully elastic soil-spring-connected units with six degrees of freedom [22,23].

In general, the superstructure of a bridge tends to maintain their elasticity under seismic activity. In the finite element software, we use the elastic frame unit to simulate the box beam, base plate, track plate, and rail [24,25]. The sliding layer, CA mortar layer, fasteners, shear tooth grooves, shear reinforcement, and horizontal blocks play pivotal roles in the transmission of internal forces within essential elements of the track structure [26]. Consequently, in the finite element software, elastoplastic connection units are utilized for simulation purposes, with a Rayleigh damping ratio set at 5%. In this simulation, the unit is divided according to the actual size of the standard track slab (6.5 m). The spacing between the box girder, the bottom plate, the track slab, and the rail is set at 0.65 m. The distance between the sliding layer, the CA mortar layer, and the fastener is also 0.65 m. The horizontal blocks units are positioned at intervals of 6.5 m, while the shear reinforcement units are located at the beam ends [27]. The bearing is simulated using a nonlinear plastic unit, featuring a dynamic hysteresis curve that mirrors the stress–strain relationship typical of ideal elastoplastic materials. The continuous beam bridge model displays the longitudinal force–displacement curves of interlayer components as shown in Figure 3b. With the unit length set at 0.65 m, the stiffness of the connecting components between layers is detailed in

Table 1. Longitudinal stiffness of interlayer components (unit: kN, m).

Interlayer Component	F0	D0	k0	k1
Fastener	8.66	2.00 × 10−3	4.33 × 103	0
CA layer	4.50 × 101	5.00 × 10−4	9.00 × 104	0
Sliding layer	6	5.00 × 10−4	1.20 × 104	0
Fixed bearing	5.16 × 103	2.00 × 10−3	2.58 × 106	2.58 × 104
Sliding bearing	-	-	2.58 × 104	2.58 × 104
Lateral block	6	5.00 × 10−4	1.20 × 104	0
Sheer teeth	1.20 × 105	1.20 × 10−4	1.00 × 109	0

. The materials and material properties of key components in the HSRTBS are shown in

Table 2. Material properties of critical components.

Component	Material	Elastic Modulus (N·mm−2)	Density(kg·m−3)	Poisson Ratio
Main beam	C50	3.85 × 104	2400	0.2
Bridge pier	C30	3.05 × 104	2400	0.2
Base plate	C35	3.25 × 104	2400	0.2
Track slab	C55	4.05 × 104	2400	0.2
Rail	CHN60	2.1 × 105	7850	0.3
Friction plate	C30	3.05 × 104	2400	0.2

.

The track structure exhibits longitudinal continuity in both the subgrade and bridge sections, particularly when considering the longitudinal constraint effects of the SSTS. As a result, the modeling of the track structure in the upper part of the subgrade section is consistent with that of the bridge structure. Additionally, the subgrade section also includes friction plates, end spurs, and water-hardened support layers. According to Yan’s research, most components of the subgrade structure maintain an elastic state under longitudinal seismic excitation. In this study, it is assumed that the bottom constraint of the subgrade structure is fixed, and the influence of the deformation of the foundation and the change of internal force on the subgrade structure can be ignored. In the finite element software, friction plates, end spurs, and water-hardened support layers can be simulated using boundary elastic joint unit pairs.

4. Earthquake Input

Seismic waves contain three elements: peak, spectrum, and hold time [28,29]. Each of them affects the response of the structure under seismic action. Even under the action of seismic waves with the same peak ground acceleration, the calculation results can be very different due to differences in spectrum and holding time. The ground vibration input method used in this study is ground vibration acceleration time-range, which is used to analyze the nonlinear time-range of two bridge models, BMCS and BMWS, respectively.

Since there are no historical earthquake records for the bridge and the site type is classified as Category II with a seismic fortification intensity of VII, the design acceleration response spectrum was selected as the reference seismic acceleration response spectrum curve in this study [30,31]. As shown in Figure 4, the damping ratio of HSRTBS is assumed to be 0.05, with the bridge’s characteristic seismic period set at 0.25 s, and a dynamic amplification factor of the seismic spectrum at 2.25. Concurrently, this study generated three artificial seismic acceleration time histories, fitted to the reference seismic acceleration response spectrum curve, to be used as seismic inputs. From these, the highest value among the trio of seismic response datasets is selected as the definitive seismic response result [32,33].

In this study, the selected load combination is a combination of longitudinal direction and vertical direction [34,35]. For analyzing the differences in the seismic response of HSRTBS under normal earthquakes, design earthquakes, and rare earthquakes, the peak ground acceleration (PGA) of three artificial seismic acceleration time histories can be taken as 0.1 g, 0.2 g, and 0.4 g, respectively. In this way, the seismic response of each critical component of the two bridge models, BMCS and BMWS, is obtained under three different seismic IM (intensity measure) levels. The proportional coefficients of seismic load components are shown in

Table 3. The proportional coefficients of seismic load components.

Working Condition	PGA in the Longitudinal	PGA in the Vertical
Case 1	0.1	0.0666
Case 2	0.2	0.1333
Case 3	0.4	0.2666

. This study includes a total of 18 conditions.

5. Seismic Response Analysis of Each Critical Component in HSRTBS

With the aim of facilitating a clear understanding of the specific impact of the longitudinal constraint effect of the SSTS on each critical component in the HSRTBS, two impact parameters, Δ and ε, are defined in this paper. Δ represents the difference between the seismic response of the BMCS and the BMWS. ε represents the rate of change of the seismic response of the BMCS and the BMWS.

Table 4. Comparison result of the seismic response of the two bridge models.

Object	Impact Parameters	U1, mm	U2, mm	Px, kN	V2, kN	V3, kN	M3, kN·m
Main beam	Δ	−	/	…	…	…	…
	Δmax	−5.1	1.7	…	…	…	…
Bearings	Δ	+	/	+	+	+	…
	Δmax	−3.9	−0.2	−227	−139	−14	…
	ε	…	…	−	+	−	…
	εmax	…	…	18.7%	−5.5%	−17.4%	…
Left pier (1#)	Δ	+	/	+	+	+	+
	Δmax	−1.7	−0.02	459	−1513	−7	−15,106
	ε	…	…	+	+	+	+
	εmax	…	…	8.6%	−43.1%	−8.7%	−47.2%
Fixed pier (2#)	Δ	+	/	+	+	+	+
	Δmax	−1.4	−0.03	1311	−1476	−24	−16,187
	ε	…	…	+	+	+	+
	εmax	…	…	21.0%	−14.7%	−5.7%	−25.5%
Non-fixed pier (3#)	Δ	+	/	+	+	+	+
	Δmax	−1.4	−0.01	1466	−586	−9	−4227
	ε	…	…	+	+	+	+
	εmax	…	…	18.3%	−8.61%	−6.9%	−8.8%
Right pier (4#)	Δ	+	/	+	+	+	+
	Δmax	−1.8	−0.01	502	−1009	−6	−10,298
	ε	…	…	+	+	+	+
	εmax	…	…	7.8%	−44.28%	−7.0%	−45.4%
Foundation piles	Δ	…	…	+	+	+	+
	Δmax	…	…	−1176	−223	−13	−341
	ε	…	…	/	/	/	/
	εmax	…	…	−24.6%	−25.9%	−26.3%	−27.4%

Note: “+”: ∆ or ε gradually increases with the increase in the peak ground acceleration (PGA); “-”: ∆ or ε gradually decreases with the increase in the PGA; “/”: no significant change in ∆ or ε with the increase in the PGA; “…”: the results are not relevant to the research and will not be studied in this paper; “U1”: longitudinal displacement or longitudinal deformation; “U2”: lateral displacement or lateral deformation; “Px”: vertical axial force; “V2”: longitudinal shear; “V3”: transverse shear; M3: transverse bending moment.

shows the results of the comparison of the seismic response of the BMCS and the BMWS, and the specific analysis process will be discussed in the following section.

5.1. Seismic Response Analysis of Main Beam

The main beam is a crucial component of the railway track–bridge system, with its displacement and deformation having a direct impact on the smoothness of the overlying track structure and, by extension, the safety of rail traffic. To assess this, we analyzed the longitudinal and vertical displacements of the main beam under varying peak ground accelerations for the two bridge models, BMCS and BMWS. The comparative results of these displacements are meticulously presented in Figure 5 and Figure 6.

The results show that under the combined effect of longitudinal direction and vertical ground vibration, the longitudinal confinement effect of SSTS leads to a reduction in the longitudinal displacement produced by the main beam, while there is no significant change in the vertical displacement. This phenomenon is attributed to the SSTS’s continuity along the bridge’s longitudinal direction, which imparts additional longitudinal stiffness to the HSRTBS boundary, with minimal influence on its vertical stiffness. Notably, as the PGA incrementally increases, the SSTS’s influence on the main beam’s longitudinal confinement correspondingly intensifies. This is because the seismic response of the bridge structure is almost linearly proportional to PGA variations. In contrast, the seismic response of the flexible subgrade escalates more gradually and nonlinearly when PGA increases. When the value of PGA is taken as 0.4 g, the longitudinal confinement effect of SSTS leads to a reduction of 5.1 mm in the longitudinal displacement and an increase of 1.7 mm in the vertical displacement produced by the main beam.

5.2. Seismic Response Analysis of Bearing

Bearings play a pivotal role in the seismic analysis of bridges, significantly impacting the bridge structure’s internal forces, resultant displacements and deformations, and the dynamic characteristics of the structure itself. The comparative analysis of the longitudinal deformations and shear forces endured by the bearings in the two bridge models, BMCS and BMWS, under various PGAs, is meticulously illustrated in Figure 7 and Figure 8.

The analysis reveals that the longitudinal constraint effect of the SSTS can reduce the longitudinal displacements of all the bearings under the combined effect of longitudinal and vertical ground vibration. Notably, the longitudinal deformations of the fixed pier bearings (bearings 3# and 4#) are less impacted by the longitudinal confinement effect of the SSTS compared to other pier bearings (bearings 1#, 2#, 5#, 7#, and 8#). Additionally, the longitudinal confinement of the SSTS results in a decreased shear force on the fixed bearing, while the shear force on the sliding bearings remains relatively unaffected. This is attributed to the fact that bearing 3# is a fixed bearing, immobile in both longitudinal and transverse directions, primarily bearing the longitudinal seismic inertia force of the main beam. In contrast, the rest of the bearings are sliding bearings, which are movable in the longitudinal or transversal direction. Their longitudinal stiffness is less than that of fixed bearings. The longitudinal constraint effect of the SSTS has a significantly greater effect on the longitudinal stiffness of the sliding bearing than that of the fixed bearing. As a result, the longitudinal deformation changes generated by the sliding bearings are more obvious when the seismic response generated by the bridge structure is transferred to the bearing structure.

As the PGA incrementally rises, the longitudinal constraint effect of the SSTS affects the bearing’s longitudinal deformation to a progressively greater extent. Specifically, the longitudinal deformation of the sliding bearing displays an almost linear escalation. At a PGA of 0.4 g, there is a notable surge in the longitudinal deformation of the fixed bearing, beyond which the longitudinal shear force ceases to increase. This phenomenon occurs because at PGA values up to 0.2 g, the longitudinal deformation of the fixed bearing remains below its damage threshold. In this scenario, the bearing remains intact, with the seismic response of the bridge structure primarily borne by the fixed bearing. However, at a PGA of 0.4 g, the fixed bearing enters a yielding state, causing the seismic response of the bridge structure to be transmitted through the superstructure of the track to adjacent abutments and subgrade structures. To prevent the risk of beam collapse due to excessive longitudinal slip in the bearing superstructure, the longitudinal restraint effect of the SSTS comes into play. This demonstrates that the SSTS’s longitudinal confinement effect on the seismic response of the bearing is a non-negligible factor in the face of strong seismic activity. With a PGA of 0.2 g, the longitudinal confinement effect of the SSTS reduces the longitudinal displacement of the fixed bearing by 3.9 mm and diminishes the longitudinal shear force by 139 kN.

5.3. Seismic Response Analysis of Piers

During seismic events, the upper track structure of the bridge not only transmits gravity and inertia forces to the lower foundation structure via the piers but also receives ground vibration inputs through these piers. This study compares the seismic responses of the BMCS and BMWS piers, including longitudinal displacement, longitudinal shear, and transverse bending moment, at varying PGA values. The results of this comparative analysis are comprehensively illustrated in Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14.

It is shown that the longitudinal constraint effect of the SSTS reduces the seismic response of the continuous beam bridge’s piers under the combined influence of longitudinal and vertical ground shaking. This is due to the fact that the CRTSII ballastless track structure remains longitudinally continuous in the HSRTBS. The seismic response of the continuous beam bridge’s piers is transmitted through the track structure to the subgrade structure at both ends of the bridge. In particular, the longitudinal constraint effect of the SSTS has a greater impact on the longitudinal displacement of the pier tops compared to the pier bottoms and a greater impact on the seismic response of the side piers compared to the main piers because the seismic inertia forces in the bridge structure are mainly concentrated at the top of the pier, while the bottom of the pier is restrained by the lower foundation. Additionally, the height of the side piers is greater than that of the main piers, resulting in the main piers possessing greater longitudinal stiffness. Consequently, under seismic conditions, the side piers exhibit a more pronounced seismic response than the main piers.

6. Transfer of Bridge Seismic Risk

During seismic events, the bridge structure will have a more pronounced displacement response compared to the flexible subgrade structure [36]. The track structure, serving as a longitudinal connector between the bridge and subgrade structure, plays a role in restraining the bridge’s displacement to a certain degree [37]. However, this restriction comes at a cost: the track structure in the transition section of the subgrade structure will generate large internal forces and deformations. In other words, a portion of the seismic force on the bridge structure is transferred to the subgrade structure through the track structure, with dissipation occurring at the subgrade–bridge transition section. Despite its importance, the confinement effect of the track is often overlooked in bridge design. This oversight results in underutilization of the potential to harmonize the differences in seismic responses between the beam–beam and beam–subgrade interactions. Therefore, the protective capabilities of track structures in safeguarding bridges have not been prominently recognized or discussed in past practical engineering applications.

In this study, a risk-transferring connecting beam device (RTCBD) is used, which can enhance the longitudinal connection effect between beams [38,39,40]. This device not only enhances the bond between beams but also significantly boosts the track structure’s capability in transmitting seismic forces. Consequently, this facilitates the transfer of seismic risk from the bridge structure to the subgrade structure, effectively redistributing the seismic load [41]. The detailed arrangement and construction of this risk-transferring connecting beam device are shown in Figure 15.

6.1. Seismic Response Analysis of Bridge Section

Figure 16 shows the effect of the RTCBD on the displacements and internal forces of each critical component of the track structure in the bridge section. It is found that the longitudinal displacements generated by the critical components of the continuous beam bridge section (including the main beam, base plate, track plate, and rail) are significantly reduced and more evenly distributed after the installation of the RTCBD. Notably, the abrupt drops or surges at the beam spacing are eliminated. In the approach bridge section, there is a slight increase in the longitudinal displacement of the track plate and base plate. Regarding vertical displacement, there is no significant change in the key members of the track structure, but the vertical displacement of the track structure are slightly reduced at mid-span in the main and approach bridge segments.

The analysis reveals that the installation of the RTCBD reduces stresses on the base plate, track plate, and rail over the continuous beam bridge section. This results in a more uniform internal force distribution within the track structure and a considerable reduction in peak stress. The vertical axial force and longitudinal shear force of the bearings in the main bridge section are also significantly reduced, and the internal forces of the bearings are more evenly distributed over the high-speed railway track–bridge system. This demonstrates that the installation of the RTCBD can be effective in improving the utilization of the bearings across the bridge. The longitudinal shear force on the shear grooves and blocks are significantly reduced and more evenly distributed, thus reducing the stress concentrations at the beam spacing.

6.2. Seismic Response Analysis of Subgrade Section

Figure 17 shows the effect of the RTCBD on the displacement and internal force of each critical component of the track structure in the subgrade section. It is indicated that the seismic response (longitudinal displacement and axial force) of the base plate, track plate, and rail on the subgrade section increases after the installation of RTCBD. Notably, the closer to the bridge, the greater the seismic response of the base plate, track plate, and rail.

Upon analyzing the seismic response data, we observe notable increases in both longitudinal displacement and axial force across various components of the subgrade section. Specifically, the longitudinal displacement of the base plate experiences an increase ranging from 25% to 46%, while its axial force escalates by 19% to 56%. Similarly, the longitudinal displacement of the track plate rises by 14% to 19%, and its axial force increases by 3% to 24%. For the rail, there is an increase of 12% to 18% in longitudinal displacement and a 14% to 35% rise in axial force.

In conclusion, the longitudinal displacements and internal forces of the track structure on the bridge section are significantly reduced and more evenly distributed after the installation of the RTCBD. Conversely, there is a significant increase in these parameters in the track structure on the subgrade section. This indicates that the RTCBD is effective in reducing the seismic response of the track structure in bridge section. Furthermore, it can also transfer the seismic response to the subgrade section, thus successfully realizing the design purpose of transferring the bridge seismic damage to the subgrade section. Since the cost of repairing post-earthquake damage to subgrade structures is much less than that of bridge structures, the installation of the risk-transferring connecting beam device can also significantly reduce the seismic maintenance costs of bridge structures [42]. This not only has great economic benefits but also can provide a completely new research direction for future seismic isolation design. The schematic diagram of seismic risk transfer for the risk-transferring connecting beam device is shown in Figure 18.

7. Conclusions

Utilizing the finite element software SAP2000, this study establishes a comprehensive model that integrates the continuous beam main bridge, simply supported beam approach bridge, subgrade structure, and CRTSII ballastless track structure. The nonlinear time history analyses of the BMCS and BMWS are conducted to investigate the specific influence of the SSTS’s longitudinal confinement effect on the seismic response of each critical component of the HSRTBS under varying ground shaking intensities. Additionally, the risk-transferring connecting beam device is employed to effectively transfer the damage of the bridge structure to the subgrade structure. By comparing and analyzing the differences in the seismic response of critical components of the bridge structure and the subgrade structure, the following conclusions can be drawn:

• Under the joint influence of longitudinal bridge direction and vertical ground vibration, the longitudinal constraint effect of the SSTS diminishes the longitudinal displacement of the main beam, bearings, piers, and foundation piles.
• Under the joint influence of longitudinal bridge direction and vertical ground vibration, the longitudinal confinement effect of the SSTS significantly reduces the longitudinal shear force and the transverse bending moment of the piers and foundation piles. This influence intensifies progressively with the incremental increase in the peak ground acceleration.
• The installation of a risk-transferring connecting beam device optimally utilizes the differential seismic responses between the bridge and the subgrade. It effectively mitigates the internal forces and displacement deformations in the bridge’s critical track structure components, thereby transferring the seismic damage from the bridge structure to the subgrade structure.