Study on the Seismic Performance of High-Speed Railway Extradosed Cable-Stayed Bridge Considering CRTS III Slab Ballastless Track Structure

This paper explores the seismic damping mechanism and performance of CRTS III slab ballastless track on an isolation system extradosed cable-stayed bridge during rare earthquakes. It serves as a guide for designing slab ballastless tracks on high-speed railway extradosed cable-stayed bridges. Using a high-speed railway extradosed cable-stayed bridge as a case study, we established a Midas finite element model to optimize the track plate parameters by adjusting the fastener stiffness and plate joint length. The optimization process and method can be applied as a reference for similar bridge designs. The research findings reveal that, under rare earthquake conditions, the CRTS III slab ballastless track model (with a plate joint length of 90mm and fastener stiffness of 30kN/mm) has a minimal impact on increasing the longitudinal internal force at the pier’s base. It, at most, raises the earthquake internal force response by 5%. The model significantly reduces the overall relative displacement of the bridge pier and girder, with a notable 15.5% reduction in the relative displacement of pier 143# on the side pier. Therefore, when conducting internal force tests for the bridge, it is crucial to consider the influence of track plate restraint.


Introduction
On the basis of systematically introducing mature high-speed railway technology from developed countries such as Germany and Japan, China's slab ballastless track insists on original innovation, integrated innovation, and digestion and absorption on the basis of foreign excellent track slab structure, and then carries out local innovation [1].Years of technology and theoretical accumulation have completed CRTS Ⅲ slab ballastless track independently developed by China.Researchers [2], [3] conducted many analyses on the parameters and structure of the CRTS Ⅲ slab ballastless track structure and the layout of the base plate.Researchers [4] established the train-slab ballastless track-bridge calculation model of CRTS Ⅲ slab ballastless track structure, and analyze the dynamic response of the structure and the law of load transfer.Researchers [5], [6] mainly innovated the calculation theory and test method of track structure.Researchers [7], [8] provide technical theoretical support for the adaptability of broad gauge and prestressed rail slabs in CRTS III ballastless track.LOU Ping [9] established the track-CRTS III slab ballastless track spatial coupling vibration system and considered the combined load finite element analysis model to study the influence of the width and length of the gap between layers on the force and deformation of the track structure.ZHANG Pengfei [10] established a refined spatial coupling model of CRTS III slab ballastless track on the bridge based on the finite element method to analyze the influence of different factors on the structural forces.WU Bin [11] conducted a full-scale text on the CRTS III track slab structure to simulate the load of high-speed trains, and analyzed the evolution law of the acceleration of the fastener, isolation layer and other components stiffness.ZENG Zhiping [12] studied the influence of the gap between the track slab and the self-compacting concrete layer on the dynamic characteristics of the ballastless track structure.WANG Liu-chong [13] et al. evaluated the dynamic characteristics of the slab ballastless track by combining experimental modal analysis and operational modal analysis techniques.Baye Mbaye Diouf [14] et al. established a train-track subgrade two-dimensional dynamic interaction model, and used the CA mortar layer to analyze the dynamic response of the track slab under different fault distributions.Sakdirat Kaewunruen [15] et al. introduced the spatial dynamic mode coupling effect on the composite track slab on the railway bridge.
At present, slab ballastless track is rarely considered in the railway seismic design code, and the stiffness and damping contribution of the track system to high-speed railway bridges is often ignored in practical design.This paper establishes the CRTS Ⅲ slab type independently developed by China on the basis of the model established and optimizes the fastener stiffness of the track structure in the range of 15~45kN/mm and the slab joint width in the range of 60~100mm.A total of 35 calculation models were established to propose the optimal structural calculation parameters for this bridge.

Project Overview
Taking a span distribution of (65+85+178+93)m high-speed railway extradosed cable-stayed bridge as an example, and the main bridge structure adopts double-tower double-plane prestressed concrete extradosed cable-stayed bridge.The main bridge adopts the girder-tower fixed and pier-beam separated structure.Bearings are installed between main beam and pier.Fixed pier in the direction of the bridge set at the main pier on the small mileage side.The main beam is a three-dimensional prestressing structure.The piers and towers are made of reinforced concrete structure.The stay cables are arranged in a sector shape.The distance between the stay cables on the main beam is 8m.The main tower adopts double-column bridge tower.The height of the tower above the bridge deck is 26m.The main tower adopts solid rectangular cross section.The width of the double columns of the main tower above the bridge deck is 2.0m in the transverse direction and 3.5m in the transverse direction.The pier adopts a round-end solid slab pier with a width of 5m along the bridge and a width of 17.3m along the bridge.The elevation diagram of the entire bridge is shown in figure 1 below.rare earthquake acceleration is 0.38g.The seismic fortification intensity is 8 degrees, the site category is Class II, and the characteristic period is 0.4s.For seismic input longitudinal seismic action, this paper referred to the railway engineering seismic design code.Three sets of ground motions should be used in the model for time-history analysis.Due to space limitations, the seismic response calculation result takes the maximum of the three sets.The ground motion input is analyzed by fitting three artificial seismic wave acceleration time history curves according to the seismic acceleration response spectrum curve shown in figure 2.

The Main Calculation Parameters of the Model
The main components of the CRTS type III slab ballastless track structure is the rail at the top of the structure, the elastic fasteners between the rail and the track slab, the concrete track slab in the middle, the self-compacting concrete between the track slab and the base plate, the concrete base plate at the bottom of the track structure, the convex stopper and the filling resin.In the model, the rail, track plate and base plate are simulated by using beam units, the fasteners, self-compacting concrete and convex block and filling resin are simulated by using the elastic connection in the software to simulate the stiffness characteristics and the linear dampers in the general connection in the software to simulate the damping characteristics, the model calculation diagram is shown in figure 3, the main calculation parameters in the model are shown in table 1.From figure 4(b) we can obtain that considering the model of CRTS type III slab ballastless track, the relative displacement of each pier changes in a similar trend with the change of plate joints, decreasing first, reaching the minimum value at 70mm slab joints, and then changing insignificantly.
The optimum plate joint parameter for the CRTS III slab ballastless track model was selected to be 90mm for subsequent optimization, mainly with reference to the relative displacement of the piers and girders, based on the results of the internal force and displacement calculations for each pier of the bridge.

Effect of CRTS III fasteners stiffness
In this paper, under the premise that the plate joint of CRTS Ⅲ slab ballastless track is 90mm, the fastener stiffness is optimized, and the analysis is carried out according to the optimization range of 15~45kN/mm, the maximum longitudinal bending moment at the bottom and relative displacement of the piers and girders are extracted by the each pier of the whole bridge, as demonstrated in figure 5.As can be seen from figure 5 (b), considering the model of CRTS III slab ballastless track, the relative displacement of pier and girder of the whole bridge shows an insignificant change with the increase of fastener stiffness, and then a small increase appears when the fastener stiffness is greater than 35kN/mm.
The internal forces and displacements of each pier of the bridge were calculated, and the optimum plate joint parameter for the CRTS III slab ballastless track model was selected as 90mm, and the fastener stiffness was chosen as 30kN/mm.

Analysis of seismic mitigation and isolation effects
In order to further investigate the seismic isolation effect of the model with a CRTS Type III slab ballastless track plate joint parameter of 90mm and fastener stiffness of 30kN/mm, the results of the seismic response of the common application model without consideration of the track slab were compared and analyzed to obtain the results in table 2.
ballastless track plate joint 90mm and fastener stiffness 30kN/mm has increased the longitudinal internal force of pier bottom of 139# and 140# piers by 5.0%, and the rest of piers have increased the internal force response by about 2%.The track structure is not effective in controlling the longitudinal displacement of the top of the pier of the whole bridge, and the variation range is 5% or less.The track structure has a large reduction in the relative displacement of the full bridge pier and girders, within 15.5%.In summary, the optimum plate joint parameters for the model of CRTS III slab ballastless track were selected to be 90mm and the fastener stiffness to be 30kN/mm

Conclusion
The optimization of plate joints and fastener stiffness is undertaken, followed by a seismic isolation analysis of the bridge.The following conclusions have been derived and can serve as valuable references for the study of extradosed cable-stayed bridges in high-intensity seismic zones.
(1) When subjected to rare earthquakes, the CRTS III slab ballastless track with a 90mm plate joint and fastener stiffness of 30kN/mm model exhibits minimal increase in longitudinal internal forces at the bottom of the pier, with a maximum 5% rise in seismic internal force response.
(2) The impact on controlling the longitudinal displacement at the top of the entire bridge is not pronounced, with changes remaining within a 5% range.
(3) A substantial reduction in the relative displacement between the pier and girder of the entire bridge is observed, resulting in a 15.5% decrease in the relative displacement of the side pier #143.
The cumulative outcome of the above analyses supports the adoption of a CRTS Type III slab ballastless track featuring a 90mm plate joint and a fastener stiffness of 30kN/mm.

Figure 1 .Figure 2 .
Figure 1.The layout of entire elevation of a high-speed railway extradosed cable-stayed bridge (unit: cm)

5. Optimizations of Structural Parameters 5 . 1 . 4 .
Effect of CRTS III plate joint length Under different plate joint conditions of CRTS Ⅲ slab ballastless track, with the change of track plate joint parameters, the maximum longitudinal bending moment at the bottom and relative displacement of the piers and girders are extracted by the each pier of the whole bridge, as explained in figure 4. (a) Bending moment of pier bottom (b) Pier beam relative displacement Figure The calculation results of CRTS Ⅲ type ballastless slab track with the plate seam length variety It can be obtained from figure 4: From figure 4(a) we can obtain that considering the model of CRTS Ⅲ slab ballastless track, with the change of the track plate joint, the bending moment at the bottom of the longitudinal pier of 139#, 140#, and 143# is smaller, and the longitudinal bending moment of the pier bottom of 141# and 142# is larger; for the 141# pier, it increases first when the plate joint is in the range of 60~70mm, and then the change is not obvious in the range of 70~100mm; the remaining piers have insignificant variations in bending moment, the graph line is close to a straight line.

5 .
(a) Bending moment of pier bottom (b) Pier beam relative displacement Figure The calculation results of CRTS Ⅲ type ballastless slab track with fastener stiffness variety It can be obtained from figure 5: From figure 5 (a), it can be illustrated that, considering the model of CRTS Ⅲ type slab ballastless track, with the change of fastener stiffness, the effect on the longitudinal bending moment at the bottom of pier 140# and 141# is first insignificant and then decreases.The remaining piers show the same trend in longitudinal bending moments, all varying insignificantly with increasing fastener stiffness.

Table 1 .
CRTS Ⅲ type ballastless slab track main calculation parameters

Table 2．Calculation
The table is calculated using equation (1), α represents the rate of change, I represents the calculation in the common application model and I1 represents the calculation in the CRTS III slab ballastless track joint parameter of 90mm and fastener stiffness of 30kN/mm model.