Keywords

1 Introduction

China is a country with frequent earthquakes [1, 2]. Meanwhile, the development time of rigid frame Bridges of high-speed railway in China is late, and there are many rigid frame Bridges of high-speed railway across gullies in western China, many of which are located in seismic zones with high activity [3,4,5]. Therefore, according to the dynamic behavior characteristics of rail-bridge system of high-speed railway under earthquake action, establishing the integrated model of high-speed railway continuous rigid frame composite beam bridge and studying the response law of key components of the bridge are of great significance for the optimization design and reinforcement maintenance of practical engineering.

Scholars at home and abroad have studied the integrated model of high-speed railway line bridge and the seismic response of rigid frame bridge under earthquake. Lai Z [6] established a refined finite element model of rail-bridge considering interlayer hysteretic characteristics, and carried out nonlinear dynamic response analysis of rail-bridge system under typical near-field earthquakes. Yu M [7] established a rail-bridge model of a simply-supported beam bridge, and discussed the changes of various near-fault pulse ground motions to the dynamic response of the rail-bridge system. Taking the rigid frame continuous beam bridge as an example, Liang Y [8] took rigid structure-continuous beam Bridges as an example to study the response mechanism of Bridges under large earthquakes based on time-varying vulnerability. Wei J [9] established a finite element model of abutment-approach bridge-rigid frame continuous beam bridge to explore the influence of structural parameters on collision effects at expansion joints and seismic response of bridge structures. Zhao J [10] studied the vulnerability of multi-span high-pier continuous rigid frame Bridges under near-field rotating seismic waves, relying on five-span high-pier continuous rigid frame Bridges.

There are few studies on the seismic response mechanism of rigid frame Bridges of high-speed railway considering track constraints. Therefore, based on the characteristics of CRTS I double-block ballastless track structure, this paper establishes three continuous rigid frame composite girder bridge models, which consider track and subsequent structure constraints, only consider track constraints and do not consider track constraints, to compare and study the key parts of structural system damage under earthquakes, in order to provide theoretical basis for the maintenance and reinforcement of similar Bridges and the study of seismic design optimization.

2 Project Overview and Research Model

2.1 Project Overview

The main bridge is a (48 + 80 + 48) m double-line rigid frame box beam bridge, the beam body material is C50 concrete, the roof width is 13.4 m, the floor width is 5.5 m, the beam height at the rigid frame pier is 7.4 m, the beam height at the mid-span section is 2.4 m, and the bottom line is a quadratic parabola. The rigid frame pier is a thin-wall pier spanning a gully, 40 m high, 6m long section, 3 m wide, 0.6 m thick, and made of C40 concrete. The approach bridge is a simple beam bridge with 12m pier height, 6m section length and 2.5 m width. The material is C35 concrete. HRB335 steel bars with a diameter of 20mm are used for the stirrup and longitudinal reinforcement of the pier. The concrete strength of the track plate and the base plate is C40, and the section dimensions are 2.8 × 0.26 m and 3.4 × 0.175 m, respectively.

2.2 Track System Simulation

The track system of the model adopts CRTS type I double block ballastless track, which is composed of base and groove (or convex), isolation layer, track plate, double block sleeper, rail and fasteners. The beam body is provided with embedded steel bars, which are used to connect with the track base plate. The road bed plate and the base plate are isolated by geotextile. The groove is arranged around the elastic plate with high stiffness [11]. The track structure is shown in Fig. 1.

Fig. 1.
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CRTS I double block ballastless track structure diagram

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Ignoring the longitudinal resistance effect of the track fastener, the rail, double-block sleeper and track bed plate are integrated into one section. The integration method is to convert the section of the rail into the section of concrete according to the elastic modulus ratio of steel and concrete materials to ensure the constant stiffness and the total mass is maintained by adjusting the bulk density of the material. The converted rail section size is 0.176 × 0.44 m, the concrete density is 2.5 \(\text{t/}{\text{m}}^{3}\), the unit mass of the rail is 60 kg/m, the equivalent mass of the integrated section of the track is 2.1t/m, and the integrated rail is used to describe the rail system. A rigid arm is used to simulate the connection between the embedded steel bar and concrete between the base plate and the main beam. The friction stiffness of the isolation layer between the track plate and the track plate and the stiffness of the groove gasket are superimposed and simulated by linear spring. The successor structure is simulated by linear spring.

2.3 The Establishment of Research Model

Combined with the characteristics of CRTS I double-block ballastless track structure, the integrated model of the cable bridge was established. Basin rubber supports were selected for the support, which was established with the master-slave constraint. The stiffness values of each component were shown in Table 1. Bridge and track system are simulated by beam element, rigid pier and beam body are consolidated and connected by rigid arm. Six linear springs are applied to the bottom of the cap to simulate the foundation stiffness, and the spring parameters are calculated by m method. The pier adopts elastoplastic fiber cross section. The concrete constitutive model is Mander model, and the reinforcement constitutive model is Menegotto-pinto model.

Table 1. Stiffness of each component
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A high-speed railway bridge model of simple supported beam bridge+rigid frame bridge+simple supported beam bridge (5 × 32 m + 48 m + 80 m + 48 m + 5 × 32 m) was established by using MIDAS, which includes three models considering track and subsequent structure constraints, only track constraints and no track constraints, as shown in Fig. 2 and Fig. 3. There are 2,724 beam units in the integrated model, including 2,004 beam units for the track system, 496 beam units for the main beam, 224 beam units for the bridge pier, and 1,368 spring units.

Fig. 2.
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Finite element calculation model

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Fig. 3.
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Structure diagram of bridge cross section

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2.4 Introduction of Study Methods

Response spectrum method is an equivalent static method based on linear elastic analysis of a single degree of freedom system under uniform seismic excitation. The response spectrum refers to the spectrum curve of different single-degree-of-freedom systems whose period is horizontal coordinate and whose maximum relative bit, maximum relative velocity and maximum absolute acceleration are vertical coordinate. The response spectrum can be used to quickly calculate the peak value of structural response, which is simple in concept and calculation and suitable for engineering applications. It is the first calculation method for seismic design of common span Bridges in current national norms.

2.5 Study Condition

In order to study the seismic response mechanism of structural system, the study conditions are defined by adjusting the height of rigid frame pier. Working condition 1: the pier of rigid frame bridge is 40m, which is the pier height of rigid frame bridge in actual engineering; Working condition 2: Take half of the pier height of rigid frame bridge, that is, 20 m; Working condition 3: Taking the height of rigid frame pier 17 m, the internal force at the bottom of rigid frame pier under earthquake tends to be equal to that of simply-supported beam bridge, but this is not an accurate value, and the accurate value will be determined by calculation in this paper. Working condition 4: The height of rigid frame pier and simple supported beam pier is equal, which is 12 m.

3 Dynamic Characteristics of Different Bridge Types

The modal analysis of the three bridge models was carried out under working condition 1. The calculation results of the first 5 natural vibration periods of the structural system are shown in Table 2, and Fig. 4 is the corresponding vibration pattern diagram under working condition 1.

Table 2. The first five natural vibration periods of the three models
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Fig. 4.
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The mode of each model is described in the working condition

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It can be seen from Table 2 that the restraint effect of the track and the subsequent structure reduces the natural vibration period of the structure. According to the calculation of the first 5 orders of natural vibration period, the average natural vibration period of model 1 is reduced by 35.2%, and that of model 2 is reduced by 17.55%. It can be seen that the restraint effect of the subsequent structure has a certain inhibition effect on the natural vibration period of the structure, with the inhibition effect reaching 17.66%. As can be seen from Fig. 4, this is because the track constraints make the separate vibration of the rigid frame bridge and the simply-supported beam bridge become the overall vibration of the entire combined bridge, resulting in shortened natural vibration period of the bridge.

4 Study on Seismic Response of Different Bridge Types

The seismic responses of the three models under four working conditions were compared by the response spectrum method. Bridge type B, regional characteristic period 0.45 s, site type I, fortification intensity 7 (0.15 g) degree, seismic code E2, damping ratio 0.05. The peak seismic acceleration of horizontal design is 0.39 g, the first 200 vibration modes are selected, and the participating mass of vibration modes is more than 95%. The combination of vibration modes adopts CQC method.

4.1 Analysis of Bridge Pier Bottom Internal Force

The seismic internal forces at the bottom of the pier of the three models under four working conditions are shown in Fig. 5.

Fig. 5.
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Distribution of internal forces at the bottom of pier of bridge system

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It can be seen from Fig. 5 that under different working conditions, track constraints change the internal force behavior of composite girder Bridges. When the height difference between rigid frame pier and simply supported beam pier is too large, transition pier is the main energy dissipating member. The seismic responses of the two types of piers tend to be equal, and further studies are needed to determine their exact values.

4.2 Analysis of Influence of Rigid Frame Pier Height on Structural System

Figure 6 shows the variation of the internal forces at the bottom of the three models with the change of the height of the rigid frame pier, the transition pier and the rigid frame pier. The internal forces at the bottom of the rigid frame pier and the transition pier of each model are plotted, and the intersection point is the place where the internal forces at the bottom of the pier are equal, so that the height of the rigid frame pier at this time can be determined.

Fig. 6.
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Diagram of internal force change of model pier bottom when pier height changes

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It can be seen from Fig. 6 (a) and (b) that, considering the track constraint, the seismic internal forces at the bottom of rigid frame pier increase with the decrease of the height of rigid frame pier, and the seismic internal forces at the bottom of transitional pier decrease with the decrease of the height of pier. The internal forces of model 1 and model 2 are equal when the rigid frame pier is 16.7 m and 16.4 m respectively. It can be seen that it is reasonable to use model 1 to study the influence of the subsequent structure. In Fig. 6(c), the internal force at the bottom of model 3 rigid frame pier is always greater than that of transition pier. Therefore, when considering the track constraint and the successor structure, when the difference between the height of rigid frame pier and the height of simple beam pier is greater than 28%, the main energy dissipation member of the structural system is the transition pier. When the difference between the height of rigid frame pier and the height of girder pier is less than 28%, the main energy dissipation component of the structure is rigid frame pier. Therefore, in the actual project, in view of the difference between the height of continuous rigid frame pier and the height of simple supported beam pier, strengthening measures are taken to strengthen the pier bottom of the transition pier and rigid frame pier respectively, or the energy dissipation capacity of the pier bottom is enhanced in the design, such as using self-resetting pier, which can effectively improve the seismic performance of the bridge.

4.3 Integrated Track Stress Analysis

Figure 7 shows the track stress distribution of model 1 and Model 2 under four working conditions.

Fig. 7.
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Integrated track stress profile

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It can be seen from Fig. 7 that the maximum stress of each span bridge occurs at the beam expansion joint, and the track stress is the largest at the beam joint at the top of the transition pier, which is the first to be damaged under the earthquake. In addition, the track stress increases with the increase of pier height. From working condition 4 to working condition 1, the maximum track stress of model 1 increases by 50%, and that of model 2 increases by 65%. It can be seen that the change of pier height has a significant effect on the seismic response of the track, and the subsequent structure has a certain inhibitory effect on the seismic response of the track, with the average inhibitory effect of 4.18% under the four working conditions.

5 Conclusion

By studying the seismic response mechanism of three calculation models of high-speed railway Bridges, the following conclusions are drawn:

  1. (1)

    The track constraint reduces the natural vibration period of the structural system, and the subsequent structure has a certain inhibitory effect on the natural vibration period of the structural system and the seismic response of the track system, with a suppression effect distribution of 17.66% and 4.18%. It is more reasonable to use Model 1 when studying the seismic response of structural systems.

  2. (2)

    The height difference between rigid frame pier and simply supported beam pier has a significant effect on the seismic response of the track system. The maximum rail stress increases with the increase of rigid frame pier height, and the maximum rail stress increases by 50% in model 1 and 65% in model 2. The maximum stress of the track occurs at the top beam joint of the transition pier, where the track is damaged first under the earthquake. Energy dissipation devices can be installed at the beam joint to reduce the damage of the track.

  3. (3)

    When there is a 28% difference between the height of rigid frame pier and that of simple beam pier, the internal forces of the two piers are equal. When the difference is greater than 28%, the main energy-consuming member of the structural system is the transition pier, and the bottom of the pier first becomes the plastic hinge area. When it is less than 28%, the main energy-consuming member of the structural system is rigid frame pier, and the bottom of the pier first becomes the plastic hinge area. Therefore, for bridge types with different pier heights and differences, corresponding reinforcement measures should be taken at the bottom of transition pier and rigid frame pier respectively, or piers with good energy dissipation capacity, such as self-resetting pier, should be used to improve the seismic performance of the structural system.

In this paper, the response spectrum method is used to study the seismic response mechanism of each component, but the energy dissipation capacity of each component under earthquake cannot be calculated, and the energy dissipation law of each component of the structural system can be further studied by the dynamic time history method.