Dynamic Adaptability of Spherical Bearings in Small-Span Bridges for Heavy-Haul Railways
1
School of Safety Engineering and Emergency Management, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
2
Key Laboratory of Railway Industry of Infrastructure Safety and Emergency Response, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
3
School of Civil Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
*
Author to whom correspondence should be addressed.
Buildings 2025, 15(4), 619; https://doi.org/10.3390/buildings15040619
Submission received: 18 January 2025
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Revised: 11 February 2025
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Accepted: 15 February 2025
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Published: 17 February 2025
(This article belongs to the Topic Advances on Structural Engineering, 3rd Edition)
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Figure 1
<p>Various failures of plate bearings.</p> "> Figure 2
<p>Structural composition of spherical bearing.</p> "> Figure 3
<p>Beam lifting operation.</p> "> Figure 4
<p>Bearing replacement construction.</p> "> Figure 5
<p>Flowchart of bridge bearing replacement construction.</p> "> Figure 6
<p>Dimensions of bridge piers (Unit: m).</p> "> Figure 7
<p>Test bridge measuring point layout diagram.</p> "> Figure 8
<p>Field records.</p> "> Figure 9
<p>Dynamic deflection of the middle section.</p> "> Figure 10
<p>Maximum dynamic deflection.</p> "> Figure 11
<p>Lateral amplitude.</p> "> Figure 12
<p>Lateral acceleration.</p> "> Figure 13
<p>Maximum lateral amplitude.</p> "> Figure 14
<p>Maximum lateral acceleration.</p> "> Figure 15
<p>Maximum vertical amplitude.</p> "> Figure 16
<p>Maximum vertical acceleration.</p> "> Figure 17
<p>Lateral displacement at bearings.</p> "> Figure 18
<p>Vertical displacement at bearings.</p> "> Figure 19
<p>Lateral displacement amplitude.</p> "> Figure 20
<p>Vertical displacement amplitude.</p> "> Figure 21
<p>Maximum lateral amplitude at the pier top.</p> "> Figure 22
<p>Simulation model and beam cross-section.</p> "> Figure 23
<p>Vertical loads (Unit:m).</p> "> Figure 24
<p>Lateral forces.</p> "> Figure 25
<p>Dynamic response at a speed of 55 km/h (pier height).</p> "> Figure 26
<p>Maximum dynamic response (pier height).</p> "> Figure 27
<p>Maximum dynamic response (bridge span).</p> ">
Versions Notes
<p>Various failures of plate bearings.</p> "> Figure 2
<p>Structural composition of spherical bearing.</p> "> Figure 3
<p>Beam lifting operation.</p> "> Figure 4
<p>Bearing replacement construction.</p> "> Figure 5
<p>Flowchart of bridge bearing replacement construction.</p> "> Figure 6
<p>Dimensions of bridge piers (Unit: m).</p> "> Figure 7
<p>Test bridge measuring point layout diagram.</p> "> Figure 8
<p>Field records.</p> "> Figure 9
<p>Dynamic deflection of the middle section.</p> "> Figure 10
<p>Maximum dynamic deflection.</p> "> Figure 11
<p>Lateral amplitude.</p> "> Figure 12
<p>Lateral acceleration.</p> "> Figure 13
<p>Maximum lateral amplitude.</p> "> Figure 14
<p>Maximum lateral acceleration.</p> "> Figure 15
<p>Maximum vertical amplitude.</p> "> Figure 16
<p>Maximum vertical acceleration.</p> "> Figure 17
<p>Lateral displacement at bearings.</p> "> Figure 18
<p>Vertical displacement at bearings.</p> "> Figure 19
<p>Lateral displacement amplitude.</p> "> Figure 20
<p>Vertical displacement amplitude.</p> "> Figure 21
<p>Maximum lateral amplitude at the pier top.</p> "> Figure 22
<p>Simulation model and beam cross-section.</p> "> Figure 23
<p>Vertical loads (Unit:m).</p> "> Figure 24
<p>Lateral forces.</p> "> Figure 25
<p>Dynamic response at a speed of 55 km/h (pier height).</p> "> Figure 26
<p>Maximum dynamic response (pier height).</p> "> Figure 27
<p>Maximum dynamic response (bridge span).</p> ">
Abstract
:Plate bearings in existing small-span bridges for heavy-haul railways have exhibited corrosion, detachment, and surface cracks under large axle loads, making them inadequate for the “capacity expansion and renovation” of heavy-haul railways. Therefore, identifying new bearings suitable for small-span bridges and developing a rapid bearing replacement method tailored to the operational needs of heavy-haul railways are urgent priorities. This paper takes spherical bearings as an example and proposes a method for rapidly replacing plate bearings with spherical bearings. The bearing replacement tests of six simply supported beams were carried out to verify the effectiveness of the proposed method. Dynamic performance tests of bridges and bearings were performed before and after the replacement. A finite element model was established to analyze the effects of bridge span and pier height. The results show that the entire bearing replacement process for a span bridge could be completed within 4 h using the proposed method. Compared to plate bearings, spherical bearings could improve the lateral dynamic performance of both the bridge and bearings. However, the improvement decreases as bridge span and pier height increase. For 2.2 m diameter cylindrical piers commonly used in heavy-haul railways, the pier height with spherical bearings should be limited to 10 m.
1. Introduction
Heavy-haul railway, renowned for its efficiency, energy conservation, and environmental sustainability, has emerged as the global direction for freight transportation development [1,2]. To further enhance the transport capacity of heavy-haul railways, increasing the axle load of trains is widely regarded as the most effective approach [3,4]. However, as axle loads increase, the structural stresses and dynamic impacts on small-span bridges become more pronounced. The bridge may need strengthening or replacement of vital structural components to manage the new conditions [5]. Plate bearings, commonly used in the early construction of small-span railway bridges due to their simple structure, clear load transfer mechanism, and ease of construction, have experienced various failures, as shown in Figure 1. Statistics from several heavy-haul railways in China indicate that plate bearings are used in all bridges with spans below 16 m, which account for 14% of the total number of bridges [6]. Consequently, the failures of plate bearings pose significant threats to the operational safety and transport efficiency of heavy-haul railways [7].
Under heavy-haul railway transportation conditions, there is an urgent need to find new bearings suitable for small-span bridges. Spherical bearings, known for their superior mechanical performance, higher load-bearing capacity, and enhanced durability, have become the preferred choice for new bridge constructions [8]. As illustrated in Figure 2, a spherical bearing consists of an upper bearing plate, spherical crown plate, flat sliding plate, spherical sliding plate, and lower bearing plate. The flat sliding plate and spherical sliding plate, serving as the primary sliding components, are typically made of polytetrafluoroethylene or similar materials. The flat sliding plate, usually circular, is embedded in a recessed groove on the upper surface of the spherical crown plate. Together with the stainless steel plate welded to the upper bearing plate, it forms the first sliding surface. The spherical sliding plate, with its concave spherical shape, is embedded in the spherical recess of the lower bearing plate. Along with the stainless steel plate covering the spherical crown plate, it forms the second sliding surface. The horizontal displacement of the bearing is realized through the first sliding surface, while the rotation is generally achieved by the combined action of the first and second sliding surfaces.
Extensive theoretical and experimental research has been conducted on the application of spherical bearings in existing railway bridges, leading to significant findings. Chen et al. [9] conducted comparative studies based on field tests to investigate the effects of plate bearings and spherical bearings on the vibration, impact, and deformation of heavy-haul railway bridge structures. The results indicated that spherical bearings provide better stability and reliability to the bridge structure compared to plate bearings. Jiang, Peng, and Nie et al. [10,11,12,13], based on theoretical analysis and dynamic testing, developed seismic isolation bearings with good adaptability, which effectively improved the overall seismic performance of structures. He et al. [14] performed a comprehensive nonlinear contact finite element analysis of spherical bearings using ANSYS 2021 R1 software, studying the effects of polytetrafluoroethylene plate area, the friction coefficient between concrete piers and cast steel structures, and concrete stiffness on bearing performance, and proposed several optimization design solutions. Yang et al. [15] developed a full-scale finite element model of spherical bearings using ABAQUS 2021 software and simulated the mechanical performance of bearings under varying inclination angles of the upper plate. The results showed that the ultimate load-bearing capacity of the bearing decreased as the inclination angle of the upper plate increased. Adamov et al. [16,17] found that altering the inclination angle of the friction layer could effectively reduce the maximum values of contact parameters and deformation characteristics within the structure, thereby improving the overall performance of spherical bearings. Additionally, to further enhance the performance advantages of spherical bearings, Nosov et al. [18] analyzed the impact of the lubricating groove in the spherical hole friction layer of spherical bearings on the contact deformation characteristics of bridge bearings. Their findings showed that this feature distributes the contact parameters between the steel plate and the friction layer more uniformly, effectively reducing the maximum plastic deformation. Guo et al. [19] developed an intelligent load-sensitive spherical bearing based on an optical interferometer and comprehensively evaluated its performance through loading tests and finite element simulations. The results demonstrated that, after temperature compensation, the load-sensing accuracy of the spherical bearing could reach a high level of approximately 6%.
Although spherical bearings are widely used in bridge design and perform excellently, challenges remain in their practical application, especially regarding bearing replacement technologies. Due to the heavy transportation tasks undertaken by heavy-load railways, any delays in the bearing replacement process may result in transportation schedule disruptions, significantly increasing logistics costs associated with traffic interruptions. Therefore, the development of timely and efficient bearing replacement technologies is crucial for ensuring the safety and stable operation of heavy-load railways. Ma et al. [20,21] analyzed the causes of damage in plate bearings and proposed remediation measures for defective bearings and recommendations for replacing them with spherical bearings. They also verified the feasibility of the proposed bridge jacking schemes and bearing replacement techniques. To avoid secondary damage to the bridge superstructure during construction, Ma et al. [22] monitored the bridge structure during the bearing replacement process and successfully replaced the old bearings with spherical bearings using a synchronized jacking technique, minimizing traffic disruption. Existing research has mainly focused on bearing replacement methods for general freight railway bridges and the design optimization of spherical bearings, while research on the application of spherical bearings in heavy-haul railway bridges with small spans remains insufficient. Specifically, studies on bearing replacement technology and dynamic adaptability in such applications are still in their early stages.
Based on the above, a method for the rapid replacement of plate bearings with spherical bearings is proposed. On-site replacement tests were conducted to validate the efficiency of the proposed method and evaluate the dynamic performance of spherical bearings. Furthermore, a finite element model was established to analyze the effects of bridge span and pier height on the dynamic adaptability of spherical bearings. The present work aims to provide theoretical support for replacing plate bearings with spherical bearings in small-span bridges for heavy-haul railways.
2. Rapid Replacement Method for Spherical Bearings
In China, for operational heavy-haul railways, facility and equipment maintenance is limited to a continuous four-hour window, requiring the completion of bearing replacement within this time frame. The limited duration and high precision demand present significant challenges. To address these, a construction process for the rapid replacement of plate bearings with spherical bearings is proposed, based on the principle of overall synchronous jacking of the bridge. The process is as follows:
Step 1: Pre-construction preparation. Adjust or relocate any communication and optical cables that interfere with the work, and erect a standardized work platform. Verify and measure the bearing specifications, jack positions, temporary pier layout, base stone dimensions, and the clear height under the girder. Install and calibrate dial indicators near the bearings to be replaced to enable real-time monitoring of girder elevation changes. Remove and lubricate the bolts of the old bearings, and clear any debris around the girder ends to ensure unobstructed work.
Step 2: Beam lifting. Release stress of the continuous welded rails on the bridge by removing the track fasteners. Determine jacking positions on the inner side of the top caps beneath the beam, arranging four jacks at each beam end per span. A total of 16 jacks, including four spares at each end, should be prepared. Use a programmable logic controller synchronized system and dial gauges to control the lifting process, ensuring precise and uniform speed. Conduct a trial jacking to simulate and validate the entire bearing replacement procedure. Perform the lifting in three stages: 2 cm, 3 cm, and 3 cm increments, achieving a total lift of 8 cm to allow for bearing removal. The beam lifting construction diagram is shown in Figure 3.
Step 3: Bearing replacement. Remove the upper and lower bearing plates of the old plate bearings. Clean rust and debris from the bottom steel plate of the girder, and chisel away the bearing pad stone affected by the bearing height. Position the spherical bearing under the girder by translating it into place. Tighten the bolts of the upper bearing plate first. Once the girder is lowered into place, secure the bolts of the lower bearing plate. Arrange the bearing pad stone and new bearing using a cross-pattern layout. Install and weld the steel formwork for grouting, ensuring the weld parameters are consistent with the bottom steel plate of the girder. Fill the bearing pad stone and embed the bolts for the lower bearing plate using rapid-hardening grout designed for bearings. The bearing replacement construction diagram is shown in Figure 4.
Step 4: Girder lowering and finalization. Lower the girder to its original elevation in 5 mm increments using jacks, ensuring both sides of the girder in the same section are lowered simultaneously. Perform leveling and height adjustments to ensure the bridge deck elevation meets the required standards. Once the girder is properly positioned, coat the existing bottom steel plate of the girder with anti-corrosive paint. Install limiters, verify alignment, fill ballast, and perform tamping for compaction. Confirm alignment restoration and resume train operations. Adjust the stress of the seamless track rail sections to their original state.
The outlined procedure is visually represented in Figure 5. This illustration provides a step-by-step overview of the key actions, ensuring a comprehensive understanding of the workflow.
During the bearing replacement process illustrated in Figure 5, the key monitoring indicators include jacking force, girder displacement, and girder strain (or stress), with vertical jacking displacement of the girder serving as the primary focus. Real-time monitoring of jacking force is essential to ensure that the applied force remains safe and controllable limits, preventing structural damage to the girder. Furthermore, precise synchronization across all jacking points is critical to avoid issues such as girder tilting, stress concentration, or cracking, particularly in scenarios with uneven load distribution.
The rapid replacement method for spherical bearings proposed in this chapter not only significantly reduces maintenance time but also mitigates construction risks and enhances operational efficiency. Moreover, with the ongoing increase in demand for heavy-haul railways, the application prospects of this technology are extensive, providing crucial support for the maintenance and upgrading of future railway infrastructure, thus facilitating the safe and efficient development of railway transportation.
3. On-Site Tests
3.1. Bearings Replacement
Two bridges (Bridge 1# and Bridge 2#) on a heavy-haul railway in China were selected for bearing replacement and performance comparison tests before and after bearing replacement. Both bridges consist of three 16 m simply supported T-beam spans. The design axle load for both bridges is 250 kN. The beam dimensions are as follows: height 1.1 m, top width 1.92 m, bottom width 1.06 m, and the distance between beam web centers is 1.8 m. The girder is made of C50-grade concrete, and the piers are single-line reinforced concrete cylindrical piers with a 2.2 m diameter. The foundations are pile-based, with the pier concrete being C40-grade. The pier dimensions are shown in Figure 6, and an overview of the bridge is provided in Table 1. In Figure 6 and Table 1, H represents the total pier height (from the base or pile cap bottom to the top of the pier), H1 represents the height from the top of the base or pile cap to the pier top, H0 represents the height of the pier shaft, and B represents the average lateral width of the pier shaft (2.2 m). H2 corresponds to the tray-type top cap.
The plate bearings used in the bridges were TBZ2000ZX-e30-0.2P-F (Hebei Baoli Engineering Equipment Group Co., Ltd., Hengshui City, China), designed with a vertical load capacity of 2000 kN, a displacement of ±30 mm, and a horizontal load capacity of 20% of the vertical design load, intended for cold-resistant longitudinal sliding. The spherical bearings used for replacement were TJQZ-8160-2000 ((Hebei Baoli Engineering Equipment Group Co., Ltd.)), with a vertical load capacity of 2000 kN, a displacement of ±30 mm along the bridge axis, and a rotational angle of 0.02 rad.
Using the rapid replacement method for spherical bearings, the time required for replacing the bearings on each span is summarized in Table 2.
As shown in Table 2, the bearing replacement for each span was completed within 4 h. The construction time for the first span was longer due to the workers’ lack of experience with the procedure. However, as the number of replacements increased, the time required decreased with improved proficiency.
3.2. Test Scope and Measurement Point Arrangement
The mid-span spans of Bridge 1# and Bridge 2# (called Span 1# and 2#) were selected for testing to compare the performance of the two bearing types. Four vibration sensors and one displacement sensor were installed at the mid-span of one test bridge to measure the lateral and vertical displacements, accelerations, and dynamic deflection during train passage. Additionally, two displacement measurement points were placed at the active ends of both the old and new bearings to monitor the vertical and horizontal displacements. A measurement point was also positioned at the top of the bridge pier to track variations in lateral amplitude. The locations of the measurement points are shown in Figure 7.
An 891-II vibration pickup device, along with an amplifier and data acquisition system, was used for dynamic testing. The CDP series displacement transducers, in conjunction with strain gauges and intelligent signal acquisition instruments, were utilized to measure bearing displacement. For deflection testing, both SDP and CDP series displacement transducers were employed alongside strain gauges and data acquisition systems. The relevant parameters of the instruments are provided in Table 3, and the field records are shown in Figure 8.
During the testing phase, C80 (25t axle load) heavy-haul trains were used as the primary test vehicles, fully loaded, and over 50 valid test runs were conducted on Span 1# and 2#. After the bearing replacement, performance testing of the bridges was carried out immediately. To ensure operational safety, the initial train speed was set within the V1 range (45–60 km/h). Once the overall bridge’s performance stabilized, the train speed was increased to the V2 range (65–75 km/h).
3.3. Test Results and Analysis
3.3.1. Dynamic Deflection of Middle Section
Dynamic deflection of the middle section is a key indicator of the vertical stiffness of a bridge. For heavy-haul railway bridges, the magnitude of the parameter provides insight into the vertical stiffness and overall stability of the bridge under train loading. Figure 9 shows the time history curve of the dynamic deflection for Span 1#. The train speeds for both curves in Figure 9 are approximately 71 km/h, but the significant difference in train lengths causes noticeable variations in waveform duration.
As shown in Figure 9, the dynamic deflection of the middle section with the spherical bearings is greater than that with the plate bearings. This is because the longitudinal sliding of old plate bearings is more restricted than that of new spherical bearings, and the longitudinal movement of bearings on the sliding side is more restricted with old plate bearings due to the higher friction associated with accumulated years of service. Additionally, due to the presence of a locomotive with a smaller axle weight in the middle of the train formation, both curves exhibit prominent peaks at the midpoint.
Figure 10 summarizes the maximum dynamic deflection for each passing train. Table 4 summarizes the maximum and mean of the maximum dynamic deflection according to different speed ranges.
As shown in Figure 10 and Table 4, after replacing the plate bearings with spherical bearings, the maximum dynamic deflection of both Span 1# and Span 2# increased, as reflected in both the maximum and mean values. The differences in the statistical results between Span 1# and Span 2#, both before and after the bearing replacement, were minimal, indicating that the pier height had minimal impact on the mid-span dynamic deflection.
3.3.2. Lateral Vibration of Middle Section
Figure 11 and Figure 12 show the lateral amplitude and lateral acceleration time history curves of the middle section for Span 1#.
As shown in Figure 11 and Figure 12, replacing plate bearings with spherical bearings significantly reduces the fluctuation ranges of lateral amplitude and lateral acceleration. Figure 13 and Figure 14 summarize the maximum lateral amplitude and lateral acceleration for each passing train. Table 5 summarizes the maximum and mean of the maximum lateral amplitude and lateral acceleration according to different speed ranges.
Replacing the plate bearings with spherical bearings, as shown in Figure 12 and Figure 14, and Table 5, reduces the lateral amplitude and lateral acceleration of Spans 1# and 2#, both in maximum and mean values. This indicates that spherical bearings effectively absorb and dissipate lateral vibration energy from train loads, enhancing the bridge’s stability and reliability. Additionally, Figure 12 and Figure 14 reveal that lateral amplitude and lateral acceleration of the middle section increase with train speed, displaying some dispersion. Under identical train speeds, Span 1#, with its greater pier height, shows higher lateral amplitude and lateral acceleration than Span 2#, highlighting the significant influence of both train speed and pier height on these dynamic responses.
3.3.3. Vertical Vibration of Middle Section
Vertical amplitude and vertical acceleration of the middle section are crucial indicators of a bridge’s vertical vibration characteristics. Figure 15 and Figure 16 summarize the maximum vertical amplitude and vertical acceleration for each passing train. Table 6 summarizes the maximum and mean of the maximum vertical amplitude and vertical acceleration according to different speed ranges.
Figure 15 and Figure 16, and Table 6 show that replacing the plate bearings with spherical bearings reduced the vertical amplitude of the middle section for both Span 1# and Span 2#, reflected in both maximum and mean values. The maximum vertical acceleration decreased, while the mean values exhibited two distinct trends: in the V1 speed range, maximum vertical acceleration for both spans decreased after the bearing replacement, whereas in the V2 speed range, it increased. In the V1 speed range, the higher stiffness of spherical bearings effectively dampens low-frequency vibrations, significantly reducing vertical acceleration. The relationship between maximum vertical amplitude and speed before and after bearing replacement was not significant, while maximum vertical acceleration tends to increase with speed. It could be concluded that vertical amplitude is mainly influenced by the bridge’s vertical stiffness, whereas vertical acceleration is primarily driven by the vertical impact forces from the train.
A comparative analysis of lateral and vertical vibration data of Span 1# and Span 2# shows that after replacing plate bearings with spherical bearings, the reduction in vertical vibration is less pronounced than in lateral vibration, indicating that spherical bearings are more effective in mitigating lateral vibrations. For Span 1#, with its higher pier height, both the maximum and mean values of maximum vertical acceleration before and after bearing replacement are significantly lower than those of Span 2#, suggesting that increased pier height suppresses vertical acceleration.
3.3.4. Dynamic Response of Bearings
Monitoring bearing displacements under train loading offers valuable insights into their operational condition, including proper functioning, potential slipping, misalignment, and other related issues. This is essential in the performance testing before and after bearing replacement. Figure 17 and Figure 18 display the time history curves of lateral and vertical displacements of the bearings in Span 1#.
From Figure 17 and Figure 18, it is evident that before and after bearing replacement for Span 1#, the time history curves of lateral and vertical displacements show significant differences. The lower stiffness of the plate bearings results in larger deformations and higher vibration amplitudes for both lateral and vertical displacements. After replacing the plate bearings with spherical bearings, the increased stiffness significantly reduces the amplitudes of both lateral and vertical displacements, leading to smoother time history curves with markedly reduced fluctuations.
Figure 19 and Figure 20 summarize the lateral and vertical displacement amplitudes for each passing train. Table 7 summarizes the maximum and mean values of the lateral and vertical displacement amplitudes across different speed ranges, where the displacement amplitudes are derived from the peak-to-peak values extracted from the time history curves following the passage of each train.
As shown in Figure 19 and Figure 20, and Table 7, after replacing the plate bearings with spherical bearings, both lateral and vertical displacements decreased significantly, with this trend reflected in both maximum and mean values. This demonstrates a notable improvement in the lateral constraint capability and vertical stiffness of spherical bearings compared to plate bearings.
A comparison of the bearing displacement data for Span 1# and Span 2# reveals that, before replacement, the maximum lateral and vertical displacement amplitudes of the plate bearings were relatively close and both exceeded 0.20 mm. After replacing the plate bearings with spherical bearings, both lateral and vertical displacement amplitudes decreased significantly, with lateral displacement being smaller than vertical displacement. This suggests that spherical bearings provide superior vertical stiffness and lateral constraint capability compared to plate bearings, with a more pronounced control effect on lateral displacement.
3.3.5. Dynamic Response of Piers
In the Code for rating existing railway bridges [23], the lateral amplitude at the pier top serves as the control index for the lateral stiffness of bridge piers. Monitoring changes in the lateral amplitude at the pier top enables further assessment of the impact of replacing plate bearings with spherical bearings on the lateral vibration of the bridge structure. Figure 21 summarizes the maximum lateral amplitude for each passing train. Table 8 summarizes the maximum of the maximum lateral amplitude according to different speed ranges.
From Figure 21 and Table 8, it can be observed that, under train loads, replacing the plate bearings with spherical bearings results in an increase in the lateral amplitude at the pier top for both Span 1# and Span 2#, with both maximum and mean values reflecting this trend. The differences in the connection methods between plate bearings and spherical bearings with the bridge lead to varying lateral loads transmitted downward by the train. Spherical bearings, with higher stiffness, are fixed to both the pier and the main girder, partially absorbing and dissipating vibration energy caused by lateral loads on the bridge. This helps reduce the transmission of vibration to the pier and other parts of the bridge structure, providing a certain degree of lateral vibration damping for the main girder and typical bridge piers. However, as Span 1# and Span 2# have cylindrical piers with relatively low stiffness, the lateral forces transmitted to the piers by the train increase after replacing the bearings, exacerbating the lateral vibration of the piers.
In conclusion, the application of spherical bearings significantly enhances the performance of the bridge structure, demonstrating the effectiveness and practicality of the rapid bearing replacement technology. Additionally, the variation in pier height following the replacement influences the dynamic response of the bridge structure, warranting further in-depth analysis.
4. Numerical Simulation
4.1. Model Establishment and Verification
The simulation model of Bridge 1# was established with the finite element software ANSYS, as shown in Figure 22.
In the model, beams, piers and caps were simulated by solid elements, while steel bars were represented by link elements. Bearings were modeled with spring elements. Structural mass elements were used to define the center positions of the upper and lower bearing plates, with each node assigned three translational and three rotational degrees of freedom. The beam cross-sectional dimensions with varying spans are summarized in Table 9.
In Figure 22, spherical bearing (GD) supports vertical loads and multi-directional horizontal loads, offers vertical rotational capacity, and restricts horizontal displacement in all directions. Spherical bearing (HX) supports vertical loads and longitudinal horizontal loads, provides vertical rotational capacity, and permits lateral displacement. The stiffness values of the spherical bearings utilized in this study are listed in Table 10.
The 25 t axle load of the C80 trains was applied and simplified as moving loads, consisting of vertical loads of 250 kN, as shown in Figure 23, and lateral forces of 27.5 kN per wheelset, as illustrated in Figure 24.
To validate the accuracy of the simulation analysis model, the dynamic response of the mid-span was compared to the test data after bearing replacement. The comparison between the test results and the simulation results is presented in Table 11.
Table 11 shows that the deviation between the test results and the simulation results remains within ±10%. This confirms that the finite element analysis method demonstrates a satisfactory level of accuracy and reliability.
4.2. Factor Analysis
4.2.1. Analysis Conditions
To examine the impact of pier height and bridge span on the dynamic response of bridges constrained by spherical bearings, the conditions outlined in Table 12 were applied.
For 2.2 m diameter cylindrical piers commonly used in heavy-haul railways, the cross-sectional area of the piers remains unchanged.
4.2.2. Pier Height
When the train speed was set to 55 km/h, the dynamic response is shown in Figure 25.
Figure 26 illustrates the maximum values of each dynamic response parameter as they vary with pier height under different train speed conditions.
From Figure 25 and Figure 26, it can be observed that the dynamic response of the bridge varies significantly with changes in pier height and train speed. The lateral amplitude at the pier top and middle section, lateral acceleration of the middle section, and vertical displacement of the bearings increase with the pier height, while the vertical acceleration of the middle section decreases as the pier height increases. The vertical dynamic deflection of the middle section shows minimal correlation with pier height. Additionally, the lateral amplitude at the pier top and middle section, as well as the lateral and vertical accelerations of the middle section, increase with higher train speeds. However, the vertical dynamic deflection of middle section and vertical displacement of the bearings show little correlation with train speed
Furthermore, when the pier height is 10 m and the train speed exceeds 65 km/h, the maximum lateral amplitude at the pier top ranges from 0.868 mm to 0.953 mm, surpassing the typical value of 0.85 mm as specified in the Code for Rating Existing Railway Bridges. This could adversely affect the long-term performance and safety of the bridge. Therefore, adopting a conservative design approach, it is recommended that for small-span railway bridges in China, the height of cylindrical piers with a diameter of 2.2 m should not exceed 10 m.
4.2.3. Bridge Span
Figure 27 illustrates the maximum values of each dynamic response parameter as they vary with bridge span under different train speed conditions.
As shown in Figure 27, the maximum dynamic deflection and lateral amplitude of the middle section, the maximum pier top lateral amplitude, and the maximum vertical displacement of bearing increase with the bridge span. Notably, the maximum dynamic deflection of the middle section and the maximum pier top lateral amplitude exhibit an approximately linear increase. At a train speed of 80 km/h, when the bridge span increases from 8 m to 16 m, the maximum dynamic deflection of the middle section rises by 2.23 mm (a 67.6% increase), and the amplitude increases by 0.22 mm (a 96.4% increase). As the bridge span increases, the ratio of maximum dynamic deflection of the middle section to the bridge span gradually decreases, indicating a reduction in beam stiffness. This decrease in stiffness also leads to a downward trend in the maximum vertical acceleration of the middle section. The dynamic response parameters generally exhibit an increasing trend with the rise in train speed, with the maximum vertical acceleration of the middle section showing a particularly notable increase due to the higher train speed. It can be concluded that spherical bearings are well-suited for small-span heavy-haul bridges, particularly those with spans of 16 m or less.
5. Conclusions
This paper proposed a construction process for the rapid replacement of spherical bearings for small-span heavy-haul railway bridges. During the construction process, the dynamic response of tested bridges was measured before and after the bearing replacement to evaluate the feasibility of replacing plate bearings with spherical bearings. Numerical simulations were used to analyze the influence of train speed, pier height, and bridge span on the adaptability of spherical bearings for small-span bridges. The main conclusions are summarized as follows:
(1) The present study proposes a method for the rapid replacement of bearings, which ensures that the bearing replacement for a small-span bridge is completed within 4 h, fully meeting the requirements for heavy-load railway maintenance windows.
(2) Based on on-site comparative tests, the application of spherical bearings can improve the lateral restraint of small-span railway bridges, significantly reducing the lateral amplitude and vibration acceleration of both the beam and bearings under heavy-haul railway loads. However, their impact on the vertical dynamic characteristics of the beam is minimal, with only the vertical vibration of the bearings showing a significant reduction.
(3) With fixed pier cross-sectional dimensions, the dynamic performance improvement of small-span bridges for heavy-haul railways using spherical bearings diminishes as the bridge span and pier height increase. For 2.2 m diameter cylindrical piers commonly used in heavy-haul railways, the pier height with spherical bearings should not exceed 10 m.
Author Contributions
Conceptualization, S.C. and K.X.; Data curation, Y.Z., P.Z. and C.L.; Funding acquisition, S.C. and K.X.; Investigation, S.C., Y.Z. and P.Z.; Methodology, S.C. and K.X.; Software, Y.Z. and C.L.; Writing—original draft, Y.Z. and K.X.; Writing—review and editing, S.C. and K.X. All authors have read and agreed to the published version of the manuscript.
Funding
This research was supported by the National Key R&D Program Projects (2023YFB2604301, 2023YFB2604303); the National Natural Science Foundation of China (52378171); and the Hebei Provincial Science and Technology Program (225A0802D); the Natural Science Foundation of Hebei Province (E2022210046).
Data Availability Statement
Data that support the findings of this study are available from the corresponding author upon reasonable request.
Conflicts of Interest
The authors declare no conflicts of interest.
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Figure 1.
Various failures of plate bearings.
Figure 2.
Structural composition of spherical bearing.
Figure 3.
Beam lifting operation.
Figure 4.
Bearing replacement construction.
Figure 5.
Flowchart of bridge bearing replacement construction.
Figure 6.
Dimensions of bridge piers (Unit: m).
Figure 7.
Test bridge measuring point layout diagram.
Figure 8.
Field records.
Figure 9.
Dynamic deflection of the middle section.
Figure 10.
Maximum dynamic deflection.
Figure 11.
Lateral amplitude.
Figure 12.
Lateral acceleration.
Figure 13.
Maximum lateral amplitude.
Figure 14.
Maximum lateral acceleration.
Figure 15.
Maximum vertical amplitude.
Figure 16.
Maximum vertical acceleration.
Figure 17.
Lateral displacement at bearings.
Figure 18.
Vertical displacement at bearings.
Figure 19.
Lateral displacement amplitude.
Figure 20.
Vertical displacement amplitude.
Figure 21.
Maximum lateral amplitude at the pier top.
Figure 22.
Simulation model and beam cross-section.
Figure 23.
Vertical loads (Unit:m).
Figure 24.
Lateral forces.
Figure 25.
Dynamic response at a speed of 55 km/h (pier height).
Figure 26.
Maximum dynamic response (pier height).
Figure 27.
Maximum dynamic response (bridge span).
Table 1.
Overview of the test bridges.
| Bridge | Pier Type | B (m) | H (m) | H0 (m) | H1 (m) | H2 (m) |
|---|---|---|---|---|---|---|
| 1# | Cylindrical | 2.2 | 9.5 | 6.0 | 7.5 | 1.5 |
| 2# | Cylindrical | 2.2 | 6.0 | 2.5 | 4.0 | 1.5 |
Table 2.
Time consumption for bearing replacement of each span.
| Bridge | First Span (hours) | Second Span (hours) | Third Span (hours) |
|---|---|---|---|
| 1# | 4.0 | 3.5 | 3.2 |
| 2# | 3.8 | 3.4 | 3.0 |
Table 3.
Test instrument parameter table.
| Equipment Name | Model | Range | Error | Application |
|---|---|---|---|---|
| High-speed dynamic data acquisition system | IMC C1-LEMO-ET | ±10 V | 0.1% | To collect bearing displacement data |
| Intelligent signal acquisition and analysis system | INV3062 | ±10 V | 1% | To collect mid-span amplitude and acceleration data |
| Vibration sensor | 891-II | 0.25~100 Hz | 1.0% | To convert vibration signals into electrical signals for subsequent data acquisition and analysis |
| Displacement sensor | CDP-10 | 0~10 mm | 0.2% | To measure bearing displacement |
| Displacement sensor | CDP-10 SDP-50C | 0~10 mm 0~50 mm | 0.2% | To measure bridge dynamic deflection |
Table 4.
Statistical results of maximum dynamic deflection amplitudes.
| Speed Range | Statistics | Span 1# | Span 2# | ||||
|---|---|---|---|---|---|---|---|
| Plate Bearing (mm) | Spherical Bearing (mm) | Change (%) | Plate Bearing (mm) | Spherical Bearing (mm) | Change (%) | ||
| V1 | Max | 5.280 | 5.972 | 13.1 | 5.280 | 5.750 | 8.9 |
| Mean | 4.578 | 5.336 | 16.6 | 4.451 | 5.044 | 13.3 | |
| V2 | Max | 5.682 | 5.950 | 4.7 | 5.668 | 5.690 | 0.4 |
| Mean | 4.746 | 5.657 | 19.2 | 4.736 | 5.572 | 17.7 | |
Table 5.
Statistical results of maximum lateral amplitude and lateral acceleration.
| Speed Range | Span | Statistics | Maximum Lateral Amplitude | Maximum Lateral Acceleration | ||||
|---|---|---|---|---|---|---|---|---|
| Plate Bearing (mm) | Spherical Bearing (mm) | Change (%) | Plate Bearing (m/s2) | Spherical Bearing (m/s2) | Change (%) | |||
| V1 | 1# | Max | 0.810 | 0.750 | −7.4 | 0.223 | 0.210 | −5.8 |
| Mean | 0.586 | 0.443 | −24.4 | 0.209 | 0.137 | −34.4 | ||
| V2 | 1# | Max | 0.820 | 0.510 | −37.8 | 0.413 | 0.247 | −40.2 |
| Mean | 0.518 | 0.428 | −17.4 | 0.231 | 0.165 | −28.6 | ||
| V1 | 2# | Max | 0.570 | 0.501 | −12.1 | 0.182 | 0.181 | −0.5 |
| Mean | 0.464 | 0.396 | −14.7 | 0.205 | 0.130 | −36.6 | ||
| V2 | 2# | Max | 0.660 | 0.560 | −15.2 | 0.392 | 0.271 | −30.9 |
| Mean | 0.465 | 0.460 | −1.1 | 0.222 | 0.215 | −3.2 | ||
Table 6.
Statistical results of maximum vertical amplitude and vertical acceleration.
| Speed Range | Span | Statistics | Maximum Vertical Amplitude | Maximum Vertical Acceleration | ||||
|---|---|---|---|---|---|---|---|---|
| Plate Bearing (mm) | Spherical Bearing (mm) | Change (%) | Plate Bearing (m/s2) | Spherical Bearing (m/s2) | Change (%) | |||
| V1 | 1# | Max | 0.810 | 0.790 | −2.5 | 1.050 | 1.042 | −0.8 |
| Mean | 0.661 | 0.584 | −11.6 | 0.876 | 0.661 | −24.5 | ||
| V2 | 1# | Max | 0.950 | 0.720 | −10.5 | 1.310 | 1.070 | −18.3 |
| Mean | 0.681 | 0.602 | −8.5 | 0.913 | 1.038 | 13.7 | ||
| V1 | 2# | Max | 0.630 | 0.610 | −3.2 | 1.480 | 1.460 | −1.4 |
| Mean | 0.490 | 0.448 | −8.6 | 0.905 | 0.699 | −22.8 | ||
| V2 | 2# | Max | 0.780 | 0.541 | −30.6 | 1.540 | 1.480 | −3.9 |
| Mean | 0.495 | 0.480 | −3.0 | 1.065 | 1.087 | 2.1 | ||
Table 7.
Statistical results of lateral and vertical displacement amplitude.
| Speed Range | Span | Statistics | Lateral Displacement Amplitude | Vertical Displacement Amplitude | ||||
|---|---|---|---|---|---|---|---|---|
| Plate Bearing (mm) | Spherical Bearing (mm) | Change (%) | Plate Bearing (mm) | Spherical Bearing (mm) | Change (%) | |||
| V1 | 1# | Max | 0.261 | 0.182 | −30.3 | 0.216 | 0.100 | −53.7 |
| Mean | 0.169 | 0.073 | −56.8 | 0.182 | 0.087 | −52.2 | ||
| Standard deviation | 0.042 | 0.017 | −59.5 | 0.022 | 0.007 | −68.2 | ||
| V2 | 1# | Max | 0.260 | 0.075 | −71.2 | 0.216 | 0.095 | −56.0 |
| Mean | 0.142 | 0.060 | −57.7 | 0.169 | 0.081 | −52.1 | ||
| Standard deviation | 0.027 | 0.010 | −63.0 | 0.015 | 0.010 | −33.3 | ||
| V1 | 2# | Max | 0.258 | 0.081 | −68.6 | 0.220 | 0.101 | −54.1 |
| Mean | 0.180 | 0.057 | −68.3 | 0.207 | 0.077 | −62.8 | ||
| Standard deviation | 0.014 | 0.016 | 14.3 | 0.004 | 0.006 | 50.0 | ||
| V2 | 2# | Max | 0.259 | 0.034 | −86.9 | 0.219 | 0.054 | −75.3 |
| Mean | 0.175 | 0.030 | −82.9 | 0.204 | 0.050 | −75.5 | ||
| Standard deviation | 0.034 | 0.002 | −94.1 | 0.017 | 0.002 | −88.2 | ||
Table 8.
Statistical results of maximum lateral amplitude.
| Speed Range | Statistics | Span 1# | Span 2# | ||||
|---|---|---|---|---|---|---|---|
| Plate Bearing (mm) | Spherical Bearing (mm) | Change (%) | Plate Bearing (mm) | Spherical Bearing (mm) | Change (%) | ||
| V1 | Max | 0.430 | 0.540 | 25.6 | 0.150 | 0.230 | 53.3 |
| Mean | 0.363 | 0.421 | 16.0 | 0.131 | 0.185 | 41.2 | |
| V2 | Max | 0.480 | 0.541 | 12.7 | 0.240 | 0.290 | 20.8 |
| Mean | 0.365 | 0.497 | 36.2 | 0.168 | 0.230 | 36.9 | |
Table 9.
Beam cross-sectional dimensions.
| Span (m) | Beam Length (m) | Beam Height (cm) | Beam Web Width (m) | Distance Between Beam Web Centers (cm) | Beam Top Width (m) | Beam Bottom Width (m) |
|---|---|---|---|---|---|---|
| 8 | 8.5 | 55 | 1.06 | 170 | 1.92 | 1.06 |
| 10 | 10.5 | 70 | 0.46 | 170 | 1.92 | 1.06 |
| 12 | 12.5 | 85 | 0.26 | 180 | 1.92 | 1.06 |
| 16 | 16.5 | 110 | 0.26 | 180 | 1.92 | 1.06 |
Table 10.
Stiffness values of spherical bearings.
| Bearing Type | Vertical Rotational Stiffness (kN·m/rad) | Vertical Stiffness (kN/m) | Lateral Horizontal Stiffness (kN/m) |
|---|---|---|---|
| Spherical Bearing (GD) | 1 × 1010 | 1 × 106 | 1 × 1010 |
| Spherical Bearing (HX) | 1 × 1010 | 1 × 106 | 1 × 104 |
Table 11.
Comparison of results.
| Test Parameter | Test Results | Simulation Results | Deviation |
|---|---|---|---|
| Dynamic deflection of the middle section (mm) | 5.319 | 5.556 | −4.5% |
| Lateral amplitude of middle section (mm) | 0.448 | 0.447 | 0.2% |
| Lateral acceleration of middle section (m/s2) | 0.138 | 0.131 | 5.1% |
| Vertical acceleration of middle section (m/s2) | 0.665 | 0.642 | 3.5% |
| Pier top lateral amplitude (mm) | 0.414 | 0.433 | −4.6% |
Table 12.
Classification of cases.
| Case | Research Focus | Bridge Span (m) | H1 (m) | Train Speed (km/h) |
|---|---|---|---|---|
| 1 | Pier height variation | 16 | 1.5, 4.5, 7.5, 9.0, 10.0 | 55, 60, 65, 70, 75, 80 |
| 2 | Span differences | 8, 10, 12, 16 | 7.5 | 55, 60, 65, 70, 75, 80 |
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Chen, S.; Zhou, Y.; Xie, K.; Zhang, P.; Li, C. Dynamic Adaptability of Spherical Bearings in Small-Span Bridges for Heavy-Haul Railways. Buildings 2025, 15, 619. https://doi.org/10.3390/buildings15040619
AMA Style
Chen S, Zhou Y, Xie K, Zhang P, Li C. Dynamic Adaptability of Spherical Bearings in Small-Span Bridges for Heavy-Haul Railways. Buildings. 2025; 15(4):619. https://doi.org/10.3390/buildings15040619
Chicago/Turabian StyleChen, Shuli, Ye Zhou, Kaize Xie, Panhui Zhang, and Chen Li. 2025. "Dynamic Adaptability of Spherical Bearings in Small-Span Bridges for Heavy-Haul Railways" Buildings 15, no. 4: 619. https://doi.org/10.3390/buildings15040619
APA StyleChen, S., Zhou, Y., Xie, K., Zhang, P., & Li, C. (2025). Dynamic Adaptability of Spherical Bearings in Small-Span Bridges for Heavy-Haul Railways. Buildings, 15(4), 619. https://doi.org/10.3390/buildings15040619
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