• Steel and Composite Structures
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• v.33 no.2
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• pp.209-224
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• 2019

This paper describes a study of the mapping relationship between the vertical deformation of bridge structures and rail deformation of high-speed railway, taking the interlayer interactions of the bridge subgrade CRTS II ballastless slab track system (HSRBST) into account. The differential equations and natural boundary conditions of the mapping relationship between the vertical deformation of bridge structures and rail deformation were deduced according to the principle of stationary potential energy. Then an analytical model for such relationship was proposed. Both the analytical method proposed in this paper and the finite element numerical method were used to calculate the rail deformations under three typical deformations of bridge structures and the evolution of rail geometry under these circumstances was analyzed. It was shown that numerical and analytical calculation results are well agreed with each other, demonstrating the effectiveness of the analytical model proposed in this paper. The mapping coefficient between bridge structure deformation and rail deformation showed a nonlinear increase with increasing amplitude of the bridge structure deformation. The rail deformation showed an obvious "following feature"; with the increase of bridge span and fastener stiffness, the curve of rail deformation became gentler, the track irregularity wavelength became longer, and the performance of the rail at following the bridge structure deformation was stronger.

• Steel and Composite Structures
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• v.46 no.1
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• pp.93-105
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• 2023

This paper examines a high-speed railway CRTS-II ballastless track-bridge system. Using the stationary potential energy theory, the mapping analytical solution between the bridge deformation and the rail vertical geometric irregularity was derived. A theoretical model (TM) considering the nonlinear stiffness of interlayer components was also proposed. By comparing with finite element model results and the measured field data, the accuracy of the TM was verified. Based on the TM, the effect of bridge deformation amplitude, girder end cantilever length, and interlayer nonlinear stiffness (fastener, cement asphalt mortar layer (CA mortar layer), extruded sheet, etc.) on the rail vertical geometric irregularity were analyzed. Results show that the rail vertical deformation extremum increases with increasing bridge deformation amplitude. The girder end cantilever length has a certain influence on the rail vertical geometric irregularity. The fastener and CA mortar layer have basically the same influence on the rail deformation amplitude. The extruded sheet and shear groove influence the rail geometric irregularity significantly, and the influence is basically the same. The influence of the shear rebar and lateral block on the rail vertical geometric irregularity could be negligible.

• Steel and Composite Structures
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• v.32 no.4
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• pp.467-478
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• 2019

Running safety and ride comfort of high speed railway largely depend on the track geometry that is dependent on the bridge deformation. This study presents a theoretical study on mapping the bridge vertical deformations to the change of track geometry. Analytical formulae are derived through the theoretical analysis to quantify the track geometry change, and validated against the finite element analysis and experimental data. Based on the theoretical formulae, parametric studies are conducted to evaluate the effects of key parameters on the track geometry of a high speed railway. The results show that the derived formulae provide reasonable prediction of the track geometry change under various bridge vertical deformations. The rail deflection increases with the magnitude of bridge pier settlement and vertical girder fault. Increasing the stiffness of the fasteners or mortar layer tends to cause a steep rail deformation curve, which is undesired for the running safety and ride comfort of high-speed railway.

• Proceedings of the KSR Conference
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• 2005.05a
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• pp.115-122
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• 2005

This study analyzed the characteristics of four kinds of bridge rubber pads and suggested how to determine the stiffness the pads. The stiffness of rubber pads can be estimated by a direct static test. In the procedure to estimate the stiffness of a pad, the dead load(preload) of a bridge and live load of a vehicle are considered. The polyurethane rubber pads have larger hardness than natural and chloroprene rubber pads and thus carry larger load bearing capacity. In addition, they showed higher stiffness with the same shape factor than the others and thus are more avaliable as for bridge bearings. Although natural and chloroprene rubber pads are elongated to large deformation in horizontal direction due to vertical loads, polyurethane rubber pads almost do not generate horizontal deformation due to vertical loads regardless to the thickness and hardness of the pads. Therefore, they do not need reinforced plate to restrict horizontal deformation.

• Steel and Composite Structures
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• v.44 no.4
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• pp.473-488
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• 2022

A high-speed railway (HSR) bridge may undergo long-term deformation due to the degradation of material stiffness, or foundation settlement during its service cycle. In this study, an analytical model is set up to evaluate the influence of this long-term vertical bridge deformation on the track geometry. By analyzing the structural characteristics of the HSR track-bridge system, the energy variational principle is applied to build the energy functionals for major components of the track-bridge system. By further taking into account the interlayer's force balancing requirements, the mapping relationship between the deformation of the track and the one of the bridge is established. In order to consider the different behaviors of the interlayers in compression and tension, an iterative method is introduced to update the mapping relationship. As for the validation of the proposed mapping model, a finite element model is created to compare the numerical results with the analytical results, which show a good agreement. Thereafter, the effects of the interlayer's different properties of tension and compression on the mapping deformations are further evaluated and discussed.

• Geomechanics and Engineering
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• v.7 no.2
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• pp.201-212
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• 2014

Due to the sea-crossing bridge span is generally large and main pier pile foundations are located in deep water and carry large vertical load, sea-crossing bridge main pier pile foundations bearing mechanism and load deformation characteristics are still vague. Authors studied the vertical bearing properties of sea-crossing bridge main pier pile foundations through pilot load tests. Large tonnage load test of Qingdao Bay Bridge main pier pile program is designed by using per-stressed technique to optimize the design of anchor pile reaction beam system. Test results show that the design is feasible and effective. This method can directly test bearing capacity of main pier pile foundations, and analysis bearing behaviors from test results of sensors which embedded in the pile. Through test study the vertical bearing properties of main pier pile foundation and compared with the generally short pile, author summarized the main pier pile foundations vertical bearing capacity and the main problem of design and construction which need to pay attention, and provide a reliable basis and experience for sea-crossing bridge main pier pile foundations design and construction.

• Journal of the Earthquake Engineering Society of Korea
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• v.8 no.6 s.40
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• pp.1-11
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• 2004

In the previous study(1), the finite element method was used for the vertical vibration analysis of suspension bridge considering the effects of the shear deformation and the rotary inertia under moving load. This study firstly performs the eigenvalue analysis for the free vertical vibration of suspension bridge using FEM analysis. Next the equations of motion considering interaction between suspension bridge and vehicles/train are derived using mode superposition method. And dynamic analysis was performed using the Newmark $\beta$ Method. Finally through the numerical examples, the dynamic responses of bridges by this study are investigated.

• Wind and Structures
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• v.25 no.3
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• pp.215-232
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• 2017

Wind tunnel tests and numerical aerodynamic analyses were conducted for an integrated catwalk structure under strong winds. From the wind tunnel tests, it is found that the aerodynamic coefficients were different from those of the typical type. The drag coefficient was larger than typical and was sensitive to number of vertical meshes installed rather than the solidity ratio. Comparing with typical catwalk, the integrated one showed larger deformation under strong wind, and the large torsional deformation are mainly caused by drag force. It did not show aerodynamic divergence even the torsional deformation reaching $20^{\circ}$. The reason could be that the stiffness is smaller and thus the catwalk is able to deform to the shape compactable with higher loading. Considering safety for construction, storm rope system is introduced to the catwalk to reduce the deformation to acceptable level.

• Earthquakes and Structures
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• v.8 no.6
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• pp.1481-1497
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• 2015

Vertical earthquake ground motion may magnify vertical dynamic responses of structures, and thus cause serious damage to bridges. As main support structures, piers and bearings play an important role in vertical seismic response analysis of girder bridges. In this study, the pier and bearing are simplified as a vertical series spring system without mass. Then, based on the assumption of small displacement, the equation of motion governing the simply-supported straight girder bridge under vertical ground motion is established including effects of vertical deformation of support structures. Considering boundary conditions, the differential quadrature method (DQM) is applied to discretize the above equation of motion into a MDOF (multi-degree-of-freedom) system. Then seismic responses of this MDOF system are calculated by a step-by-step integration method. Effects of support structures on vertical dynamic responses of girder bridges are studied under different vertical strong earthquake motions. Results indicate that support structures may remarkably increase or decrease vertical seismic responses of girder bridges. So it is of great importance to consider effects of support structures in structural seismic design of girder bridges in near-fault region. Finally, optimization of support structures to resist vertical strong earthquake motions is discussed.

• Structural Engineering and Mechanics
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• v.77 no.5
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• pp.601-612
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• 2021

To study the vibration characteristics of a high-speed railway continuous girder bridge-track coupling system (HSRCBT), a coupling vibration analysis model of an m-span continuous girder bridge-subgrade-track system with n-span approach bridge was established. The model was based on the energy and its variational method, where both the interlaminar slip and shear deformation effects were considered. In addition, the free vibration equations and natural boundary conditions of the HSRCBT were derived. Further, according to the coordination principle of deformation and mechanics, an analytical method for calculating the natural vibration frequencies of the HSRCBT was obtained. Three typical bridge-subgrade-track coupling systems of high-speed railway were taken and the results of finite element analysis were compared to those of the analytical method. The errors between the simulation results and calculated values of the analytical method were less than 3%, thus verifying the analytical method proposed in this paper. Finally, the analytical method was used to investigate the influence of the number of the approach bridge spans and the interlaminar stiffness on the natural vibration characteristics of the HSRCBT based on the degree of sensitivity. The results suggest the approach bridges have a critical number of spans and in general, the precision requirements of the analysis could be met by using 6-span approach bridges. The interlaminar vertical compressive stiffness has very little influence on the low-order natural vibration frequency of HSRCBT, but does have a significant influence on higher-order natural vibration frequency. As the interlaminar vertical compressive stiffness increases, the degree of sensitivity to interlaminar stiffness of each of the HSRCBT natural vibration characteristics decrease and gradually approach zero.