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Bridge Insight : New Development in Long Span Arch Bridges
Rail Structure Interaction (RSI) is a complex phenomenon that occurs between the rail and the structure when Continuous Welded Rail (CWR) is used on a railway bridge. Unlike conventional rails, CWRs are continuous rails, so each displacement that occurs on bridges and rails is influenced by each other due to train loading (vertical and longitudinal direction) and temperature changes. Due to the following effects, safety problems such as buckling or fracture may occur on the rail during use. Therefore, when using CWR, it is necessary to review regardless of the type of train or track (ballast track, concrete slab track).
Fig. Rail transport
Since CWR began to be used due to the development of welding methods and research results to solve the problems of the existing method of connecting the standard length rail to the fishplate, additional stress generation and deformation phenomena were found in rails and structures due to external factors such as temperature changes. Research on RSI was conducted to solve these problems in advance. Among them, the European Rail Research Institute (ERRI) has been conducting a number of studies for a long time, and based on ERRI D213, it has been applied to UIC 774-3R (International Union of Railways) and Eurocode EN 1992-2.
A general composition of a railway bridge is shown in the figure below.
Fig. General cross-section of railway bridge
Tracks installed on deck slabs are typically composed of rails, slippers, and ballasts. Track types can be classified according to the type of rail, sleeper and ballast (ex. Ballast track and concrete slab track), but the way loads are transferred from the rail to the structure is the same.
The rail transmits the load and displacement to the structure, with the movement suppressed by fastenings, slippers and ballasts. Likewise, the displacements occurring in the structure are also transferred to the rail.
Fig. Ballast track
Fig. Concrete slab track
Even though there are structural analysis difficulties during the design stage of CWRs as well as safety issues during service stage, the use of CWRs is recently expanding due to its advantages.
The conventional jointed track uses a method of connecting approximately 20m~25m of rails with fishplates taking into consideration manufacturing, transportation construction, and temperature changes. This method creates a joint in between rails, which becomes the weakest part of the track. The noise and vibration generated by the train due to this joint not only worsens the ride comfort, but it is also the major cause of damage in vehicles and tracks.
Fig. Conventional jointed track
Fig. Continuous Welded Rail(CWR)
CWR was developed to compensate for these shortcomings, and this technology has become one of the key technologies for high speed trains. CWR is continuous rail manufactured by connecting about 20~25m of rail with flash butt welding. Since there are fewer joints, it improves ride comfort by reducing noises and vibrations, and making it possible trains to run at higher speeds. Although initial installation costs are high, maintenance costs are much lower. The CWR segment is connected up to 2km on site by thermite welding. Furthermore, expansion joints (breather switches) are installed when a connection is required.
Fig. Expansion joint (breather switch)
According to UIC 774-3R clause 1.4, the RSI should consider cases that cause relative displacement of the track and deck. (“The cases that could lead to interaction effects are those that cause relative displacement between the track and the deck.”)
The cases concerned are as follows:
In most cases, the first three effects are of major importance for bridge design.
- The thermal expansion of the deck only, in the case of CWR, or the thermal expansion of the deck and of the rail,
whenever a rail expansion device is present
- Horizontal braking and acceleration forces
- Rotation of the deck on its supports as a result of the deck bending under vertical traffic loads
- Deformation of the concrete structure due to creep and shrinkage
- Longitudinal displacement of the supports under the influence of the thermal gradient
- Deformation of the structure due to the vertical temperature gradient
- The major importance that should be considered in bridge design are as follows.
UIC 774-3R only considers thermal expansion of the deck.
- In fact, thermal action is the load case that has the greatest effect on the axial stress of the rail, but in the bridge section where the CWR is installed (central zone of CWR), there is no displacement of the rail due to thermal change, so it is not considered in the interaction.
- UIC explains this phenomenon, and the figure below shows that the expansion zone does expand and contract due to temperature changes. However, this does not happen in the central zone due to the ballast constraints
Fig. Behavior of CWR under the effects of temperature changes (UIC 774-3R Fig.1)
α : coefficient of thermal expansion
ΔTR : change in rail temperature relative to the reference or laying temperature
E : Young’s modulus for steel
A : combined cross-section of two rails
F : force in the track
The longitudinal displacement of the rail is fixed by sleepers, fasteners, and ballast, whereas the deck of the bridge is not fixed. Therefore, temperature changes occurring in the bridge causes relative displacement between the rail and the structure as shown in the figure below. Moreover, resistance of the track to longitudinal displacements is generated. This resistive force acts in the opposite direction of the rail and structure, but the magnitude of the force is the same.
Fig. Resistance of the track to longitudinal displacement
Displacements that occur on the bridge due to temperature changes and the displacements that occur on the rail due to the longitudinal resisting force occurs as shown in the figure below. This displacement causes additional axial stresses (compression or tension) in the rail.
Fig. Interaction on bridges under temperature loads
Similar to physical changes caused by thermal action, longitudinal resisting forces are also generated by the longitudinal displacement of the rail caused by braking and acceleration forces. The direction of the two forces with respect to the train’s traveling direction is opposite as shown in the figure below. If displacement occurs in the rail in the direction in which the load acts, additional displacements occur in the same direction through the interaction.
Fig. Braking and acceleration forces action on the bridge
Vertical train loads should be loaded at the most unfavorable position in accordance with what is being tested (ex. Stress occurring in rails or displacements occurring in bridges). Vertical train loads causes bending of the superstructure and causes end rotation between the upper edge of the deck end or between the upper end surface of the continuous deck as shown in the figure below.
Fig. Displacement due to deck bending
In addition, due to the rotation angle generated by bending, displacements are also transmitted to the rails, generating additional stresses. The conceptual diagram of the horizontal displacements due to bending of the superstructure are as follows.
Fig. Effect of deck bending on the end sections (UIC 774-3R)
In order to analyze RSI, it is necessary to know what parameters affect it. The parameters that affect the interaction phenomenon can be classified into bridge parameters and track parameters. Each is described below.
- Track resistance
- Specification (ex. Cross-sectional area) and material properties
(ex. Young’s modulus, coefficient of thermal expansion, poisson’s ratio) of rails.
- Expansion length and span length : The distance between fixed points is the distance between the central point of the thermal expansion of the structure (the point that does not move during thermal expansion), and the distance L between the fixed points is as shown in the figure below.
Fig. Expansion length (UIC 774-3R)
- Bending stiffness and height of the deck : The effect of RSI due to the vertical loads of the train should be taken into consideration in RSI analysis, mainly because it is influenced by the bending stiffness of the superstructure and the position of the neutral axis, the horizontal support spring stiffness of the anchorage, and the height of the superstructure.
UIC 774-3R clause 1.7.3 describes general recommendations for analyzing RSI using a structural program, and basically, modeling for structural analysis should consider all the above-mentioned parameters.
Fig. Structural diagram for the evaluation of rail-bridge interaction effect
Fig. Typical model of the rail-deck-bearing system
Modeling the track and decks as discrete elements should guarantee an accurate evaluation of the items of major interest (support reactions, absolute and relative displacements of track and decks, rail stresses). For this purpose, a finite-element model may be adopted, where the track and the deck elements are modelled discretely with a maximum element length of 2.0m. The model should also include a part of the track on the adjacent embankments of at least 100m.
The boundary condition according to the rail’s section location can be set as follows. When the rail is located in the embankment, the embankment is modelled with fully fixed support conditions that connects with the rail element using a multi-linear elastic link.
Fig. Embankment and deck start point connection
Even if the rail is located on the deck, the rail element and the deck element are modeled as a multi-linear elastic link. To take into account the deck’s height, boundary conditions are set on the bottom deck that connects with a rigid link.
Fig. Deck end and start point connection
If the substructure is assumed to be a spring type, set support/point spring support at the bottom of the deck as a boundary condition. In the case of bearing type, the bearing is modeled as elastic link that connects to the substructure element.
Fig. Spring type and bearing type connection
The figure below is an example of the RSI analytical model taking into consideration the above conditions. The superstructure, the substructure, and the rail were modeled as beam elements. The 2-track rail was modeled up to both embankment sections. The boundary conditions for the rail and superstructure were set as a multi-linear elastic link; the boundary conditions for the superstructure and bearing were set as a rigid link, and the boundary conditions of the bearing were set as elastic link.
Fig. Finite Elements Method(FEM) model for rail structure onteraction analysis
With the results obtained from structural analysis, the feasibility of the structure can be confirmed through the allowable values suggested by UIC 774-3R. Structural analysis of the rail and bridge for the load should be performed separately first and then combined. The main verification of the result values is as follows.
• The Maximum allowable additional compressive rail stress is 72 MPa
• The Maximum allowable additional tensile rail stress is 92 MPa
• The Maximum allowable displacement between the rail and deck under braking and/or acceleration forces is 4mm
• The Maximum absolute deck displacement at both ends of the bridge due to braking and/or acceleration forces is 5mm
• If there are expansion devices, the maximum allowable absolute deck displacement under braking and/or acceleration forces is 30mm
• The Maximum allowable displacement between the top of the deck-end and the embankment, or between the top of the two consecutive
deck ends due to vertical bending (including the dynamic factor) is 8mm