1. Introduction
In our previous content, we discussed how we can control the additional stress for RSI when it is beyond the permissible limit for a single track. In this content, we will explore more about RSI when two tracks are present. such as how to find the critical position of the vehicle, and controlling measures when stresses are beyond permissible limits.
The key topics include:
- The critical vehicle position and loads consideration
- How to control additional stress when stress is beyond permissible limit
Rail structure interaction (RSI) plays a crucial role in the design and analysis of railway tracks. Especially in double-track configurations, where two tracks run parallel to each other, the RSI becomes more complex compared to a single-track system. The interaction between the tracks and the supporting structures can affect various aspects of the railway system, including track stability, passenger comfort, etc. Through RSI analysis, engineers can evaluate the performance of the railway tracks, identify potential issues or areas of improvement, optimize the design to enhance track stability and reduce maintenance requirements.
2. UIC 774-3 Recommendation
When two tracks are present on the bridge the critical vehicle position should be determined by considering the number of load cases i.e., changing the vehicle position for both the tracks with load suggested by UIC 774-3 guidelines to obtain the critical stress. In previous content, detailed information regarding the different types of load and their combination is present. So, in this part, we will discuss the additional consideration when the double-track is present as per UIC 774-3 guidelines.
- Temperature load
Similar to the single track, the following temperature load should be considered as per UIC 774-3.
Rail = ± 50 °C
Bridge = ± 35 °C
- Braking, Acceleration and Vertical load
As per UIC 744-3 (2.2.1), for a bridge with two tracks, “the braking force on one track and acceleration force on the other should be considered”.
Acceleration: qlak= 33 kN/m per track, with L x qlak ≤ 1000 kN
Braking: qlbk= 20 kN/m per track, with L x qlbk ≤ 6000 kN
3. Problem Statement
Let’s consider the 3-span box girder bridge configuration similar to Part 1 with 2 tracks scenario, and perform the RSI to evaluate the additional stress.
| 1 | Deck type | PSC Box Girder |
|---|---|---|
| 2 | Number of track | 2 |
| 3 | Span length | 40m + 60m + 40m |
| 4 | Longitudinal Stiffness of Support | 60000 kN/m |
| 5 | Pier height | 7.5m |
3.1 Material and Section Properties
The material and section properties used for modelling are as follows.
- Deck section
| Grade of Concrete | C40/50 |
|---|---|
| Modulus of Elasticity,E | 3.522e+07 kN/m2 |
| Cross Section Area, A | 10.52 m2 |
| Moment of Inertia, Iyy | 11.89 m4 |
| Height of the section, H | 3 m |
| Neutral Axis of the Section | 1.70 m |
| Coefficient of Thermal Expansion, α | 1e-05 |
Figure 3.1 PSC box section property definition in MIDAS CIVIL
- Rail Section
| Modulus of Elasticity,E | 2.10e+08 kN/m2 |
|---|---|
| Cross Section Area, A | 1.54e-02 m2 |
| Moment of Inertia, Iyy | 6.07e-05 m4 |
| Coefficient of Thermal Expansion, α | 1.20e-05 |
Figure 3.2 UIC 60 rail properties
- Elastic Link
To consider the rail-structure interaction elastic link is used with a bi-linear force deformation function as specified in UIC 774-3.
Figure 3.3 Longitudinal resistance of the ballast (UIC 774-3)
3.2 Modelling in MIDAS CIVIL
Rail structure Interaction is considered for a 2-cell PSC box girder bridge with a double track having a deck width of 10m, and 3 spans of length 40m, 60m and 40m of the uniform cross-section is considered. For modelling, the bridge section & rail section are modelled using the beam elements, to consider the rail-structure interaction elastic link is used with a bi-linear force deformation function which has different resistance of ballast (loaded/ unloaded condition) depending on the presence of train loads as shown in the above image.
ℹ️ Simplified separate analysis for temperature variation, braking/ acceleration force and vertical deflection is considered, and the results are combined assuming the principle of superposition.
Figure 3.4 Schematic diagram for RSI modelling in MIDAS CIVIL
Figure 3.5 Double track bridge simulation in the program
3.3 Rail Structure Interaction (RSI) results
- Temperature Load
Similar to the single track condition, the uniform temperature load of 35°C is applied to the deck as per UIC 774-3 guidelines to evaluate the additional stress due to RSI on both tracks. Since there is no rail expansion device present to accommodate for thermal expansion and contraction of the rails, the resulting stress in the rails will remain constant and will not account for any additional stress caused by temperature variation.
Figure 3.6 Axial stress in rail (Temperature load)
- Braking/ Acceleration and Vertical Load
For the case of a double-track bridge, it is necessary to consider the braking force on one track and the acceleration force on the other track. However, for the double-track bridge, many load cases have to be considered to find the critical vehicle position and maximum additional stress due to RSI. For the above case, the total length of rail is 740m including abutments on both the side and considering the interval of 10m for change in vehicle position, the total number of load cases would be 10952 [5476 (74*74) * 2 (for train running in both the direction)].
Analyzing each and every possible load case can be a time-consuming process. In order to reduce the number of analyses, engineers can rely on their expertise and past experience to identify critical locations where the maximum additional stress due to the Rail Structure Interaction (RSI) occurs. Typically, the most critical locations are near the supports and the mid-span of the bridge. By focusing the analysis on these key locations, engineers can reduce the number of load cases that need to be considered.
For this case, the following critical location is selected as shown in the below image.
You can check more of these details in the download file.
