Introduction

# Rail Track Analysis

## Introduction

The passage of one or more trains crossing a rail bridge causes forces and moments to occur in the rails that, in turn, induce displacements in the supporting bridge deck, bearings and piers. As part of the design process for rail bridges it is necessary to ensure that any interaction between the track and the bridge as a result of temperature and train loading is within specified design limits.

## UIC774-3 Code of Practice

According to the Union Internationale des Chemins de fer (International Union of

Railways) UIC774-3 Code of Practice, the track-structure interaction effects should be evaluated in terms of the longitudinal reactions at support locations, rail stresses induced by the temperature and train loading effects in addition to the absolute and relative displacements of the rails and deck. To assess the behaviour these interaction effects should be evaluated through the use of a series of nonlinear analyses where all thermal and train loads are taken into account. These loads should be:

Track

Non-linear Springs

Representing Ballast or Connection

Rail Expansion Joint

(If Present)

Z

Z

Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z

Bridge Deck

Embankment

Figure 1: Representation of Structural System for Evaluation of Interaction Effects

1

Rail Track Analysis User Manual

Z

Non-linear spring representing ballast/connection

Z Z

Track (rail) centreline

Deck centreline

Bearing

Z

Remaining Structure

(Piers/Foundations)

Longitudinal Schematic Of The Model Transverse Cross-Section Of Track-Deck-Bearing System

Figure 2: Typical Model of Track-Deck-Bearing System

The interaction between the track and the bridge is approximated in the UIC774-3

Code of Practice by a bilinear relationship as indicated in the following figure. The resistance of the track to the longitudinal displacements for a particular track type is a function of both the relative displacement of the rail to the supporting structure and the loading applied to the track. If the track is subjected to no train loads then the ultimate resistance of the track to relative movement is governed by the lower curve in the figure (based on the track type). Application of train loads increases the resistance of the track to the relative displacements and the upper curve should be used for the interaction between the track and bridge where these train loads are present – unloaded resistance is still used for all other locations.

2

UIC774-3 Code of Practice

Resistance of rail to sliding relative to sleeper (Loaded Track)

(Frozen ballast or track without ballast)

Resistance of sleeper in ballast (Loaded Track)

Resistance of rail to sliding relative to sleeper (Unloaded Track)

(Frozen ballast or track without ballast)

Resistance of sleeper in ballast (Unloaded Track) u

0

Displacement (u)

0

(Ballast)

Figure 3: Resistance (k) of the Track per Unit Length versus Longitudinal Relative

Displacement of Rails

The values of displacement and resistance to use in these bilinear curves are governed by the track structure and maintenance procedures adopted and will be specified in the design specifications for the structure. Typical values are listed in the Code of

Practice for ballast, frozen ballast and track without ballast for moderate to good maintenance.

According to the UIC774-3 Code of Practice there is no requirement to consider a detailed model of the substructure (bearing-pier-foundation and bearing-abutmentfoundation systems) when „standard‟ bridges are considered, instead this can be modelled simply through constraints and/or spring supports that approximate the horizontal flexibility due to pier translational, bending and rotational movement. The

LUSAS Rail Track Analysis option allows this type of analysis to be carried out where the behaviour of the bearing and the pier/abutment-foundation are individually specified but also provides the capability of explicitly modelling the bearingpier/abutment-foundation systems where each component is defined, including the height and properties of the pier/abutment.

3

Rail Track Analysis User Manual

## LUSAS Rail Track Analysis

The Rail Track Analysis option in LUSAS provides the means to automate the finite element analyses required for conducting bridge/track interaction analyses in accordance with the UIC774-3 Code of Practice. The key features are:

## The Rail Track Analysis Spreadsheet

A Microsoft Excel spreadsheet is used to define the data from which a LUSAS finite element model is built and a track/bridge interaction analysis carried out. The spreadsheet is separated into a number of worksheets that relate to particular aspects of the Rail Track Analysis input requirements. These worksheets cover:

For each worksheet comments are included to advise on the appropriate input to the spreadsheet. These can be seen when hovering the mouse cursor over the cell of interest.

The template for the input spreadsheet is located in the \<Lusas Installation

Folder>\Programs\Scripts\User directory. Initially this template contains data that reproduces the E1-3 UIC test case model outlined in the code of practice as an illustration and should be edited and saved to the working directory in order to carry out analyses. metric units. The required units are indicated in the various sections of the spreadsheet and should be adhered to for the correct modelling of the interaction analysis. When the model is built, all input will be converted to SI units of N, m, kg,

C and s.

4

## Worksheet 1: Spans and Embankment Lengths

Figure 4: Definition of Number of Spans, Tracks and Embankment Lengths

This worksheet defines the global arrangement details of the bridge structure. The number of spans is initially limited to 100 but can be increased by modifying the

Structure Definition worksheet as outlined in the following section. The number of tracks can be set as either one or two. For two tracks, one will take the braking load of a trainset and the other will take the acceleration load of a separate trainset. The final input in this worksheet is the lengths of the left and right embankments. These lengths should be sufficiently long to allow the trainset loading to be placed in the model and, according to the UIC774-3 Code of Practice, should be greater than 100m (Clause

1.7.3).

Left Embankment

Figure 5: Left and Right Embankments in Model

Right Embankment

5

Rail Track Analysis User Manual

## Worksheet 2: Structure Definition

Figure 6: Structure Definition

The structure definition worksheet allows the geometry of the bridge to be input span by span. For each span the spreadsheet allows the definition of the left pier/abutment, up to eight internal piers and the right pier/abutment, each with their own support / bearing characteristics. These can include the physical modelling of the piers (by entering data into the pier height, geometric and material assignment columns) or be left blank if the behaviour of the combined pier/foundation system is to be incorporated into the spring support only.



The pier properties for the last pier of one span must exactly match the properties defined for the next span or an error will be reported when the Microsoft

Excel spreadsheet is used to carry out the analysis.

When the pier/foundation system is modelled as a spring this spring can be calculated by combining the component movements associated with the pier as indicated below and described further in the UIC774-3 Code of Practice:

 total

 p

 h

 b where d p

= displacement at top of support due to elastic deformation d

= displacement at top of support due to rotation of the foundation

6

d h

= displacement at top of support due to horizontal movement of the foundation d b

= relative displacement between the upper and lower parts of bearing (Only included if bearings effects lumped into support conditions) and the total spring stiffness is calculated from:

K

H total

(in kN/mm)

 p

 h

H H H H

Figure 7: Component Behaviour for Calculating Support Stiffness



If the piers are modelled in the analysis the rotation of the foundation is assumed to be zero in the analysis. This can be adjusted by modifying the support conditions manually after a temperature only analysis has been performed (see user interface discussions)

In addition to the general arrangement or the piers, supports and bearings, the gaps between the piers are also defined in this worksheet and should be a positive number greater than zero (in metres). The final entries in the worksheet relate to the geometric and material properties to assign to the spans. Different properties can be assigned to each segment of the span but continuously varying properties cannot be modelled. All of the geometric and material properties used in the structure definition must be defined in the geometric and material property worksheet tables described later in this manual.

Increasing the number of spans modelled

If more than 100 spans are required the Microsoft Excel spreadsheet can be modified.

To do this, scroll to the end of the Structure Definition worksheet and select the last complete span definition as indicated on the figure below.

7

Rail Track Analysis User Manual

Figure 8: Selection and Copying of Structure Definition Worksheet to Increase

Number of Spans

Copy and paste this section as many times as required at the end of the worksheet, ensuring that the row formatting is not altered as indicated below. If successful, the span number should be correctly calculated for the added entries. The number of spans in the first worksheet of the spreadsheet can now be increased to the number of spans added to the structure definition.

8

Figure 9: Pasting of Additional Spans to Ensure Formatting Maintained

## Worksheet 3: Geometric Properties

Figure 10: Geometric Properties Table for Structure

9

Rail Track Analysis User Manual

The geometric properties worksheet should list all of the section properties required for the modelling of the structure and the unique ID numbers must include all of the geometric properties that have been assigned in the Structure Definition worksheet.

The properties should be entered in metres and are all standard LUSAS values except the Depth of Section to Support entry that is needed by the model building to ensure the support conditions occur at the correct elevation.

Eccentricity

All eccentricity in the modelling is defined relative to the nodal line of the track/rail and therefore a positive eccentricity will place a section below this line as indicated in the following figure. If an eccentricity is entered for the geometric property of the rail then the neutral axis of the rail will be offset from this nodal line based on the positive sense described. For this reason the eccentricity of the rail should generally be set to zero for all cases.

The number of entries can be increased by adding data to the bottom of the table.

Data input will terminate on the first blank ID number in column B

The depth of section should not be defined for geometric properties assigned to piers

The eccentricity between the rail/slab indicated in the figure is defined later in the interaction worksheet and should not be defined as a geometric property.

Eccentricity Of Section

(+ve Sense)

Eccentricity Between Rail/Slab

(+ve Sense)

Nodal Line Of Track/Rail

Neutral Axis Of Section

Location Of Support Conditions

Depth Of Section

Figure 11: Eccentricity Definition for Geometric Properties and Depth of Section

Element Orientations

The orientations of the sectional properties should obey the element local axes indicated in the following figure where the double-headed arrow indicates the element local x-axis, the single headed arrow indicates the element local y-axis and the line without an arrowhead indicates the element local z-axis. For both the spans and the

10

piers the element local y-axis is orientated into the lateral direction for the bridge with the local z-axis orientated vertically for the spans and in the longitudinal direction for the piers.

Figure 12: Beam Element Local Axes for Span and Pier Modelling

11

Rail Track Analysis User Manual

## Worksheet 4: Material Properties

Figure 13: Material Properties Table for Structure

The material properties worksheet should list all of the material properties required for the modelling of the structure and the unique ID numbers must include all of the material properties that have been assigned in the Structure Definition worksheet.

The elastic properties are all standard LUSAS values which should be entered in

Newtons, millimetres and kilograms. The mass density (

) is not used in the analysis but is provided to allow the model to be solved with self-weight loading and for it to be combined with the thermal/train loading effects covered in these analyses.



The number of entries can be increased by adding data to the bottom of the table. Data input will terminate on the first blank ID number in column B.

12

## Worksheet 5: Interaction and Expansion Joint Properties

Figure 14: Interaction Properties Between the Track/Bridge and Expansion Joint

Definition

The main bilinear interaction effects for the track/bridge interaction are defined in this worksheet along with additional properties associated with the rail/track. These include the eccentricity between the rail/slab (see Figure 11 and the Geometric

Properties section) and the presence of any rail expansion joints.

Eccentricity Between Rail/Slab

The eccentricity between the rail/slab is used to define the distance between the nodal line or the rail/track and the top of the bridge slab/deck as indicated in Figure 11. In general, all eccentricities will be positive in the modelling unless the neutral axis of the structure section is above the level of the rails. This only happens for certain types of structures and the definitions of eccentricity should generally follow the sign conventions defined in the following figure.

13

Rail Track Analysis User Manual

Eccentricity Of Section (+ve) Eccentricity Between Rail/Slab (+ve)

Nodal Line Of Track/Rail

Neutral Axis Of Section

Location Of Support Conditions

Depth Of Section

Eccentricity Definitions (Section Neutral Axis Below Rail Level, Support At Base)

Eccentricity Of Section (-ve)

Eccentricity Between Rail/Slab (+ve)

Neutral Axis Of Section

Nodal Line Of Track/Rail

Location Of Support

Conditions

Depth Of Section

Eccentricity Definitions (Section Neutral Axis Above Rail Level, Support At Base)

Figure 15: Sign Conventions for Eccentricity Definition

The bilinear interaction properties are derived from the bilinear curves defined in the

UIC774-3 Code of Practice. Properties are entered for both the unloaded and loaded states with the contact stiffness defined in kN/mm per metre length of track, the liftoff force (onset of plastic yield) defined in kN per metre length and the lift-off springs defined as a small value so there is no stiffness once plastic yielding has started. The values in Figure 14 are for unballasted track where: u

0

05 mm k = 40kN / m (Unloaded) k = 60kN / m (Loaded)

The contact stiffness is calculated directly from: k

Contact Stiffness = u

0

14

The transverse spring properties of the interaction should always be infinite (as the analysis is two-dimensional even though the elements are three-dimensional) but the vertical spring properties can be adjusted from this to include vertical deformation effects of the ballast. If this type of analysis is carried out, care must be taken to ensure that the spring remains in the elastic regime. This is achieved by setting a very high value for the lift-off force (1.0E12 kN/mm per metre length for example) and ensuring that the lift-off springs are set to the same stiffness value as the contact stiffness.

Defining Rail Expansion Joints

If rail expansion joints are present in the bridge then the information for these can be entered into the worksheet for each track. The data input takes the form of a unique positive ID number that is placed in column B, the positions and initial gaps. The expansion joint data will be read from the spreadsheet until a blank ID entry is detected. For each unique ID number an expansion joint can be defined for either track by entering the position in metres from the start of the left-hand embankment and initial gap in millimetres.

Figure 16: Sample Expansion Joint Definitions

15

Rail Track Analysis User Manual

The temperature effects in the rails for a continuously welded rail (CWR) track do not cause a displacement of the track and do not need to be considered (UIC774-3 Clause

1.4.2). For all other tracks the change in temperature of the bridge deck and rails relative to the reference temperature of the deck when the rail was fixed needs to be considered in accordance to the code of practice and design specifications. The temperature loads for both the slab/deck and the rail should be entered (zero if not required) in Celsius (degrees centigrade) where temperature rises are entered as positive values and temperature drops are entered as negative values.

The train loading is defined in terms of the type, track, position and magnitude. The type may be Braking, Acceleration or Vertical with the first character governing the type detection and allows a more descriptive definition to be entered if required. The track to be loaded must indicate a valid track based on the data entered into the

Number of Spans, Tracks And Embankment Lengths worksheet described earlier.

The start and end positions of the loading should be defined in metres relative to the left-hand end of the left embankment which is at position 0.0m and must remain within the overall length of the model including embankments (refer to the Spans,

Tracks and Embankments worksheet which reports the total length of the model). The final data required is the amount of load to apply to the rail in kN per metre length.

For vertical loads a positive value indicates that the load acts in a downward sense and for horizontal (braking and accelerating) loads a positive value indicates that the load acts towards the right embankment.

16

As many rail/train loads as required can be defined in the spreadsheet with data input terminating when blank data is detected in the loading type column. This allows more complex loading patterns to be defined such as those illustrated below

## Rail Track Analysis Menu Options

The Rail Track Analysis option is accessed through the Bridge menu by selecting the

Rail Track Analysis UIC774-3 entry. This menu entry provides the following three options:

17

Rail Track Analysis User Manual

## Build Model Dialog

Figure 19: UIC774-3 Model Builder Dialog

If batch processing of multiple models is being performed then a batch text file listing the Microsoft Excel spreadsheets to use for defining the models should be entered into the box (must have a *.txt file extension). The batch text file can be entered explicitly into the dialog or located using the Browse… button and selecting “Batch text file (*.txt)” as the file type.

The format of the batch text file is indicated below and simply contains a list of the

Microsoft Excel files to build the models from with one file per line. If no directory structure is defined for the files then the current working directory will be assumed to contain the files, otherwise they may exist at any directory level on the computer system. If a spreadsheet file cannot be found or contains invalid data it will be skipped in the batch processing and an error reported in the “UIC774-

3_BuildModel.log” file created in the current working directory. Blank lines are ignored and batch processing will terminate at the end of the batch text file. The number of analyses in the batch process is unlimited.

18

Bridge1.xls

..\SomeDirectory\Bridge2.xls

Figure 20: Example Batch Text File With Three Bridges To Build



For large bridges and/or embankments the use of small element sizes can generate excessively large models which take significant time to manipulate / solve.

Use of element sizes below 1.0m should be used with caution.

If only a single rail loading configuration is going to be analysed for a particular model then this option should be switched on.

If, on the other hand, a range of rail loading configurations needs to be applied to a model (for different train positions with varying braking / accelerating loading configurations) then this option should be turned off to allow the rail loads to be applied separately by the Apply Rail Loads dialog described below.



The overall structure of the model should not be significantly modified, nor the loadcase layout, otherwise the application of the rail loading may fail.

19

Rail Track Analysis User Manual

Figure 21: UIC774-3 Apply Rail Loads Dialog

If the bridge model was built and solved with only the temperature loads (Apply

temperature and rail loads in same analysis turned off in model building dialog) then this model can subsequently be used for applying rail load configurations using this dialog. The dialog should not be used for models that have been built with both the temperature and rail loading applied and will report an error if attempted.

If multiple models and/or multiple rail load configurations are to be analysed then only the batch text file (which must have a *.txt file extension) listing the information

20

required by the software should be entered into this box. Alternatively, the Browse… button can be used, selecting “Batch text file (*.txt)” as the file type. For each model/rail configuration analysis the batch text file should contain a separate line of data. Each line should specify the original temperature model, the new combined loading model to create and the Microsoft Excel spreadsheet that contains the rail configuration definition. Each item on a line should be TAB delimited to allow spaces to be used in the filenames. An example batch text file is shown below.

Bridge1.mdl Bridge1_RailConfig1.mdl Bridge1_RailConfig1.xls

Bridge1.mdl Bridge1_RailConfig2.mdl

Bridge1.mdl Bridge1_RailConfig3.mdl

Bridge1.mdl Bridge1_RailConfig4.mdl

Bridge2.mdl Bridge2_RailConfig1.mdl

Bridge2.mdl Bridge2_RailConfig2.mdl

Bridge3.mdl Bridge3_RailConfig1.mdl

Bridge1_RailConfig2.xls

Bridge1_RailConfig3.xls

Bridge1_RailConfig4.xls

Bridge2_RailConfig1.xls

Bridge2_RailConfig2.xls

Bridge3_RailConfig1.xls

In the above example, three different bridge deck temperature models have been selected and four rail load configurations analysed for the first, two rail load configurations for the second and one rail load configuration for the third. The number of entries in the batch text file is unlimited and batch processing will terminate once the end of the file is reached. If any analysis fails due to missing or invalid files an error will be reported to the “UIC774-3_RailLoads.log” file in the current working directory.

## Extract Results To Microsoft Excel Dialog

Figure 23: UIC774-3 Post Processor Dialog

A dedicated post-processing dialog is provided that allows the automatic extraction of the results from the track/bridge interaction analysis to a Microsoft Excel spreadsheet.

21

Rail Track Analysis User Manual

On start-up, the dialog will inspect the active model to ensure that these are results present and also detect whether the UIC774-3 groups defined during the model building process are present. For this reason any manual editing of the model should be kept to a minimum and the “Rail 1”, “Rail 2” and “Spans” groups should not be modified. If all of the groups are found in the model separate worksheets are generated for the results in the tracks/rails and spans. If one or more of these groups are absent from the model then the dialog will attempt to use the current selection in

Modeller to perform the post-processing. If the selection is used, this must contain lines that have 3D engineering thick beam elements assigned to them.

Output Format

On clicking the OK button the post-processor will extract the results from all of the results loadcases along with all envelopes (without association) and basic combinations defined in the model file. If multiple results files are loaded on top of the model, for example if multiple rail load configurations have been analysed and the results loaded into Modeller for enveloping / post-processing, then the results loadcases for all these results files will be extracted into the Microsoft Excel spreadsheet. Microsoft Excel is currently limited to 256 columns in a worksheet and this limits the results processing to only 20 loadcases/envelopes/combinations. If this limit is exceeded the results post-processor will allow the extraction of the envelopes/combinations into one Microsoft Excel spreadsheet and all of the results loadcases into a separate spreadsheet (with the limit of 20). The results output format is indicated in the following two figures.

22

Figure 24: Microsoft Excel Spreadsheet Generated by Processing UIC774-3 Groups

Figure 25: Microsoft Excel Spreadsheet Generated by Processing Selection

23

Rail Track Analysis User Manual

The results are currently output as displacements in the longitudinal (X), vertical (Y) and major bending rotations (RZ) along with axial forces (Fx), shear forces (Fz) and bending moments (My). These results can be further post-processed in Microsoft

Excel or a separate package to determine quantities such as the axial stress in the rails of the track. The following figures show the axial stress in the rails for thermal effects only and combined effects for a sample structure.

Figure 26: Thermal Effects Only in Rails

24

25

Rail Track Analysis User Manual

## Limitations of Use

Centreline

Track 1

Centreline

Offset Track 1

Deck

Centreline

Offset Track 2

Track 2

Centreline

Abutment/Pier

Offset

Abutment/Pier

Offset

Bearing 1

Offset

Bearing CL

Offset

Bearing 2

Centreline

Bearings

Figure 28: Offsets of Tracks/Bearings/Piers from Centreline Of Deck

26