9 - Rail Support, Bending and Cracks

Question 1

How much can typical rails withstand?

Answer 1

60kg/metre of steel
But can deform visibly under a train load (5 tonnes or 50kN per wheel)

Question 2

What does rail bending depend on?

Answer 2

Track support stiffness - combined effect of ballast, sub-ballast and natural ground

Question 3

Normal rail deflection compared to problematic rail deflection

Answer 3

1-2mm is normal
20mm in problem areas

Question 4

Effect of superposition

Answer 4

Positive peak deflection gets bigger
Negative peak is reduced

Question 5

Variable support stiffness

Answer 5

Not all track built to same specification: variations in practice over time; deterioration of ballast as stones rub against one another and break up; water-logging and drainage problems can change track stiffness; migration of fine particles from lower layers up into ballast
Under-track construction: concrete bridges typically much stiffer than surroundings

Question 6

Intentional stiffness variations

Answer 6

Rail pads (made of rubber) introduced between rail and sleeper to beneficially adjust stiffness
More relevant to noise prevention than bulk bending (i.e. relevant to higher frequencies)
Cannot compensate for poor foundations

Question 7

Faults caused/accelerated by excessive rail bending

Answer 7

Cracks usually open and grow under tensile loading
Either side of wheel, rail bends upwards, opening cracks on rail head
Directly under wheel, rail foot is loaded in tension
One wheel can create multiple stress cycles as it passes

Question 8

Assumptions of Winkler beam model

Answer 8

Deflects only where there is load - adjacent material is completely unaffected
Good model for soils (poor for metals)
Beam and foundation always remain in contact, even if beam is bending upwards
Rails are supported on sleepers in reality, not continuously
Deflected rail shape from a single wheel load is a damped sine wave
As long as there are 4+ sleepers per half wavelength, there is little error in ‘smearing’ these together into a continuous foundation

Question 9

What can be worked out once the moment present is known?

Answer 9

Estimates of stresses opening cracks at head or foot of rail
Second moment of area can be calculated using approximation to real rail shape, and can take account of wear

Question 10

Where is the neutral axis?

Answer 10

The plane on which material remains the same length during bending - undergoes neither tension nor compression
1st moment of area is zero about the centroid and neutral axis lies on the centroid
Easy for uniform head wear, not easy for non-symmetric wear and off-centre loading

Question 11

Case study - Northern Ireland Railways, Michael Hendry

Answer 11

300 miles of railway track
35 trains
6.5 million passengers per year
Freight has been phased out
Originally constructed in 1850s
Particular problems on main Belfast to Dublin line
Very wet ground at Brackagh Bog and Adavoyle Bog giving poor support conditions
Both consist of low height embankments built on peat bogs
Sleepers often becoming skewed and unevenly spaced, and a deterioration of rail alignment
Train operators and maintenance concerned over large movement of track and embankment during train passage
Led to reduction of linseed from 90mph (145km/h) to 60mph (96km/h)

Question 12

Construction of problem sites in case study (on embankments)

Answer 12

Embankments constructed in 1850s using techniques current at the time
Fascines (log rafts) used to support embankment over soft peat ground
Over the years, log rafts have rotted and stopped supporting embankment - difficult to replace as this is a main line

Question 13

Ground-penetrating radar (GPR)

Answer 13

Used to determine ballast depth and embankment construction
Can determine depth of interfaces between dissimilar materials

Question 14

Automatic ballast sampling (ABS)

Answer 14

Consists of sampling a tube of ballast (65mm diameter, up to 1m long or 50mm diameter, up to 2m long)
Size depends on ground conditions

Question 15

Results of case study inspections

Answer 15

At one site - most data showed significant increase in stiffness at embankment base, consistent with tree trunk facines placed directly on natural ground surface
At second site - showed no evidence of layer of tree trunk facines at base of ballast

Question 16

Measuring rail deflection

Answer 16

Difficult to measure under train load as ground moves over large area, difficult to find fixed datum point
Measure using laser-based system from 20m away
Laser source is far enough away that it can be considered stationary
Photo-sensor array clamped to sleeper to monitor its movement

Question 17

Rail deflection measurement data

Answer 17

Measurements showed two large displacements caused by each of the locomotive bogies, and smaller displacements from each passenger car bogie
Passenger cars are much lighter than locomotive, hence smaller deflection
Datasets considered to be good quality as deflection matched passing train configurations well

Question 18

Modelling of rail deflection data

Answer 18

Conducted using Winkler beam model
Aim was to quantify embankments stiffness and subgrade material in terms of an elastic (resilient) modulus
Effects of train speed also considered
Comparison of modelling with experimental measurements showed good agreement

Question 19

NI rail findings

Answer 19

Winkler analysis provided measure of the strength of structure in form of a modulus for whole embankment/foundation structure
From application of Winkler model to both embankments, was found that there is a small increase in displacement with train speed

Question 20

Elastic modulus of material vs foundation stiffness of the system

Answer 20

Installation of geo-grid to increase elastic modulus of embankment material (not rail) would produce no significant reductions of rail displacements - increasing embankment elastic modulus 120x results in 50% displacement reduction - not effective
Stiffening foundation beneath ballast can produce a bigger benefit - doubling foundation stiffness k results in factor of 2 reduction in displacement

Question 21

How cracks behave during rail bending

Answer 21

Phase I - initiation
Phase II - contact stress driven cracking
Phase III - rail bending driven cracking

Question 22

Modelling crack growth

Answer 22

Can apply FE modelling of rail bending moments to fracture mechanics model of a crack
Model was run combining phase II and III crack growth to produce stress intensity factor data
Small cracks (<18-20mm deep) are dominated by contact stress as wheel passes, and bending stress is so low it would be unlikely to drive crack growth
At crack lengths >40mm, bending stresses were predicted to become increasingly important, and that bending stresses may subject a crack to multiple stress cycles per wheel pass
Would give accelerated growth of cracks through both high stress intensity factors and several increases in the number of stress cycles per wheel pass
Shows that once cracks become large enough to be driven by rail bending their growth will be very rapid