Most design methods for railway trackbed - ballast, sub-ballast and formation - are empirical or recipe-based. Coupled with the lack of a detailed understanding of how loads are transmitted through the track system into the soil, it is not surprising that the importance of the sub-ballast and formation is usually underestimated.
Research at the University of Southampton aims to improve understanding of factors affecting sub-ballast and formation performance by applying modern soil mechanics principles and recent advances in instrumentation.
The potential of a more fundamental understanding to provide a logical framework within which to assess performance, maintenance and remediation, and ultimately inform whole life cost modelling, will also be explored.
Modern soil mechanics The advances in modern soil mechanics of most relevance to railways relate to:
the dependence of soil stiffness on strain and stress path
cyclic loading effects
rotation of principal stresses within a soil element as a train passes over it.
The dependence of soil stiffness on strain and stress path means that even the quasi-static response of the trackbed to train loading is diffi cult to predict, even for a new well designed line.
When a soil is subjected to repeated loading under drained conditions, strain will accumulate over a large number of load cycles (Figure 1).
If the deviator stress is below that needed to cause failure - the 'threshold stress' - the incremental strain will become smaller with each load cycle until a stable condition is reached. In undrained conditions, cyclic loading can result in a build-up of pore water pressure that is almost certainly one of the triggering factors for 'wet spots'.
Rotation of principal stresses Rotation of principal stresses, although known to occur under moving loads, has until recently been largely ignored in both highway and railway engineering. As an axle load moves along the track, a soil element in the sub-ballast or formation below is subjected to a changing stress condition (Figure 2).
The change in sign and magnitude of the shear stress means the direction of the principal stresses on the soil element rotates as the axle load passes. This rotation is not modelled in conventional cyclic triaxial tests that have formed the basis for most modern work on railway trackbed behaviour. In effect, a cyclic triaxial test models the loading from a stationary train bouncing vertically up and down.
The rotation of principal stresses can be modelled in the laboratory using a cyclic hollow cylinder apparatus. A hollow cylinder of soil is tested by applying a combination of cyclic axial and torque loading, subjecting an element of soil in the specimen wall to a more realistic stress path.
Previous cyclic hollow cylinder work at the University of Southampton was carried out with South African railway company Spoornet.
Spoornet operates the Richards Bay Coal Line, a heavy haul railway built in the 1970s to carry 21M. t a year. With forecasts of the demand for coal rising, the line was upgraded in the mid-1980s to allow 26t axle loads.
A typical coal train comprises 200 wagons, each weighing 104t hauled by five locomotives, and the annual tonnage has now risen to 84M. During a recent rehabilitation of the track formations, earthworks construction accounted for 58% of the cost. It is not surprising that Spoornet places great importance on understanding how its earthworks will perform.
The parameters of primary interest to a track designer are resilient modulus and the rate of accumulation of permanent deformation.
As mentioned previously, the quasi-elastic behaviour or resilience of the soil is dependent on the strain, and for certain soil types the rotation of principal stresses will have a detrimental effect.
The permanent deformation of some soils is similarly affected by the rotation of principal stresses (Figure 3). Thus, a lack of appreciation of the effects of principal stress rotation may lead to unconservative design.
At present, the fundamental mechanisms that control resilient modulus and permanent deformation are not understood. The state of the soil (void ratio, stress), particle size and shape, and loading path hold the key to developing this understanding and these factors are the subject of testing in progress.
Site monitoring is an integral part of the work in progress; it is essential for validating models as well as testing theories and predictions.
However, access to UK sites is diffi ult for anything other than essential work and so much of the research is being conducted overseas. To overcome access difficulties, the team is trying to develop new instrumentation which is inexpensive, may be installed easily with the minimum of disruption and yet yield reliable data on the condition of the track, ballast, sub-ballast and formation.
Preliminary work was carried out with the cooperation of Balfour Beatty Rail at a site 1km south of Crewe station on the Crewe-Kidsgrove Line. A section of ballasted track was instrumented on a loop used to organise traffic approaching Crewe. The instrumented section was about 15m north of a trial length of Balfour Beatty's embedded slab-track.
Strain gauges were installed on the web of one of the rails to measure axial bending and shear strains and also lateral load strains. One result of particular note was the axial bending strain measured from a strain gauge positioned just above the bottom flange of the rail.
As Figure 4 shows, rather than the axles producing similar size strain peaks, one peak from each bogie was higher than the other two.
On site, the sleepers adjacent to the instrumented section were seen to move vertically in excess of 10mm when a train passed over them.
To investigate the effect of these hanging sleepers, the rail was modelled using beam finite elements with spring supports for the sleepers; hanging sleepers were simulated using softer springs.
Results showed the axial bending strain had been affected by the hanging sleepers with two of the strain peaks per bogie being lower than would otherwise be expected.
While the lower peak tensile strains may appear desirable, the negative strains that occur between the axle loads were significantly increased; these signify a 30-40% larger hogging moment, the consequence of which is increased tensile stresses in the railhead which has obvious implications for rolling contact fatigue.
Measuring the vertical displacements of the rail during the passage of a train is diffi cult due to the lack of a datum. To overcome this problem, a system of remote video monitoring combining a webcam and telescope was tested at Crewe (Figure 5).
The webcam was inexpensive, yet is capable of capturing digital video at 60 frames per second, 2.5 times faster than a conventional camera.
Combining the webcam with a telescope allowed a small target on the side of the rail head to be videoed from a distance of 10m - outside the range of most ground-borne vibration.
In a laboratory validation of the remote video monitoring system, with Particle Image Velocimetry (PIV) processing of the resulting videos, the sinusoidal displacements of a hydraulic actuator were measured to within 0.1mm from a distance of 15m.
Site results for the Balfour Beatty slab-track showed that the system worked very well. For the ballasted track and slab transition sections, the results included some high frequency noise, although this could be removed by averaging/filtering the data.
Figure 6 shows slab-track rail displacements; it must be noted that these are the absolute total displacements of the rail and hence include the displacement of the pad and slab. For a fi rst site trial, the remote video monitoring system appears to have great potential for measuring displacements and calculating the track support stiffness with almost no disruption to the railway.
The final type of instrumentation tested at Crewe was geophones; these are relatively cheap seismic sensors which give an output voltage proportional to velocity.
Geophones were placed at the surface of the sub-ballast to measure the vertical ground velocities.
Figure 7 shows the velocity history at 1m from the sleeper end for two locomotives pulling 12 unladen freight wagons. The heavier axle loads of the locomotives produce larger ground velocities.
However, a particularly large spike in the velocity is produced by one of the wagons towards the end of the train. This spike prompted further examination of the strain data which confi med that it was caused by a wheel flat.
In addition to laboratory work and numerical modelling, further testing and development of instrumentation techniques is under way on the Richards Bay Coal Line in South Africa.
Using this instrumentation, the main priority is to gather high quality fi eld data quantifying the behaviour of the track, sub-ballast and formation from a range of sites.
A major gap in the understanding of the railway system is the interplay between track support and vehicle dynamics. While vehicle dynamics packages incorporate the effects of track geometry, they do not generally model variations in the track support conditions.
Future work will focus on this interaction allowing the effects of poor sub-ballast and formation on the vehicle to be quantified. In addition, ground- based condition monitoring techniques (such as wheel flat detection by the geophones) will be developed to investigate the effects of vehicle condition on the sub-ballast and formation.
Ultimately, a better understanding of trackbed behaviour will lead to improved models for design and assessment of maintenance requirements and benefi ts, and allow whole life cost decisions to reflect properly this important part of the railway system.
Dr Daren Bowness, Professor Chris Clayton and Professor William Powrie work at the University of Southampton's School of Civil Engineering and the Environment.