INCREASING TUNNEL LOADING GAUGE WITHOUT LOWERING THE INVERT.
Paper presented to Railway Engineering 2001 Conference
by Professor Lewis Lesley, Dr. Fouad Mohammad,
Dr. Hassan Al Nageim School of Civil Engineering,
School of Built Environment, University of Nottingham,
Liverpool JM University, Nottingham NG7 2RD
98 Mount Pleasant,
Liverpool L3 5UZ
KEYWORDS: Loading gauge, tunnel invert, LR55 track, track loadings, foundation behaviour
ABSTRACT
With few exceptions railway tunnels in the UK were built to 19th century loading gauges, before the advent of piggyback euro standard HGV trailers, super cube ISO maritime containers, or electrification. Justifying the capital cost for the reconstruction of tunnels to larger loading gauges is difficult, even where "free" money from the EU is available. The alternative of lowering the invert is difficult, especially where tubular tunnels are involved. In any case only limited enlargement can be achieved.
Some rail lines in the UK can carry 8ft 6in high ISO containers, and with low floor wagons, 9ft 6in high containers. Neither the next generation of 10ft 6in high containers already in wide international use, nor 4m high, 2.5m wide and 12m long road trailers piggyback can be accommodated, without tunnel loading gauge enlargement.
This paper describes the development work of the LR55 track system, which can provide at least 300mm more head room in existing tunnels, within the existing invert. The LR55 track system is based on highway structural design philosophy and has been subjected to a battery of tests, including 80 tonne axles and 3m diameter tube tunnel loading.
1.0 INTRODUCTION
Since George Stephenson built railways, the sleeper with rails fixed either directly or on a base plate, has been the principal method of transmitting train loads into the sub soil via an elastic ballast. Brunel's longitudinal sleepers only found favour for bridges. Higher axle loads and train speeds, and the desire for better track standards with reduced maintenance costs, has seen traditional sleeper tracks improved incrementally with heavier rails, stronger fastenings, bigger sleepers and deeper ballast. On open tracks these improvements have been able to cope. In tunnels the situation is different, since the depth of ballast is constrained by the level of the invert, and so therefore are axle loads and speeds which can be accommodated, witnin a given loading gauge. In double track tunnels extra loading gauge can be won by singling but then there is a loss of train capacity, unless a new parallel tunnel is built. This paper discusses a new track system which requires a shallow foundation depth, even for the heaviest axle loads and high train speeds, and therefore promises larger loading gauges within existing tunnel inverts.
2.0 DESCRIPTION OF LR55 TRACK SYSTEM
Traditional track systems use bottom supported rails, which then need strong fastenings to sleepers to prevent overturning from lateral wheel loads. With discrete support on sleepers, trains experience regular hard spots at the sleepers, which are a cause of the formation of short wave corrugations on rail heads. Because spacing between sleepers is an order of magnitude larger than the sleeper width, ballast must be considerably deeper than that required for continuously supported rails. Finally rails and sleepers have to be adjusted together for line and level.
2.1 LR55 track components
There are six components to the LR55 track system (Fig. 1):
(a) compacted highway type base
(b) prefabricated concrete support troughs
(c) gauging bars between troughs
(d) ballast outside and between troughs
(e) low profile, top supported rail
(f) elastomeric grout to bond and support the rail in troughs
Figure 1. LR55 track system components
2.2 Track base
There is worldwide experience and expertise in the design and installation of compacted highway bases. The bearing quality, elasticity and life of such bases is well understood. There are many highway contractors competent to lay quickly such bases. These bases can be laid with a very high tolerance of material quality, and line and level. This is important, as the pre cast concrete support troughs sit directly on the base. The level of base, together with the prefabrication tolerance of the troughs determines the first order accuracy of the ultimate line and level of the track. The troughs are gauged together by bars, although the mass of the ballast, the lateral stiffness of the troughs and large trough sides, provide substantial lateral restraint to the track.
2.3 Concrete Support Troughs
The support troughs are vertically and laterally stiff. This is important as the rail is less stiff vertically than girder rails (eg. UIC60). The wide base of the trough, and the continuous support, means that the trough pressure into the track base typically lies between 150 and 250 MPa, for 25 tonne axles loads, depending on the stiffness of the base. Even a weak base however, like sand has a load capacity of about 5000 MPa, an order of magnitude greater than the imposed pressure.
Support Troughs are manufactured and delivered to site in lengths to suit handling and installation to the required quality. At this stage it would seem sensible that support troughs would be 6m long, which weigh about 600kg. Longer Support Troughs could be tried as part of an optimisation exercise balancing import material costs against site handling and adjustment. On curves, support troughs are laid as tangents to the required radius and design super elevation for the train speeds expected. Simple mechanical links, fix the ends of support troughs together, until the application of a bonding grout permeates between the trough ends and bonds the troughs together.
There are various methods available for prefabricating the support troughs. Many manufacturers are capable of producing the troughs to the required quality of concrete and dimensional tolerance. Pre-stressed tendons primarily fulfil the function of ensuring that troughs can be delivered to site intact. Most of the track testing however has been undertaken satisfactorily with unreinforced troughs.
2.4 LR55 rails
The LR55 rail is top supported in the pre-cast concrete trough. This makes the rail very stable and highly resistant to overturning. About 60% of the wheel loads are transmitted on the running side rail flange, about 30% on the non running side flange, and 10% by the rail base. The rails weight about 55kg per linear metre and therefore have similar electrical resistivity to girder rails of similar weight. Lateral train loads are accommodated by shear compression of the elastomeric bonding grout, and the lateral stiffness of the troughs and track construction.
The LR55 rails are welded into long strings and pre tensioned longitudinally to compensate for ambient temperature variations. The rail welds are located away from joints between the support troughs, to prevent hinges being created. The rails are supported temporarily either by stands, or wedges of pre-cured bonding material. The rails are adjusted for line, level and gauge.
Once the rails are to line, level and gauge, they are bonded into the concrete support troughs by elastomeric grout. This is the second order determinant of track accuracy. It should be possible to achieve a tolerance of 0.1mm. There is no mechanical connection between rail and trough, with the rail continuously supported vertically and restrained laterally by the elastomeric grout, rail/wheel interface forces are almost constant along the track. This should mean a better ride for vehicles (and their loads) as well as reducing the incidence of long, medium and short wave length corrugations along rail heads.
The LR55 rail is made with a built in continuous check rail. This should reduce derailments, especially by flange climbing over the rail head, since the other wheel on the axle will be restrained laterally by the check rail. In the event of a derailment, trains cannot drop because the track formation is level with the top of the rail. This also means that derailed trains are unlikely to overturn off the track.
Finally on curved tracks with high speed running, gauge corner cracking is less likely to occur, since the centrifugal wheel forces are shared between outside and inside wheels on the curve. In the less likely case of cracks progressing to failure, as occurred in October 2000, the bonding and support trough which surrounds the rail will prevent it falling apart, and thus denying the derailment mechanism which had tragic consequences at Hatfield. This continuous support for the rail, means that the more common weld failure need not be so critical, since the broken rail ends will be restrained and kept together.
2.5 Elastomeric Grout
The rails are bonded into the support troughs with an elastomeric grout which transmits the static and dynamic forces from wheels through the trough into the rail base. Polyurethane elastomers are now widely used in rail application, eg. noise reducing base plates. There are many proprietary polyurethane bonding grouts available "off the shelf", fully tested for the climatic and loading conditions experienced in railway environments.
3.0 COMPLETED MODELLING
3.1 Modelling
Static and dynamic load models were examined. Wheel loads rolling along and across the rail have been modelled. The outputs of the models are:
- rail deflection
- trough deflection
- shear forces in rail
- shear forces in trough
- bending moments in rail
- bending moments in trough
- pressure at base of trough
3.2 Analytical Models
Modelling conventional railways has been undertaken by considering the rails as a single layer beam, and the sleepers and ballast as a homogeneous elastic foundation. In the LR55 track system the rail is continuously supported in a concrete support trough. This is better represented as multi layer beams with elastic foundations. Here the rail and the support trough are considered to be beams, and the elastomeric grout and sub-base as elastic foundations with different moduli. Analytical models can only solve a limited number of idealised problems. The boundary conditions of these were discussed by Hetenyi (1946). Timoshenko et al (1932) had earlier analysed the stresses in railway tracks in the same way.
3.3 Finite Element Method
The use of the Finite Element Method (FEM) allows a wider range of problems to be solved, with different loading and boundary conditions, and non-linear foundation properties. These were applied to railway problems by Fateen (1972) and explored by Miranda et al (1996).
The analysis of the LR55 track system using FEM is based on a stiffness approach for solutions, the nodal displacements are assumed to be the basic unknowns. The nodal equilibrium may be expressed by the stiffness matrix equation (1):
[K].{∂} = {P} (1)
where [K] = global stiffness matrix of the structure
{∂} = unknown displacement vector of the structure
{P} = applied load vector on the structure.
Solving this equation with FEM requires the track to be divided into a number of elements. The contribution of the track base to shear resistance in the stiffness matrix is so small and unreliable that it can be ignored. The stiffness matrix of the LR55 track is therefore the assembly of the stiffness matrices of all its components.
3.3.1 Rail and concrete beam elements
The steel rail and concrete support trough can be treated as conventional beam elements, with two nodes per element. Each node has three degrees of freedom; horizontal displacement (u), vertical displacement (v) and rotation about the z-axis (ø). This produces a stiffness matrix, which is therefore 6 x 6. Przemieniecki (1968) discussed the coefficients of the stiffness matrix.
3.3.2 Pad Spring Elements
The elastomeric grout acts like a pad and is represented by a number of discrete vertical and horizontal springs. Each spring has one degree of freedom per node which is displaced in the axial direction. The vertical springs are assumed to be of a Winkler type, Selvadurai (1979). These can be defined as equ. (2)
K1v = Ep W
hp (2)
Where:
Ep = elastomeric pad Young's modulus
W = rail width
hp = thickness of elastomeric pad
The two ends of the grout vertical spring elements are free to displace, so the stiffness matrix is 2 x 2 in the form :
vi vj
1 -1 vi
[K]e = K1v (3)
-1 1 vj
3.3.3 Track base vertical spring elements
The track base foundation can also be considered to consist of Winkler type vertical springs. Each spring having one degree of freedom. The stiffness of each spring is then equ. 4:
K2 = k2 L (4)
where:
k2 = track base modulus
3.3.4 Input assumptions
These equations were used to predict the behaviour of the LR55 track specified with the following characteristics:
TABLE 1
PROPERTIES OF THE LR55 TRACK SYSTEM
Element SectionArea Moment of Inertia Young's Modulus Self weight
m2 x 10-4 m4 x 10-8 (N/mm2) x 104 (kN/m)
Rail 67.2 337.3 20 0.53
Trough 472 8260 2 1.13
The track base modulus is assumed to be 20 N/mm2 and the Young's modulus of the elastomeric grout is assumed to be 2.42 N/mm2 . The grout is assumed to be uniformly 20mm thick. The applied wheel load is 122.6 kN, equivalent to the 25 tonne maximum axle load permitted on Britain's railways.
3.3.5 Deflection
The maximum deflection of the LR55 rail under the above conditions is 7.8mm, and occurs at the point of wheel loading. The deflection decays to zero over a distance of 2m from the point of load. There is then a negative deflection (hogging) where the rail rises above the neutral position by up to 0.1mm over a further 2m length.