TECHNICAL ARTICLE

AS PUBLISHED IN The Journal January 2017 Volume 135 Part 1

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An introduction to AUTHORS: Constantin Ciobanu rail thermal force CEng, FPWI Principal Engineer calculations WSP | Parsons Brinckerhoff Levente Nogy CEng, MICE, FPWI Senior Design Engineer Network Rail Article 1

This article is the first in a series of articles THE PHYSICS OF RAIL THERMAL For a positive thermal variation of ΔT= 27°C intended to present complementary EXPANSION the compression force would be 500 kN. information to what is currently available This is the equivalent of an average freight car weighing 50 tonnes, pressing axially on a in the formal continuous welded rail (CWR) When exposed to temperature variations, the single CEN60 rail ( ). training courses and Railway Group or steel rail tends to vary in length and, if nothing figure 3 Network Rail Company Standards. This is constraining this length variation, the rail’s The rail alone is unable to withstand this high first article presents the general principles mid-point will stay fixed and each abutting compression force without deflecting at some and theoretical considerations on the rails half-rail length will expand equally by ΔL/2 affected by thermal variation. point along its length and thus the entire track (figure ).1 superstructure must be designed to provide the required stability and to avoid buckling in hot INTRODUCTION The total length variation can be computed as: weather and rail breaking in cold weather. ΔL = α•L•ΔT This series of articles will discuss the general principles and theoretical considerations Where: TRACK PARAMETERS on railway track which is subjected to INFLUENCING RAIL THERMAL thermal effects. These can be used by Track - ΔL is rail extension BEHAVIOUR Engineers for a better understanding of the - α is the expansion coefficient of the rail steel physics behind the rails’ behaviour when = 1.15•10-5 per °C for normal grade rail The behaviour of the track due to temperature subjected to temperature variations and can (NR/L2/TRK/3011). variations is influenced by numerous and also help to understand the specifications - L is the rail length complex parameters (UIC Code 720). This and requirements mandated in the current - ΔT is the rail temperature variation article focuses on a simplified approach standards covering the management of jointed and considers only the main parameters in respectively CWR track. Multiple thermal force If the temperature is increasing, the rail will evaluating the rail thermal behaviour: diagrams will be presented for both jointed expand. If the temperature is decreasing, the track and CWR applications. rail will be subjected to a negative expansion – • Installation parameters a contraction. The standard nominal rail length • Rail type is defined for +15°C and length measured at • Rail temperature other temperatures is corrected to take into • Track longitudinal resistance account the expansion or contraction of the rail • Joint minimum and maximum gap - for (BS EN 13674-1:2011). jointed track • Joint resistance - for jointed track On the other hand, if the expansion is not • Expansion joint gap or adjustment switch permitted and both ends of the rail are fixed, gap - the range of thermal “breathing” the thermal variation ΔT will generate a of the devices used on the transitions constant compression internal force, N (figure between sections of CWR track or 2). between CWR track and jointed track.

This internal force is defined by: The entire process presented here presumes N = (α•E •ΔT)•A = σ•A an ideal and homogenous track structure.

Where:

- E is the steel’s elasticity modulus Table 1: Cross sectional area (A) for (2.1•108 kN/m²) - A is the area of the rail section different rail types used in the UK - σ is the normal stress generated by the temperature variation, ΔT.

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INSTALLATION PARAMETERS TRACK LONGITUDINAL RESISTANCE Track installation defines the starting point of the track thermal behaviour. From this When the rail tends to move longitudinally, perspective, the main track installation either due to temperature variations or due parameters are the following: to other factors, the track will oppose this Figure 1: Free rail thermal movement through a force called track • joint installation gap and installation expansion longitudinal resistance (or track creep temperature for jointed track resistance). • stress free temperature (SFT) for CWR track This track longitudinal resistance has three levels of action (figure ).4 RAIL TYPE 1. LONGITUDINAL RESISTANCE The rail type influences the thermal behaviour P BETWEEN THE RAIL AND THE through the cross sectional area (A) which 1 defines the amount of thermal force developed FASTENING in the rail due to the temperature variation. At this level, the longitudinal resistance is (See table 1) generated by the friction between the rail and the fastening components. The European RAIL TEMPERATURE Norm BS EN 13841 mandates that the fastening longitudinal resistance on ballasted The rail temperature has a direct influence track should be at least 7 kN per fastening. Figure 2: Restrained rail thermal on the rail thermal stress and force. The rail For a normal sleeper interval of 600 mm, temperature is in relation to the air temperature expansion this is equivalent to a distributed longitudinal but is also influenced by other factors. The resistance of around 12 kN/m of rail. The location of the track has a significant impact fastenings used for high speed railway track - if the rail is exposed to direct sunlight it (V>250 km/h) are required by the same norm will absorb more caloric energy and its to provide a minimum longitudinal resistance of temperature will be higher compared to a rail 9 kN (around 15 kN/m of rail). (See image 2) located in shadow, in a cutting or a tunnel, or embedded in a material with thermal insulation At installation and in ideal conditions, all properties. Exposure to wind, humidity or fastenings can provide a certain toe load and condensation can also cause a difference consequently a longitudinal resistance. But between the rail temperature and the often, for old types of fastenings (images conventional air temperature. 3, 4) this toe load cannot be maintained at a constant reliable level throughout the service In the summer, the rail temperature can be up life of the fastening. Consequently, for such to 15-20°C higher and in the winter can go 5°C fastenings the longitudinal resistance is usually below the conventional air temperature. Based ignored in the evaluation of the track thermal on this and on the annual weather temperature response. variations, various railway administrations have adopted their own specific temperature ranges. Special fastening systems are sometimes installed on very long bridges with direct fixing, On the Network Rail railway or in other specific cases, to provide a reduced this range is considered to be [-14°C, 53°C] longitudinal resistance and separate the Figure 3: Rail thermal force (NR/L2/TRK/3011).This gives a possible thermal expansion forces of the track from the maximum annual rail temperature variation of ones of the supporting structure. An example is 67°C. In continental Europe, for the countries the Zero Longitudinal Restraint (ZLR – of temperate-continental climate, the rail image 5) that is designed to provide practically temperature range is [-30°C, 60°C]. This gives no longitudinal fastening resistance. a potential maximum annual rail temperature variation of 90°C. 2. LONGITUDINAL RESISTANCE

The rail coating and colour also influences its P2 BETWEEN THE FASTENING caloric absorption properties. A rail painted AND THE SLEEPER in white reflective coating, exposed to direct sunlight can be up to 6-10°C cooler than an The highest longitudinal resistance is uncoated rail (Ritter, Al-Nazeer - 2014). encountered between the fastening and the Painting the rails white to reduce the rail sleeper. For Pandrol fastenings, the clip’s temperature is a method used efficiently in the shoulder is embedded in the sleeper’s concrete Figure 4: The three levels of action UK and around the world (image 1). so no relative movement will happen at this of the track longitudinal resistance level. The alternative screwed fastening is similarly good and generally all modern fastenings are designed to have a very high longitudinal resistance at this level. Since the resistance at this level is significantly higher than the other two, in the calculations that model the railway track thermal behaviour, no movement is considered to happen between

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the fastening and the sleeper in which it is practically embedded.

3. LONGITUDINAL RESISTANCE

P3 BETWEEN SLEEPER AND BALLAST

This resistance is dependant on a complex set of factors e.g. the type, shape, dimensions and weight of the sleeper, the ballast volume, compaction and content of fines. The friction forces at this level are not homogeneous along the track – there can be spots with high or low resistance, even for apparent similar track conditions. Consequently, the longitudinal resistance at this level is usually the lowest and the most difficult to control. This resistance is typically considered in the range of 6 (tamped) to 10 (consolidated) kN/sleeper (Van – 1996), the equivalent of 5 to 8 kN/m of rail.

The track longitudinal resistance is the

minimum of these three resistances (P1, P2, P3) Image 1: White coated rails on Italian main lines (Milano Afori railway and the track movement due to temperature station) variation will take place at that lowest resistance level.

For modern superstructure and ballasted track, usually, the lowest longitudinal resistance is between the sleeper and the ballast.

On slab track, the third level of resistance, P3, is very high as the sleeper or the rail fastenings are embedded in the concrete slab and the only longitudinal resistance to be considered is the one developed at the first level – the fastening’s longitudinal resistance.

The longitudinal resistance for each sleeper will start to act as soon as the rail will tend to move due to temperature variation (figure ).5 The nearest sleeper to the joint will be the first one to oppose the rail expansion when the temperature is increasing. Once the thermal force has increased above the longitudinal resistance P of the first sleeper, the rail movement will be allowed at this sleeper and Image 2: Pandrol Fastclip fastening the further expansion will be opposed by the resistance at the next sleeper. The process continues in relation with the rail temperature increase, until the longitudinal resistance is activated on the entire rail length.

For calculation purposes, the individual longitudinal resistance per sleeper is converted into a distributed longitudinal force, p, defined per 1m of rail.

JOINT RESISTANCE FORCE

For jointed track, the fishplated joint provides two other parameters which are considered in the rail thermal force calculations. The first one is the joint resistance force.

Image 3: BR2 baseplate with Macbeth spring spike anchors

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The bolt tightening torque develops a tensile force, T, in the bolt. This tensile force induces a set of normal forces, N, at the contact areas between the fishplates and the rail head and foot. These normal forces can be found by decomposing the force vector T onto the two contact areas between the fishplate and the rail.

If the rail will tend to move in the joint, the normal forces will cause a set of friction forces between the fishplate and the rail figure( ).6 Any such force will be defined as N•f – where N is the value of the normal force and f is the coefficient of friction between steel and steel.

Theoretically, for each bolt, there are four friction forces that will oppose the rail Image 4: Bullhead rail Panlock chair fastening movement.

The resultant R of these friction forces is called the joint resistance force. This can be defined as:

R = 4•n•N•f

where n is the number of bolts per rail end.

The rails will move within the joint only if this resultant force R is overcome. Only then will the joint gap start closing or opening.

The rail temperature variation required to overcome the joint resistance can be computed from:

For a normal 4 bolt mechanical joint, Image 5: Pandrol ZLR fastening (source of the image – Pandrol ZLR designed for constrained thermal expansion brochure) track superstructure, lubricated and with bolts tightened at a 475 Nm torque (NR/L3/ TRK/002), the joint resistance force R is around 175 - 200 kN.

For R = 175 kN and a BS 113A rail jointed track, if the rail temperature variation relative to the installation temperature is less than 10°C no rail movement will appear within the joint.

Some of the old joint types do not have a well- defined installation tightening torque and are also lacking essential components to keep this torque constant throughout the normal usage of the joint. In such cases, the joint resistance force can be ignored in rail thermal expansion calculations even though the joint bolts have a certain tensile force and, consequently, will develop a joint resistance force. Such a joint resistance is not continuous, constant and above a well-defined limit value and it cannot be used to define the thermal behaviour of the track in a safe manner.

Figure 5: Track longitudinal resistance

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of the joint bolts when the rail contracts and it is an important parameter in the analysis of the jointed track’s behaviour due to rail temperature variations.

The track parameters described above define two distinct types of railway track superstructure:

• Free thermal expansion track superstructure • Restrained thermal expansion track Figure 6: Friction forces generated by the joint bolt superstructure

FREE THERMAL EXPANSION TRACK SUPERSTRUCTURE

The free thermal expansion track superstructure allows the rail to vary its length freely due to temperature variation. This is a case in which the joints and fastenings do not provide reliable and continuous resistance forces to the rail thermal length variation and for calculation purposes all potential resistance forces are ignored. Most of the old types of fastenings and joints can be placed in this category.

Rail anchors (image 6) are sometimes used on this type of old superstructure to provide Figure 7: Mechanical joint maximum gap a certain track longitudinal resistance and reduce the rail creep on high gradients or on sections with frequent braking or acceleration.

JOINTED TRACK - SHORT AND LONG RAILS

For the free thermal expansion track superstructure, the joint and track resistances are ignored, hence the gap variation is linearly dependant on the temperature variation. The linear joint gap variation due to the rail temperature is displayed in the following graph (figure ).8

This graph defines a reference rail length Lref which will have the gap varying between the points A and B – closing the gap, when the temperature reaches its maximum value (B) and opening the gap to Gmax when the rail temperature reaches its minimum value (A). Image 6: A1 spike fastening with rail anchors In both cases no rail force is presumed to be transferred through the joint and the axial rail The maximum expansion gap Gmax can be MAXIMUM JOINT EXPANSION force will be null. GAP computed as: The reference rail length Lref can be computed Gmax = Bf + Df + Dr – 2Db – 2Br The fishplated rail joint is designed to allow from: a gap variation and, as such, has two well Where: defined limits of this gap. The minimum gap of a mechanical rail joint is null and that is usually Bf – the distance between the centres of the achieved without exerting shear force on any of middle holes of the fishplate; the joint bolts. Df – the fishplate hole diameter; Br – the distance from the end of rail to the first The maximum expansion gap of a mechanical rail hole centre; rail joint is dependent on the position of the This reference length, Lref, defines a limit in Dr – the rail joint hole diameter; joint holes and on the diameter of the holes and the way the rail behaves. Db – the joint bolt diameter. bolts of the joint (Radu - 1999). This maximum gap is reached when the rails contract due to For any rail shorter than the reference rail The maximum gap is designed for the longest temperature decrease and are starting to exert length, if installed and maintained correctly, the rail used on jointed track to avoid the shearing shear forces on the joint bolts (figure 7). joint should never close to 0 or open to Gmax.

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Also, theoretically, for such a rail length, there will never be any thermal stress in the rail. This type of rail length is called short rail.

For any rail longer than the reference rail length, if installed correctly, the joint will close before Tmax, in a point F. If the temperature will increase to Tmax, the rail cannot expand any longer and a thermal compression stress will appear in the rail. In addition, as the temperature decreases, the rail will open to Gmax before reaching Tmin, in a point E. As the temperature goes further down to Tmin, a thermal tensile stress will appear in the rail and joint.

This type of rail length, for which the thermal stress will naturally appear during the annual temperature variation, is called long rail. But Figure 8: Joint gap variation. Short and long rail definition even a short rail may develop thermal forces if installed incorrectly and the joint gap closes before the maximum rail temperature or opens to the maximum gap before reaching the minimum rail temperature.

Table 2 presents the maximum gaps for several types of mechanical joints, applying the maximum gap formula and the standards defining the parameters of the rail joint components used in the UK.

For the majority of flat-bottom rail types quoted in table 2, the reference rail length, Lref, is approximately 18.5 m.

Hence, for these rail types and joints, the British standard rail length of 18.288 m (60 feet) is practically the reference length (figure 8), defining the limit between short and long rails. Table 2: Maximum joint gap computation. Long rail definition JOINT CLOSURE TEMPERATURE (JCT)

Since the thermal expansion and contraction is freely allowed, the Joint Closure Temperature (JCT) can be computed using this formula:

Where:

- JCT is the estimated joint closure temperature - Tr is the measured rail temperature - Gr is the measured joint gap - α is the steel’s expansion coefficient - L is the rail length

The Joint Closure Temperature Table (NR/ L2/TRK/001/Mod14) can be replicated using this formula. Table 3 shows the joint closure temperature (JCT) for 60 feet rails on free thermal expansion track superstructure.

Table 3: Joint closure temperature for a 60 feet rail The JCT values computed this way are rather theoretical and presume the free linear expansion of the rail, without the presence of any resistance force, either at the joints or of the track longitudinal resistance.

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STAGE 0 - INSTALLATION STAGE 3 - THE JOINT STARTS TO (Figure 9) OPEN Figure 9: Stage 0 - installation T = 20°C and 6 mm joint gaps. At this stage the For the rail compression force to turn null, a rail rail is stress free. temperature variation ΔT3 is required.

The standard nominal rail length is defined for 15°C (BS EN 13674-1:2011). Figure 10: Stage 1 - joint closure The rail length at T = 20°C is L = 22.710 + (20 – 5 15)•1.15•10- = 22.711m The rail temperature at this stage is the same as in stage 1. From this stage the rail The rail temperature is presumed to increase temperature is decreasing further, leading to continuously and the rails will expand freely rail contraction. This contraction continues tending to close the joint gap. The next main until the joint opens to its maximum gap, which stage of this theoretical cycle is the closure of defines the next main stage. the joint. STAGE 4 - JOINT OPENED TO Figure 11: Stage 2 - maximum rail STAGE 1 - JOINT CLOSURE GMAX temperature (Figure 10) (Figure 12)

Due to the temperature increase between The temperature variation required to reach stage 0 and stage 1 the rails have expanded this stage can be calculated considering the freely and the joint is closed. gap change from 0 (stage 3) to 14.3 mm – the maximum gap: Figure 12: Stage 4 - joint opening to The temperature variation required to close the rail is: Gmax

The temperature at this stage is -11.8°C and the rail length has contracted to 22.703m. The next stage will be reached at the minimum JCT (Joint Closure Temperature) rail temperature. = 20 + 23 = 43°C

The rail length has increased to 22.717m. STAGE 5 - MINIMUM RAIL Figure 13: Stage 5 - minimum rail TEMPERATURE, -14°C temperature After the joint closes, the temperature will (Figure 13) continue to increase until it reaches the maximum rail temperature. As the temperature decreases further from Depending on the real life track’s behaviour the previous stage, the rail contraction is no and on how these resistance forces are longer permitted since the joint is already at actually mobilised along the track, the real STAGE 2 - MAXIMUM RAIL its maximum gap. An internal tension force will joint closure temperature (JCT) may be a few TEMPERATURE, 53°C develop in the rail. degrees lower (or sometimes higher) than the (Figure 11) calculated one. For a BS 113A rail, this thermal tension force Following the joint closure, the temperature is: EXAMPLE OF LONG RAIL increase to the maximum rail temperature THERMAL BEHAVIOUR cannot cause any further rail expansion and thermal stress will develop in the rail generating an internal compression force. The thermal behaviour of the rail and track can be analysed throughout the full annual The rail length is unchanged, 22.703m. For a BS 113A rail, this thermal compression temperature variation. This can be idealised as force is: a continuous temperature variation, increasing From this stage the temperature is presumed from the installation temperature up to the to increase continuously towards the maximum maximum rail temperature and decreasing rail temperature. to the minimum rail temperature. From here this ideal cycle can be continuously repeated As the temperature increases, the rail tension The rail length is unchanged, 22.717m. between the minimum and maximum rail force will decrease. The next main stage is temperature. reached when the rail tension force is null and From this stage of the theoretical cycle the the joint gap can start to close. temperature is decreasing continuously until it A free thermal expansion track superstructure reaches the minimum rail temperature. with 22.710 m rails is used for this example. The rails are installed at 20°C and 6 mm As the temperature decreases, the rail joint gaps – according to NR/L2/TRK/001/ compression force will decrease. The mod04, table 2. The track will pass through the next main stage is reached when the rail following main stages: compression force is null and the joint can start to open.

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STAGE 6 – THE JOINT GAP STARTS TO CLOSE

A rail temperature variation ΔT6 is required for the rail tension force to turn null.

The rail temperature at this stage is the same as in stage 4.

From this stage further the cycle repeats thorough these main stages 6-1-2-3-4-5-6. The full cycle is graphically presented in figure 14.

The graph presents the ideal behaviour of Figure 14: Joint gap variation for a track with 22.710 m rails on free the rails on free thermal expansion track superstructure. Nevertheless, in real life, the thermal expansion superstructure track components will oppose some resistance to the thermal variation. The wheel loading and rail-wheel contact forces will also have an influence on the joint gap variation, generating longitudinal movements of the rail. Due to all these influencing elements, over time, the joint gap variation could significantly depart from the ideal/theoretical behaviour presented in this example and maintenance works will be required to apply the necessary corrections. The characteristic temperatures and forces for various types of rail can be evaluated using this procedure. An example of these parameters is presented in table 4 for free thermal expansion track superstructure with different rail lengths installed at 20°C and 6 mm joint gaps.

As the actual rail length increases beyond the reference length, the magnitude of compression and tensile forces can become significant, closer to values typical for CWR. Figure 15: Example of gap expansion diagram for restrained thermal In such cases, the jointed track requires maintenance and protection measures similar expansion superstructure to the ones required in CWR track.

RESTRAINED THERMAL EXPANSION TRACK SUPERSTRUCTURE

The other type of superstructure is the restrained thermal expansion track superstructure – this superstructure has fastenings and joints designed to provide well-defined and reliable resistance forces to rail thermal variation throughout the service life of the track. Almost all modern fastenings and joints are designed in this way.

For this type of superstructure, closer to the behaviour of the actual track, the thermal variation is more complex (Alias – 1984, Hila et al. – 1975, Radu – 1989). The influence of the two main resistance forces will create a delayed joint gap response to temperature Figure 16: Theoretical example of ball and claw thermal variation from the variation – a hysteresis loop (figure 15). median position

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Table 4: Thermal behaviour characteristic data for free thermal expansion superstructure. * for short rails the joint closure and opening temperatures are only theoretical values, outside of the range of the rail temperature variation.

In this case, for almost any rail temperature, REFERENCES NR/L2/TRK/001/mod14 (2012). Inspection and Tr, the joint gap will not have a single value maintenance of Permanent Way. Managing but is expected to be within a defined range Alias, J. (1984). La voie ferre, techniques de track in hot weather. Issue 6. Network Rail. (between Gr1 and Gr2 – see figure 15). The construction et d’entretien (The railway track, amplitude of this range is dependant on the construction and maintenance techniques). NR/L2/TRK/2102 (2016). Design and track resistance forces and the rail length. SNCF – Eyrolles, Paris, France. Construction of Track, Issue 7. Network Rail.

CONCLUSIONS BSI BS 11:1985. Specifications for railway rails. NR/L2/TRK/3011 (2012). Continuous Welded British Standards Institution. Rail (CWR) Track, Issue 7. Network Rail. The principles presented in this article can be used to evaluate the thermal behaviour of the BSI BS 47-1:1991. Fishplates for Railway NR/L3/TRK/002 (2007). Track – Renew jointed track in a more accurate manner and, Rails – Part 1: Specification for Rolled Steel Fishplates, Issue 2. Network Rail. in a more complex approach, of the continuous Fishplates. British Standards Institution. welded rail (CWR) track, especially on the Radu, C. (1999). Cai Ferate – Suprastructura stress transition lengths. BSI BS 64:1992. Specification for Normal and Caii (Railway – Track Superstructure) – Course High Strength Steel Bolts and Nuts for Railway notes, Faculty of Railways, Roads and Bridges The principles of the restrained thermal Rail Fishplates. British Standards Institution. – Technical University of Civil Engineering expansion superstructure including the delayed Bucharest. response to temperature variation, can also Code 720, UIC (2005). Laying and be applied to the devices used to control the Maintenance of CWR Track. International Radu, C. (2001) Realizarea si Intretinerea Caii interaction between the stock and switch rail Union of Railways (UIC), 2nd ed. Fara Joante - curs postuniversitar. Technical (ball and claw or similar – see figure 16). University of Civil Engineering Bucharest. Cope, G. (1993). British Railway Track – (Construction and Maintenance of the The next articles will present more examples Design, Construction and Maintenance. Continuous Welded Rail (CWR) Track – post- of thermal expansion calculations, for jointed Permanent Way Institution, Echo Press, university course). and CWR track and will discuss the associated Loughborough. theoretical and practical implications. Ritter, G. W., Al-Nazeer, L. (2014). Coatings Hila, V. Radu, C. Ungureanu, C. Stoicescu, G. to Control Solar Heat Gain on Rails. AREMA ACKNOWLEDGEMENTS (1975) Cai Ferate. Partea II. Suprastructura 2014 Conference. caii. (Railway Track. Part II. Track Van, M.A. (1996) Buckling analysis of The authors would like to thank the following superstructure). Institutul de Constructii continuous welded rail track. Delft University of for their comments, suggestions and support in Bucuresti. Technology, HERON, 41 (3) 1996. writing this article: Constantin Radu, Univ Prof Dr Eng – TUCE Bucharest and Tom Wilson, NR/L2/TRK/001/mod04 (2012). Inspection Technical Discipline Leader (Track) – WSP | and maintenance of Permanent Way. Rail Parsons Brinckerhoff. Joints. Issue 6. Network Rail.

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