# RECYCLED PLASTIC RAILWAY TIES

*Analysis and comparison of sleeper parameters and the influence on track stiffness and performance*

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**ABSTRACT**

**In the last years, plastic railway ties have made their introduction. Amongst its characteristics, plastic ties have a good damping and a high design freedom. If used in the proper way, plastic ties can give improvements in the track. They should not be regarded as a substitute for wood or concrete, but use should be made of their own characteristics. Existing sleeper requirements are however applicable for wood or concrete and can hardly be seen as functional requirements suitable for the development of plastic ties.**

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**The desired track stiffness is the first parameter to define in setting requirements. A good compromise between bending stresses in the rail versus noise and vibration seems to be a target track stiffness of 50 kN/mm. When making a comparison between the different sleeper materials, the target track stiffness can be reached with plastic ties, where concrete tends to be on the stiffer side and wood shows more variations. Knowing the track stiffness gives the possibility to calculate the distribution of forces over the ties. Especially at irregularities in the track, such as bridges or viaducts, forces on ties can become high. Special attention to sleeper stiffness parameters should be given at those locations, as well to bending stiffness as to compression stiffness.**

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**The sleeper stiffness parameters are input in calculating the system stiffness. Effects of sleeper bending stiffness on track stiffness, railhead stability and ballast contact stresses are discussed. For a 2600 mm sleeper, a 150-250 kNm2 bending stiffness seems appropriate, where for a 2400 mm sleeper the minimum bending stiffness should be higher. The sleeper stiffness also has effects on the strength requirements, as has the sleeper length. Where it is clear that every situation will be different, calculations have been done to give a mean value as an example. Every specific situation can be calculated accordingly.**

**INTRODUCTION**

Railway Ties have in the past been made from wood, concrete and steel. These materials have good properties, but also have their downsides. Wood has been used since the first railway track was put in place. Concrete ties are being used more than wooden ties nowadays. Concrete is however a stiff material, consequently dynamic forces and vibrations are high, which causes, for example, high wear and degradation to the ballast. Wooden ties are therefore still being used in a lot of applications where concrete is too rigid a material. However, when not treated with creosotes, the lifespan of a wooden sleeper is quite limited, giving high replacement costs. Within the European union creosotes will soon be banned, which are now used to give the wooden ties an acceptable life span. Also availability issues, especially for longer bearers, increases the desirability of an alternative. Tropical hardwood can do without creosotes, but its environmental implications and availability do not make it a viable alternative for large scale application. In the last years, recycled plastic ties have made their introduction (see Figure 1).

*Figure 1: Plastic railroad ties in track.*

Plastic ties are a good alternative that can give solutions for specific problems in the track. Plastic is however a material with other characteristics than wood or concrete. It should not be regarded as a substitute for wood or concrete, but its unique characteristics should be made use of.

**POSSIBILITIES AND LIMITATIONS OF PLASTIC TIES**

To make a suitable plastic rail road tie, the material choice to get to a pricewise compatible tie should be one of the bulk plastics, most likely Polyethylene or Polypropylene. These materials have a bending stiffness and a thermal expansion coefficient, that makes them unsuitable to be used as is. Solving these issues can be done by either reinforcing them, for example with glass fibers, creating a composite tie, or by embedding reinforcing elements, such as steel or glass fiber bars, creating a hybrid railroad tie. Figure 2 shows an example of a hybrid sleeper. In this case there are 4 reinforcing metal bars in the corners of the sleeper.

*Figure 2: Steel reinforced KLP-S® tie.*

Ties can be made by either extrusion or injection moulding technologies. In extrusion the sleeper is formed continuously by pressing heated plastic through a die. The shape of the sleeper is therefore uniform in longitudinal direction, except for any mechanical treatments that are done afterwards. With injection moulding, the heated plastic is pressed into a mould, after which the material is cooled. The mould can have any desired shape and so can the sleeper.

**The pros and cons of plastics:**

- Plastic can be shaped in any desired shape. This is primarily the case for injection moulded ties. Optimization is possible, which for example can lead to (see Figure 3):
- Reduction of material use.
- The ballast is partly on top of the sleeper, thereby increasing the vertical stability of the sleeper.
- The change in width (and the profiled underside) of the sleeper increases the lateral stability of the sleeper.

*Figure 3: Optimized railway tie shape.*

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- Plastic is a material with time dependent stiffness properties. That means that, static test outcomes should not be used one on one to predict dynamic behaviour. Testing should be done at the appropriate speed of utilization, thus measuring dynamic material properties, as is being done with railpads. There is a lot known about the time related behaviour of plastics, so interpretation of static tests is possible when material properties are available.
- Plastic materials have a high damping. This results in good performance in the area of sound or vibration reduction. Measurements on a steel girder bridge showed a 3-5 dB noise reduction after replacing wooden sleepers for plastic ties of the type as in Figure 2, see Figure 4 (Movares, 2010).

*Figure 4: Sound measurements on a Steel girder bridge near Raalte in The Netherlands*.

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- The thermal expansion of plastics is too large to use as is in a sleeper; normally in the range of 15·10-5 to 20·10-5 °C
^{-1}. Adding glass fibers can bring the expansion rate down with about a factor 2 at maximum. A more effective solution is for example to use steel inserts, which brings down the expansion rate to the level of steel or concrete, around 1,2·10-5 °C^{-1}.This will exclude all problems, especially on bridges where the ties do not have temperature shielding by the ballast. - Plastics are highly resistant against degradation from weather influences. This will in general give an advantage against wooden ties. Specific area’s where wood cannot dry properly are very suitable for the use of plastic railroad ties. See for example Figure 5.

*Figure 5: Switch and ties built into the pavement.*

- Plastic materials have a high flexibility. This is a disadvantage in creating the desired bending stiffness. Adding glass fibers or reinforcements or adjusting the sleeper height is needed to get the proper bending characteristics. The flexibility is an advantage in the compression of the sleeper. This compressive flexibility gives a good distribution of the wheel loading over multiple rail ties, and also high dynamic forces will be distributed more easily. The high flexibility also gives a high local pressure to the ballast under the ties. In the case of a composite sleeper, the stiffness of the sleeper is more or less the same in all directions (in flow direction of the plastic somewhat higher). Creating a high bending stiffness will therefore result in unwillingly creating a high compressive stiffness. In the case of a hybrid sleeper, the properties in axial and lateral direction can be decoupled. A higher bending stiffness can be reached (using lower sleeper heights and less material) where the compression stiffness can be optimized independently, creating the more optimal solution. Because a more ductile plastic material can now be chosen and the deformation that this kind of material can experience before break can be much higher, an unbreakable sleeper can be made in a hybrid construction.
- Plastic has a good chemical resistance. Concrete sometimes experiences problems in this area on industrial tracks.
- Plastics have high rebound resilience. See Figure 6.

*Figure 6: No indentation under baseplate after 133 million tons of load (30 tons axle loads).*

- Plastics can be drilled and milled like wood. In concrete every bolt hole (dowel) has to be pre- casted in the factory. For example the replacement of a switch in concrete would require measuring the complete switch, where plastic railroad ties can be easily fitted in track.

*Figure 7: Switch with plastic ties.*

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- Plastic rail road ties are normally made of 100% recycled plastic. That gives 80-160 tonnes of high value recycling for a kilometer of track. After its lifetime, the railroad tie can be regrinded and the material can be used again for the next generation of ties. Inserts can be removed and reused.

*Figure 8: Connectable switch sleeper with constant bending characteristics over its length.*

- Plastic railway ties can be designed for a specific problem. For example when very long ties are needed for switches, a connectable sleeper can solve transportation problems of the switch, see Figure 8. Another solution can be seen in Figure 9, where a bridge sleeper is shown. Ties that are used on steel girder bridges have to be measured sleeper by sleeper to compensate for the tolerances in the steel girders. The sleeper in this picture can be adjusted to the right height and angle by mounting insertion blocks of the right dimensions. The insertion blocks are fixed by the screw spikes.

*Figure 9: Bridge sleeper with insertion blocks.*

- The expected service life of plastic railroad ties is long. Although the experience in this field is limited, there is a good track record with similar products. Table 1 gives an estimation of the expected service life for the different sleeper materials.

*Table 1: Expected service life of sleepers for UIC class 4 track (11 MGT/yr) (Prorail, 2014)*

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**RAIL TIE REQUIREMENTS**

Difficulty in the development of plastic rail ties is that wood has been used for over 150 years in the track. We all know that it works, but the real mechanical requirements are not very clear. If you look into a standard for wooden ties, you will find requirements for the dimensions, the allowable warpage and the amount of knots, but you will not find strength or stiffness requirements. The chosen type of wood makes sure these characteristics are incorporated. It would however be too simple to regard the properties of wood or concrete as requirements for the development of plastic rail road ties. The fact that these materials possess certain mechanical characteristics does not mean it is necessary for its function. Doing this would give some serious mistakes:

- The requirements might become much higher than necessary. The costs of the sleeper would therefore also be much higher than necessary.
- Some requirements have effect on each other. For example for strength you could require as a minimum the values that you experience in wood. For stiffness you do the same. But then you neglect the fact that when you have a stiffer sleeper, the forces on the sleeper will be higher and the strength requirement might not be high enough. The relations that exist in wood between the different properties are impossible to copy.
- Requiring exactly the same range as a wooden sleeper would give the problem that wood has a huge spread in its properties and that the wood properties change during the lifetime due to decay.
- Some properties that exist in wood/concrete, might not be the best properties.

It will be clear that this route is not the best way forward. At the same time it describes the current problem in developing plastic railties. Functional requirements for ties, that exist independently from the materials used, should be developed.

**OPTIMAL TRACK STIFFNESS**

To determine the necessary sleeper properties, the first priority is to determine the required system stiffness. The deflection of the rail on a train passage has to be within certain limits. If the deflection is too high, the bending moments in the rail become too high and fatigue in the rail can become an issue. Arema advises a deflection of 3,2 - 6,35 mm (AREMA, 2006). If the deflection is too low, impact loads on the ballast and sleeper become higher, which enhances degradation of the track and leads to more maintenance. Also ground borne noise and vibration increases with a stiff rail construction. Riessberger advises a minimum deflection of 2 mm for this reason (Riessberger, 2014). The system stiffness also determines how much of the wheel load is transferred to one sleeper and is therefore necessary information as input for the strength analysis. The stiffer the system is, the higher the load on one sleeper is and therefore the higher the strength requirements should be.

The track stiffness k is defined as the relation between the wheel load Q and the deflection δ directly under the wheel.

The wheel load is determined by the axle load and the dynamic amplification factor fd. When taking a maximum axle load of 22,5 tons and an fd of 2, the minimum track stiffness should be 35 kN/mm, to comply with the maximum deflection as stated by Arema. For determination of the maximum track stiffness according to Riessberger, not the maximum permitted loading is of interest, but a mean expected loading. Taking as an estimate 2/3 of the maximum allowed loading and f_{d}, the maximum track stiffness should be 50 kN/mm. An appropriate target track stiffness would therefore be 50 kN/mm.

As derived by Zimmermann in 1888, we can calculate the relation between the wheel load Q and the load F that is applied on the sleeper (Esveld, 2007) with Equation 2 in Table 2. As shown in Figure 10, with a target track stiffness of 50 kN/mm, we can expect that 28-37% of the wheel load is transferred to the sleeper directly under the wheel, depending on the rail profile (NP46, UIC54 and UIC60 are analyzed).

This distribution is required as input for the strength calculations.

*Figure 10: Sleeper load variations, c.t.c. distance of ties 600mm.*

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**STIFFNESS MODELLING OF TIES**

In analyzing the system stiffness, there are three stages of load distribution, see Figure 11.

*Figure 11: Load distribution on sleeper.*

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- The distribution of forces caused by the wheel over the different railway ties. This is analyzed considering the rail profile as a beam on a resilient support as determined by Zimmermann in 1888, see Equation 2. The track modulus u of the system is the main stiffness parameter of the system and has to be calculated. This is done by determining the foundation stiffness of baseplate (K
_{P}), sleeper (K_{S}) and railpad (K_{RP}) with help of Equation 3. - The distribution of the force through the baseplate over the sleeper is determined by the bending stiffness of the baseplate and the compression of the sleeper. This can also be done considering the baseplate as a beam on a resilient support (the resilient support being the sleeper). Assuming an appropriate baseplate has been chosen, a simplified assumption is often used, which assumes that the baseplate has an evenly distributed support, and that the force distribution through the sleeper occurs under a 45 degree angle (see Equation 4). In the width direction the spreading of the force will be limited by the width of the sleeper.

Part of the system stiffness is determined by the dynamic stiffness of the rail pad K_{RP}, which is added in Equation 3. - The distribution of the support load under the sleeper caused by the bending stiffness of the sleeper EIS and the resilient support of the ballast. This distribution has been analyzed by Hetenyi in a similar way as the Zimmermann formula (Hetenyi, 1946), see Equation 5. The bedding modulus C of the ballast is a major variable here and can be expected to vary between 0,04 and 0,16 N/mm
^{3}(Manalo, 2010). The bedding modulus is the spring constant (N/mm) of the underground, defined per mm^{2}surface, giving units of N/mm^{3}.

*Table 2: Equations for stiffness calculation. *(van Belkom, Railway sleeper design manual, 2014)

**TRACK STIFFNESS EVALUATION**

The derived equations have been used to make a rough comparison of the different construction materials for railties with respect to the expected track stiffness. A 1435 mm gauge track with sleepers spaced at 600 mm and a UIC54 rail profile has been used for the evaluation. The input parameters have been specified in Table 3.

*Table 3: Assumed properties for stiffness comparison (source material data plastic: (van Belkom, Material calculation data, 2013), wood: (Green, Winandy, & Kretschmann, 1999), concrete: NEN- EN 206:2014).*

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In Figure 12 the effects of the ballast and sleeper stiffness on the track stiffness can be seen. The two lines represent the upper (P95) and lower limit (P5) of the sleeper properties that can be expected. The target track stiffness value of 50 kN/mm is highlighted in the graph. What can be seen is that the most important effect is caused by the bedding modulus of the ballast and subgrade. Whatever you do, sleeper properties can never compensate the variations in bedding modulus. It can further be seen that:

- Concrete ties tend to create a stiff structure, usually stiffer than the target track stiffness.
- Wood ties give a rather broad range of possible track stiffnesses, due to the large variety in possible mechanical properties.
- Plastic ties give the possibility to aim for the target track stiffness, provided bedding modulus is appropriate.

*Figure 12: Bedding modulus - Track stiffness relation for some sleeper materials, sleeper properties according to Table 3.*

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**FORCE DISTRIBUTION OVER THE RAIL ROAD TIES**

When looking at the force distribution over the railway ties, the support modulus of the total construction and the rail stiffness define how much of the wheel force is distributed to the underlying sleeper, and how much to adjacent ties. For the case of the mean plastic sleeper (see Table 3) on a mean bedding modulus of 0,1 N/mm^{3}, Figure 13 gives the distribution graph. The wheel is here on top of sleeper 0. About 32% of the wheel force, including dynamic effects, will be distributed to this sleeper. Up to 3 ties to the left and the right (about 2 meter), the influence of the load can be seen.

*Figure 13: Force distribution over ties for mean plastic sleeper of Table 3.*

Due to variations in the bedding modulus and in the sleeper properties, the force distribution, and thus the maximum force on one sleeper can vary. Table 4 shows the in the first column the most flexible sleeper on the most flexible bedding. This gives the lowest sleeper load. The second column shows the most rigid sleeper on the most rigid bedding, giving higher sleeper loads. The highest sleeper loads however can occur when a more rigid sleeper from the tolerance range is placed amidst more flexible railties, which can be seen in the most right column. The wood ties seem to have a higher possible maximum load than concrete, which would in the first glance be strange. The concrete sleeper in this analysis however does have a more flexible rail pad (Table 3), but also the wider stiffness range of the wooden ties causes this effect.

*Table 4: Load on sleeper as % of wheel load, for sleepers according to Table 3.*

The analysis in Table 4 assumes the bedding modulus doesn’t change from sleeper to sleeper, which in general won’t happen. This is however different when the track runs over a bridge, a viaduct or any other obstacle causing a disruption of the bedding stiffness. Figure 14 shows the distribution of forces over railties on a bridge. Sleeper 0 is the first sleeper on the bridge, the bridge extends to the right. The track sleepers are concrete, bridge ties are Azobé, all according to Table 3, now considering a mean sleeper and bedding stiffness.

*Figure 14: Force distribution over ties on edge of bridge. Sleeper 0 is the first sleeper on the bridge, the bridge extends to the right. Track ties are Concrete, bridge sleepers are Azobé, all according to Table 3.*

Because of the missing flexibility of the ballast and subgrade on the bridge, we can see here that the force on the railroad ties can be much higher than in track, specifically for the first sleeper on the bridge. These situations should be avoided. Sleeper compressive flexibility on a bridge should be much higher than in track to compensate for the missing flexibility of the ballast. A hybrid plastic sleeper can have a much higher compressive flexibility than wood or concrete and would be a good choice for a solution.

This analysis was just one example. For each case specifically the optimal compressive sleeper stiffness should be defined to get a continuous track stiffness. The analysis hasn’t considered any dynamic effects yet or settlement of the track before and after the bridge, giving a height difference between bridge and ballasted track. Settlement is not prevented by a continuous track stiffness, but it does have a positive effect. Height adjusting means of the ties on the bridge would be an additional aid to compensate any track settlements.

Also the situation in a switch requires special consideration. Since the ties in a switch are much longer and the distribution of forces over the ties is not done by 2 rails, but by 4, the load on one sleeper is less than in regular track. Also the track stiffness in a switch is higher because of this. Rail road ties with a higher flexibility should therefore be used in a switch to create a continuous track stiffness.

**EFFECTS OF SLEEPER BENDING STIFFNESS**

The basic thought on sleeper bending stiffness seems to be that the higher the sleeper bending stiffness is, the better the sleeper performance. The system performance has been analyzed for a change in sleeper bending stiffness to create a better picture of these effects.

__Effects of sleeper bending stiffness on track stiffness__

When analyzing the plastic sleeper of Table 3, and evaluating possible different bending values for the stiffness, keeping the compressive stiffness constant as mentioned in the table, the calculation model is as depicted in Figure 15A, being the beam on a resilient support, as previously used for the track stiffness evaluation.

*Figure 15: Calculation models.*

The outcome of this calculation can be seen in Figure 16. A maximum (0,16 N/mm^{3}), minimum (0,04N/mm^{3}) and a mean value (0,10N/mm^{3}) for the bedding modulus has been used.

*Figure 16: Track stiffness as a function of sleeper stiffness, for 3 different bedding moduli of the ballast (N/mm ^{3}), properties according to Table 3.*

What can be observed is that a low bedding modulus prevents the system of achieving the target stiffness and there is nothing that even the stiffest sleeper can do to prevent that. Targeting at a mean bedding modulus, the sleeper bending stiffness should be in the area of 150-250 kNm^{2}.

__Effects of sleeper bending stiffness on rail head stability__

Limiting the lateral displacement of the railhead when a train passes is an important function of the system and of the sleeper in particular. While this regards safety, it is not a serviceability limit state (SLS), as was the case for the track stiffness, but an ultimate limit state (ULS). The calculation model is therefore not done regarding mean values, but extreme values. The calculation model according to Figure 15B is therefore applicable, which describes a worst case support situation with regard to the possible rotation of the rail seat area. The support is a uniform distributed load, which can be expected for a deteriorated track. The horizontal deflection δ_{H} of the railhead can then be given as (van Belkom, Railway sleeper design manual, 2014):

Since the load situation is now a ULS calculation, worst case loads and support situations are analyzed. All applicable safety factors according to ISO 13230-6:2014 are incorporated. Doing this calculation for the plastic sleeper of Table 3, gives the outcome as can be seen in Figure 17. An axle load of 22,5 ton is taken and a speed of 140 km/h. Be aware that the loads are the extreme loads, mean loads will be a factor 3 lower. The minimum bedding modulus of 0,04 N/mm^{3} has been used.

*Figure 17: Maximum (extreme) horizontal deflection of railhead as a function of sleeper stiffness, for 3 different sleeper lengths (L _{S}), properties according to Table 3, C=0,04 N/mm3.*

Figure 17 shows the horizontal rail deflection for extreme loading on a straight track, for sleeper lengths of 2400, 2600 and 2700 mm. What can be seen is that the higher the sleeper bending stiffness, the lower the deflection. The sleeper length has a lot of influence: a sleeper length of 2600 mm gives a more stable railhead than a 2400 mm sleeper. The optimum for this analysis lies somewhere around 2730 mm. At that length the loading does not have any effect on the bending of the sleeper (for this particular load case).

Railties that are even longer will give an inward bending when loaded. When taking for example a 3 mm deflection as a maximum, the consequential minimum sleeper bending stiffness for a 2600 mm sleeper will be around 120 kNm^{2}, whereas for a 2400 mm sleeper this should be 300 kNm^{2}. This analysis only considers straight track. For the situation in curves, additional analysis would be required.

__Effects of sleeper bending stiffness on ballast contact stresses__

If the contact stresses in the ballast are high the ballast will degrade more rapidly, with higher maintenance costs as a result. The stress in the ballast is best kept below 0,5 MPa to prevent this (Esveld, 2007). The highest contact stress between sleeper and ballast will occur under the rail seat, as can be seen in Figure 11. It is obvious that the stiffer the sleeper is, the more evenly distributed the stresses will be.

Therefore the sleeper bending stiffness is of interest in determining ballast stresses. Performing a static analysis however gives only a partial answer. Aspects that cannot be seen from this analysis are:

- The dynamic effects: the more rigid the system is, the higher the dynamic impulses will be.
- The effective area of the ballast – sleeper contact: If the sleeper is made of a very rigid material, the contact area of the ballast will be very small, creating very high stresses on sleeper and ballast. When the sleeper is softer, the point of highest stress will be moved a layer downwards, where the ballast interacts with itself. Because this is a lower layer, the force is already more distributed, lowering stresses.

Dynamic analyses or field tests should be done to asses this subject. It is known from praxis that concrete ties have more problems with ballast degradation than wooden ties. Since concrete sties are stiffer than wooden ties, it can be concluded that a high system stiffness and high contact stiffness are the main contributors to ballast wear. Since plastic railroad ties have a comparable system and contact stiffness as wood, degradation of ballast is also expected to be comparable. If the bending stiffness is much lower, localizing the contact area can increase the stresses. The stresses at the rail seat can be calculated with help of (Esveld, 2007):

We can calculate the force on the sleeper F with help of Equation 2 and the foundation stiffness of the sleeper K_{S} with help of Equation 5. Performing this calculation with the parameters of Table 3 gives the graph according to Figure 18, and shows the stresses in the ballast as a function of the bending stiffness of the sleeper. As can be seen the sleeper bending stiffness should be kept over 100 kNm^{2}.

*Figure 18: Stress in ballast at rail seat as a function of sleeper bending stiffness for 3 different bedding moduli (N/mm ^{3}).*

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**STRENGTH EVALUATION**

The distribution factors that have been calculated with help of the sleeper stiffness can now be used for calculating the sleeper strength requirements. Strength analyses of the sleeper can be done according to the calculation model of Figure 15. The maximum bending moment in the centre of the sleeper will occur in load case B, which in praxis occurs in a deteriorated ballast bed. The maximum centre bending moment M_{C} is defined in Table 5. In the area under the rail seat, the maximum bending moment Ma will occur after tamping, which load case situation is depicted in load case C of Figure 15.

*Table 5: Equations for strength calculation*

When for example taking the parameters of Table 6, this gives a required design centre bending moment of 9,8 kNm for a 2600 mm sleeper and 14,3 kNm for a 2400 mm sleeper. For the required design bending moment at the rail seat area this value is 15,7 kNm for a 2600 mm sleeper and 11,4 kNm for a 2400 mm sleeper.

*Table 6: Assumed properties for strength analysis.*

While these figures are given as an example, the method of calculation can be applied for any specific situation. Doing such an analysis gives more insight in the requirements than copying wooden sleeper properties. It shows that the system stiffness has a distinct influence on the strength requirements. It also shows that requirements cannot be set without taking the sleeper length into consideration.

**CONCLUSIONS**

Plastic rail ties can offer solutions in the track at positions where concrete ties are too stiff. In particular this is true for bridges, viaducts, and other places in the track where the ballast stiffness has an increased value. Also switches induce an increase in track stiffness that should be compensated.

More in general, to create a proper track stiffness from a point of view of wear and vibration plastic railties can provide a good solution. Adaptability at site, for example for switches and the one-on-one exchange with wooden ties for partial renewal of wooden track, is possible with plastic rail ties. The design freedom of plastic gives the opportunity to create optimal solutions for specific problems.

Initiating the use of plastic railroad ties creates the necessity to have proper functional requirements for plastic railties, or better, for railties in general. The stiffness of the system plays an important role in this analysis. It should be looked at, not only from the point of view of determining proper track stiffness, but also to form the basis for the strength calculations. Sleeper bending stiffness requirements should not only incorporate a minimum value, but should define a range, as is the same for compressive stiffness.

Also to define strength requirements, the system stiffness as well as sleeper length should be known variables.

NOTATIONS

*a **: distance between end of sleeper and centre of rail (mm)*

*c :** distance between centre of sleeper and centre of rail (mm) c*

_{V }

*: coefficient of variation (%)*

*C **: bedding modulus (N/mm*^{3}*)*

*E*_{C }*: E-modulus of sleeper in compression (N/mm*^{2}*)*

*EI*_{R}*: Product of Young’s modulus E and moment of inertia I of rail (N/mm*^{2}*)*

*E*_{S }*: Young’s modulus of sleeper in bending (Nmm*^{2}*)*

*EI*_{S}*: Product of Young’s modulus E and moment of inertia I of sleeper (Nmm*^{2}*)*

*f*_{d} *: dynamic amplification factor (-)*

*F **: applied force on sleeper (N)*

*h*_{R }*: height of rail (mm)*

*h*_{S} *: height of sleeper (mm)*

*k **: track stiffness (N/mm)*

*K*_{P }*: foundation stiffness caused by bending of baseplate & compression of sleeper (N/mm) *

*K*_{RP}*: dynamic stiffness of rail pad (N/mm)*

*K*_{S }*: foundation stiffness caused by bending of sleeper & compression of ballast /subgrade (N/mm)*

*L*_{P} *: length of baseplate (mm)*

*L*_{S }*: length of sleeper (mm)*

*M*_{a }*: maximum bending moment at rail seat (Nmm)*

*M*_{c }*: maximum bending moment at centre of sleeper (Nmm) *

*Q : wheel load = axle load/2 (N)*

*S **: center to center distance of ties (mm)*

*t*_{P }*: thickness of baseplate (mm)*

*t*_{RP}*: thickness of railpad (mm)*

*u **: track modulus (N/mm**2**)*

*u*_{B} *: support modulus of ballast/subgrade (N/mm**2**)*

*w*_{B} *: width of sleeper at bottom in contact with ballast (mm) w*

_{P}*: width of baseplate (mm)*

*w*_{S} *: mean width of sleeper (mm)*

*δ **: deflection (mm)*

*δ*_{H} *: horizontal deflection of railhead (mm)*

*λ **: characteristic of the rail (1/mm)*

*λ*_{S }*: characteristic of the sleeper (1/mm)*

*Ϭ*_{B }*: stress in ballast at rail seat (N/mm*^{2}*)*

* *

LITERATURE

AREMA. (2006). Manual for railway Engineering. In *Volume 4, Chaper 16, part 10.*

Esveld, C. (2007). *CT3041-Constructief ontwerp van spoorwegen. *Delft: TUDelft.

Green, W., Winandy, J., & Kretschmann, D. (1999). *Wood Handbook - Wood as an engineering material*

*- Chapter 4, mechanical properties of wood. *Forest Products Laboratory, US department of Agriculture.

Hetenyi, M. (1946). *Beams on elastic foundation. *University of Michigan.

Manalo. (2010). *Fibre**composite sandwich beam. *University of Southern Queensland. Movares. (2010). *Geluidproductie spoorbrug Laag Zuthem. *Utrecht.

Prorail. (2014). *Levensduurverwachting**spoor en wissels ten behoeve van vervangingsplannen BID00020-V001.*

Riessberger, K. (2014). Presentation on Rail technology conference, 18-20 March 2014. Dusseldorf: University of Graz.

van Belkom, A. (2013). *Material**calculation**data. *Sneek: Lankhorst Engineered Products.

van Belkom, A. (2014). *Railway**sleeper**design**manual.*Sneek: Lankhorst Engineered Products. Young, W. C. (1989). *Roark's formulas for stress & strain. *McGraw-Hill.

--------------------

Aran van Belkom

Lankhorst Engineered Products

Prinsengracht 2

8607AD Sneek

The Netherlands

avb@klp.nl