Road Wear from Heavy Vehicles – an overview

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Road wear from Heavy Vehicles - an overview Report nr. 08/2008 NVF committee Vehicles and Transports


Titel: Serie: Upplaga: Utgivningsort:

Mattias Hjort Mattias Haraldsson Jan M. Jansen Road Wear from Heavy Vehicles – an overview NVF-rapporter 100 Borlänge, Sverige


Vägverket 2008



NVF-rapporterna kan beställas via respektive lands sekretariat per telefon, fax, e-post eller post. Se kontaktuppgifterna på näst sista sidan. En uppdaterad rapportförteckning finns på förbundets nordiska hemsida,

Road Wear from Heavy Vehicles - an overview

Report nr. 08/2008 NVF committee Vehicles and Transports


Denna rapport är en sammanställning över hur olika fordonsberoende parametrar för tunga fordon inverkar på vägslitaget. Exempel på sådana parametrar är axellast och däckstorlek. Studien baseras huvudsakligen på Cebons Handbook of Vehicle-Road Interaction, DIVINE projektet, och COST 334. Syftet har varit att sammanställa olika resultat utan att göra någon egen utvärdering av resultaten.


Tämä raportti on yhteenveto raskeiden ajoneuvojen eri ajoneuvoperusteisten parametrien vaikutuksesta teiden kulumiseen. Tällaisia parametreja ovat esimerkiksi akselipaino ja rengaskoko. Tutkimus perustuu pääasiallisesti Cebon's Handbook of Vehicle-Road Interaction käsikirjaan, DIVINE -projektiin ja COST 334:än. Tarkoituksena on yksinomaan ollut kerätä yhteen tulokset ilman sen enempää analysointia.


This report is an overview on how different studies of road wear have reported the effect of various vehicle dependent parameters, for heavy vehicles, such as axle load, tyre properties etc. The intention with this overview has only been to collect the different results, without any kind of evaluation. The overview is mainly based on Cebon’s Handbook of Vehicle-Road Interaction, the DIVINE project, and COST 334.


Table of contents 1. Introduction


2. Pavement distress modes


2.1 Introduction


2.2 Pavement construction


2.3 Pavement distress modes


2.4 Actual road wear


2.5 Pavement sustainability


3. Vehicle Effects


3.1 Introduction


3.2 Relative effects of different axle loads


3.3 Dynamic axle loading


3.4 Effects of different axles: single axles, tandem axles and tri-axles 19 3.5 Tyre specific effects


3.6 Suspension effects


4. Experimental results from the literature


4.1 Overview


4.2 Experimental findings: static axle load


4.3 Experimental findings from using different tyres


4.4 Experimental findings regarding suspensions and dynamic loading 33 4.5 A model taking all factors into account 5. Calculation models used in the Nordic countries 5.1 Classification of special heavy transport in Denmark

33 36 36

5.2 The Swedish Road Administration method of calculating the equivalent number of standard axles


6. Acknowledgements


7. References




1 Introduction This report within NVF ‘Fordon och Transporter’ is intended as an overview on how different studies of road wear have reported the effect of various vehicle dependent parameters, such as axle load, tyre properties etc. The intention with this overview is only to collect the different results, without any kind of evaluation. Chapter 2 gives a short introduction to pavement construction, and the various modes of damage that occurs. Chapter 3 describes the vehicle dependent parameters and the models that are normally used for predicting vehicle induced road wear. The range of reported values in the literature of these vehicle parameters are given in chapter 4. Two examples of calculation models used in Denmark and Sweden are described in some detail in chapter 5. Some major works have been conducted in recent years, and form the basis of this report. The primary sources are •

“Handbook of Vehicle-Road Interaction” [1] (1999) by David Cebon.

DIVINE (Dynamic Interaction between Vehicle and INfrastructure Experiment) [2], OECD project 1992-1998. An experimental study focusing on how dynamic loads are affecting road deterioration.

COST 334 – “Effects of Wide Single tyres and dual Tyres” [3] (1996-2000). Full scale tests were carried out, in addition to literature studies, in order to describe all tyre parameters that affect the road wear, and how their combined effect can be determined.

A general description of the field of Interaction between vehicle/climate and the road, including a discussion on the further need of research, has recently been written in Swedish. : •

“Interaktion mellan fordon/miljö och väg” [4] (2004) by Ulf Isacsson, KTH

That report has also been used as a basis for this report. . The present increase in deployment of mechanistic design, especially in USA, of course enhances the world wide research and development within the issue of this report. Some very interesting results have been presented recently from USA, but they have not been discussed in context of this report. These new results are described very briefly below. From implementation Mechanistic-empirical design in USA, the 3 major approaches about axle load versus road wear are: 1. Development of a load damaging factor. The dynamic effect of road unevenness adds a factor to the road wear calculated from static axle loads. This effect is caused by an interaction between the dynamic of the vehicle and the wave length and amplitude of the road surface roughness, and depending on the travel speed. Thereby the damaging factor results, such that the effect on road wear will relate to class of road, i.e. different effect on motorways and minor roads as well as rural and urban roads. 2. Effect of axle loads, repetitions and spacing on dissipated creep strain energy, DCSE, in relation to development of cracks in pavement materials.


Traditional road wear is viewed in relation to strain-fatigue caused by load repetitions, however new research focus on dissipated creep strain energy induced in the pavement materials by the actual strain work under the repeated axle loads. In this relation the spacing between the load repetitions are taking into account, because with narrow spacing complete strain release doesn’t happen between the load applications. This effect change the traditional way of perceiving road wear always as repeated single loads toward regarding road wear differently from axle groups. This is an important effect to obey, when calculating road wear applied by modern lorries and semitrailers often having dual, triple or maybe quad-axle configurations 3. Investigation of axle load spectra’s from regular lorry traffic The variation in axle loads from different axle load levels are examined to establish a representative value for axle loads based on weigh-in-motion, WIM, registrations of regular traffic load’s exposure on pavements. The results indicate the use of lognormal distribution for description of normal axle load distribution. Especially inference of axle loads from WIM registration must be investigated in relation to calculation of road wear from regular traffic flow.


2. Pavement distress modes 2.1 Introduction Pavement wear is a process in which several different deterioration processes act and interact, influenced by a variety of factors. (These factors include environmental factors such as temperature and moisture, but only the traffic-related factors will be considered in this report. For the effects of environmental factors, see e.g. [1, 4]). The focus of this report is instead on the influences of various vehicle parameters, such as tyre type (single / dual / wide single), tyre size, wheel load, inflation pressure. To describe the effect a vehicle has on road deterioration, a distinction has to be made into different modes of distress. The different distress modes are described in section 2.3

2.2 Pavement construction A typical flexible (or asphalt) pavement can be divided into four layers

Figure 2.1: A typical asphalt pavement construction The top layer is normally an asphalt layer. In British English, the word 'asphalt' refers to a mixture of mineral aggregate and bitumen. Bitumen is a mixture of organic liquids that are highly viscous, black, sticky, entirely soluble in carbon disulfide, and composed primarily of highly condensed polycyclic aromatic hydrocarbons. Bitumen is the residual (bottom) fraction obtained by fractional distillation of crude oil. It is the heaviest fraction and the one with the highest boiling point. The base layer is an unbound layer which typically consists of unstabilized aggregates. The aggregate bas could also be stabilized with asphalt, portland cement, or another stabilizing agent. The subbase is mostly a local aggregate material. Also, the top of the subgrade is sometimes stabilized either cement or lime.


Rigid pavements are mostly found in major highways and airports, and like flexible pavements they are designed as all-weather, long lasting structures to serve modern day high speed traffic. The rigid pavement has a top layer consisting of a concrete slab of thickness of 10-30 cm. The load transmission mechanisms of these two pavement types are different. The rigid pavement distributes the load over a large area, while flexible pavements, when the traffic load is applied on top of the surface layer, a localized deformation occurs under the load, as shown in Fig. 2.1. “The load is distributed over a small area at the surface, but as the depth increases, the same load is distributed over a larger area. Therefore, the highest stress occurs at the surface and the stress decreases as the depth increases. Thus, the highest quality material needs to be at the surface, and as the depth increases, lower quality materials can be used. When the load is removed the pavement layers rebound. A very small amount of deformation, however, could stay permanently which could accumulate over many load repetitions causing rutting in the wheel path.” [7]. The design life of a flexible pavement may be in the range of 15-20 years, while it is common for a concrete pavement to be designed with a service life of 30-40 years.

2.3 Pavement distress modes Pavement wear or pavement distress is the degradation of pavement quality due to loading by traffic and/or climate. For flexible pavements, the following distress modes (visible distress together with the deterioration process causing it) are relevant (definitions and descriptions are based on ref [3]): Cracking •

fatigue cracking: being cracking in the bituminous or cement bound material originating at the bottom of the respective layers, due to fatigue of the material by a great number of repetitions of bending due to wheel loads (Fatigue defined in this way is used as a parameter in pavement design. This does not include surface cracking and cracking due to thermal cycling, although these are also due to fatigue because of repeated stress cycles.)

thermal cracking: being cracking in the bituminous material due to tensile stresses caused by temperature changes

surface cracking: being cracking in the bituminous material originating at the surface of the pavement, due to fatigue of the material by a great number of shear loadings of the pavement surface by the tyre (Ageing of bituminous materials plays an important role here, too.)

reflective cracking: being cracking of the (top) bituminous layers (often in a composite structure) as a result of cracks or joints in bound layers below.

Rutting Rutting is the development of depressions in the pavement surface along the wheel paths, typically with a width of several decimetres and a length of tens to thousands of meters. The three main categories are •

Primary rutting: rutting due to permanent deformation of bituminous layers, (Permanent deformation can be due to (post)compaction or (plastic and viscous) deformation caused by shearing stresses.)


Secondary rutting: rutting due to permanent deformation in the subgrade or in granular layers below the asphalt layers.

Rutting due to abrasion of the pavement surface by studded tyres.

Other distress modes •

Ravelling: being the loss of stones in the surface of the pavement as a result of failure of the bond between the aggregate and the binder by a great number of shear loadings in combination with ageing of the material. The primary case, is however insufficient quality of the pavement material.

Roughness: being (longitudinal) unevenness of the pavement, mostly due to several combined factors (rutting, cracking, potholes, uneven settlements, etc.)

Potholes: resulting either from local collapse due to structural defects, or from frost acting on water ingress (often through cracks). Potholes are not necessarily caused by loading but mainly due to insufficient quality of the pavement

The more important of these distress modes are shown in Figure 2.2.

Figure 2.2. Various modes of pavement distress. (from Ref. [3]). For explanation on nomenclature, see Sec.2.2. HMA is short for Hot Mix Asphalt.) The main distress modes, especially from the point-of-view of traffic loading are:


1. Fatigue cracking. This occurs mainly on relatively weak / thin pavements (Visible cracking in thick pavements is likely to originate (at least partly) at the surface.) 2. Primary rutting. This occurs mostly on main roads with thick bituminous layers. 3. Secondary rutting. This occurs mainly on relatively weak / thin pavements. It is clear that these different distress modes react differently to changes in the influencing factors. Take e.g. the influence of tyre type, where the stress and strain conditions near the surface of the pavement are strongly influenced by the contact stresses and their distribution in the tyre-pavement interface, whereas the stresses and strains deeper in the structure are mainly influenced by the total load. Therefore, a change in contact stress distribution due to a change in tyre type can generally have most influence on the upper layers2. Most design methods for flexible pavements since the 1960s are based on the prevention of fatigue cracking and secondary rutting. In relatively weak /thin pavements this does not always succeed, but in thick pavements it generally succeeds. Then, primary rutting may become the dominant distress. Permanent deformation of bituminous layers is usually not considered as a part of structural design. With proper bituminous mixture design the tendency for permanent deformation can be decreased. However, the bituminous mixture design is always a compromise between many properties (including price) and small changes in mixture composition during the manufacturing may worsen the properties of bituminous mixtures. It is possible to manufacture mixtures, which will not deform easily, by using modified bitumens but they are much more expensive and thus their use is limited. Ravelling and surface cracking, being the most superficial distress modes, may be influenced by any differences in contact stress distributions between different tyre types.

2.4 Actual road wear The road wear from actual commercial vehicles of course depends on the degree of loading and type of goods carried by the vehicle. The actual road wear exposed by the traffic on pavements can only be determined by weighing of actual lorries, busses, semi- trailers etc. in traffic flow. Maximum permissible gross weight and axle loads are not always reached by regular commercial vehicles, because a great proportion of the freight is volume based. Besides distinction in type of vehicle classes the road wear from typical vehicles is also different from traffic on rural and urban roads. The actual road wear exposed by the traffic flow very much also depends on the traffic composition. The discussion in this report therefore must be seen in relation to actual axle loads from vehicles in regular traffic flow.


However, exceptions to this rule may occur, depending on structure and material quality (e.g. a very critical stress-sensitive granular layer below a rather thick AC layer may be the main cause of rutting increase due to a slight increase in stresses).


2.5 Pavement’s sustainability The road wear from the traffic will be exposed to road pavements, and depending on the ability of the pavement materials and design the pavement will develop distresses over time. With time the pavement will develop described distress modes in various degrees until the pavement reaches an unacceptable condition and will be rehabilitated by resurfacing and possibly strengthening. Therefore road wear is a very important parameter to focus at for design and maintenance of road pavements. Prescription of thresholds for unacceptable condition normally relates to functional and structural properties of the pavement. Classical functional criteria’s related to the road surface are building of rut depth and deterioration of the evenness and the structural criteria is proportion of cracked area in wheel tracks, related to the bound pavement materials e.g. asphalt.


3 Vehicle effects 3.1 Introduction This section describes the influence of properties of different vehicle components on exposed road wear. It is the intention of this chapter to explain the concepts, and to briefly describe what kind of road damage the different factors leads to. Experimental findings concerning these factor are reported in Chapter 4. The basic parameter is the axle load. The effect of different axle load sizes is described in section 3.2, explaining the concept of Load Equivalency Factors. It is important to realise that the actual forces on the road are not equal to the static axle loads, but vary because of vehicle dynamics. This is the topic of section 3.3, where dynamic loads are described. Also, the effect of axle loads may be influenced by neighbouring axles, as explained in section 3.4. Another factor to be taken into account is the lateral wander of the traffic, elaborated in section 3.5. In section 3.6, the load sharing between twinned tyres is discussed. The influence of different tyres are described in section 3.7, introducing the concept of super single tyres. Finally, different kind of suspensions are described in section 3.8.

3.2 Relative effects of different axle loads For pavement design, but also to determine the pavement wear effect of different tyres, the pavement wear effects of different axle loads have to be determined. Generally this is described by a Load Equivalency Factor (LEF), where an axle load is said to be equivalent (producing equal pavement wear) to a number of applications of a reference (standard) axle load. The most well-known of such a LEF is the so called “fourth power law” which is expressed mathematically as follows:

N ref Nx

⎛W =⎜ x ⎜W ⎝ ref

⎞ ⎟ ⎟ ⎠



where Wx and Wref are axle loads and Nx and Nref are the corresponding number of load applications. The exponent 4 in the fourth power law was found in the AASHO Road Test, carried out in USA between 1958-1960.. However, it was not strictly constant in that test but varied from about 3.6 to 4.6. Later experimental and theoretical research has indicated greater variability in the exponent, but has not been conclusive. As an example, it was found in the OECD FORCE project that the exponent depends also on the extent of distress, the exponent being smaller in earlier phases than in later phases of failure. It must be understood that the fourth power law includes all distress modes. The most important at the AASHO road test were rutting (caused by subgrade deformation) and roughness (unevenness) of the road. Cracking had a minor effect and deformation of bituminous mixtures was not important. When individual distress modes are considered, different exponent values are found. E.g. COST 334 reports that cracking of bituminous layers has a value of 4 − 7, permanent deformation of the subgrade has an exponent of perhaps 3 − 4 and permanent deformation of bituminous layers a value of 1 − 2. As these values depend on many factors (a.o. material variations) and are not fully known, the stated values should be regarded as “best estimates” [3].


For use in pavement design, where the actual spectrum of axle loads has to be converted to an equivalent total number of standard axle loads, COST 334 concludes that the precise exponent value is not very important. For exponent values between 2 and 6, most actual axle load spectra were found to translate to roughly the same equivalent number of standard axles. (For low exponents, the multitude of smaller axle loads contribute to the bulk to the total equivalent number. For high exponents, the few overloaded axles contribute the most.) It was thus concluded that the “overall” value of 4 is well suited [3]. For detailed studies into pavement wear effects the exponent values for the individual distress modes should be distinguished. This is especially the case when conclusions should be drawn from accelerated tests at high load values. Besides being used within road design, the fourth power law has also been used for evaluating the road damaging potential of abnormal vehicles. E.g., in Denmark, a formula based on the fourth power law is currently used for classifying the road damage of Heavy Abnormal Transports, and is the base for taking decisions on allowed routes for heavy transports. This formula is described in some detail in section 5.1. However, according to Cebon [1], “the validity of the ‘fourth power law’ is questionable, particularly for current axle loads and axle group configurations; tyre sizes and pressures; road construction; and traffic volumes: all of which are significantly different from the conditions of the AASHO road test”. The Divine project comes to a similar conclusion, and write that “the use of the ‘fourth power law’ may not be appropriate in all situations unless the environment, traffic, pavement type and pavement construction methods are the same as, or very similar to, those in the AASHO Road Test” [2]. Note that the fourth power law was derived from measurements on heavy vehicles. To apply the law also on light vehicles, such as passenger cars, would imply a vast extrapolation outside the range of vehicle loads used in the AASHO experiments. The Swedish Road Administration advice against comparisons between heavy vehicles and passenger cars, with respect to the concept of an equivalent number of vehicles [8]. An example on how to apply the fourth power law on measured axle loads is taken from Denmark. From weighing of actual axle loads at weighing stations or weigh-in-motion bridges, the load equivalent of vehicle classes can be obtained for ordinary traffic using the fourth power law. Results from these measurements, compared with the ESAL resulting from maximum allowed weights of these vehicles, are shown in table below: Table 3.1: Load equivalent of vehicle classes obtained from weighing the actual axle loads Road wear in 10 T ESAL by Typical permissible Gross Typical Vehicle classes 4th-power law weight From From max. measured load loads 2-axle lorry 0.3 1,4 18000 kg Lorry with trailer 1,1 3,4 38000 kg Semitrailer 0.9 2,6 42000 kg Busses 0,4 1,4 18000 kg For more details regarding this study, we refer to Jan M. Jansen, Vejdirektoratet, Denmark.


3.3 Dynamic axle loading When a vehicle is not moving, the vertical (axle, wheel and tyre) loads it imparts on the pavement, due to the force of gravity, are constant. These are the static loads. When the vehicle is moving along a road, however, unevenness of the road will cause the vehicle to move up and down. This will cause a dynamic variation of the loads on the pavement, above and below their static values. The magnitude of this dynamic variation depends also on the vertical dynamics of the vehicle, including such factors as the mass and stiffness distribution of the vehicle structure, payload mass distribution, suspension and tyres, and on the road surface’s longitudinal profile and the speed of the vehicle. The variation generally increases with both speed and nature road unevenness. The magnitude of dynamic loads is mostly expressed as the Dynamic Load Coefficient (DLC), defined by the OECD as the ratio of the RMS (root mean square) dynamic wheel load to the mean wheel load. The RMS of the dynamic wheel load is essentially the standard deviation of the probability distribution of the total wheel load. The mean value reflects the static wheel load. So, the DLC is the coefficient of variation of the total wheel load. This is reported by OECD to range between •

5 − 10% for well-damped air suspensions and soft, well-damped steel leaf suspensions.

20 − 40% for less road-friendly suspensions (OECD 1992).

Dynamic loading increases pavement wear. Because of the power-law dependency of pavement distress on axle loads, the loads above the static load increase the pavement wear more than the decrease in wear due to the loads below the static load. Besides load magnitude, also frequency content is important for pavement wear. Most heavy vehicles have dynamic wheel loads either in the 1.5 − 4 Hz range, associated with bounce (up/down) and pitch (rotating forward/backward) motions of the vehicle body, or in the 8 − 15 Hz range, associated with axle-hop vibration. Axle hop vibrations are more significant if the pavement is rough and the vehicle speed is higher than approximately 40 km/h. As stated before, the tyre characteristics (vertical spring compliance and damping) influence the dynamic vehicle loads. Therefore, these should be considered when establishing pavement wear effects of different tyres.

3.4 Effects of different axles: single axles, tandem axles and tri-axles According to COST 334, tandem axles and tri-axles (see the definitions in Table 3.1) generally cannot be treated by summation of the effects of their constituting individual axles, because of two reasons: •

The load spreading of thick pavements may be such that the responses (stresses and strains) due to neighbouring axles in a tandem or tri-axle configuration may substantially increase the responses under the axle considered. Due to the non-linearity of the performance relations, such increased responses will lead to much more pavement wear than the summed responses of individual axles.

Due to the visco-elastic nature of bituminous materials, stresses and strains caused by an axle load need some time to relax after the axle has passed. When another axle arrives within that period, some residual stresses and strain will still be present, which may


compound with the stresses and strains caused by the new axle, resulting in higher total values. The effects of this mechanism are not well understood. For axle load limitations, this is reflected in maximum allowed tandem axle (and tri-axle) loads which are less than twice (or three times) the allowed single axle load. (Two axles at more than 1.8 m spacing are not considered a ‘tandem axle’ but a ‘double axle’ and are treated as two single axles.) Cebon concludes the opposite, and writes that “It is generally concluded that for equal damage to flexible and rigid pavements, tandem and triaxle groups can carry more weight than the same number of widely spaced single axles, because the primary response fields of nearby axles overlap”. The complicated relation between inter-axle spacing and relative road damage is illustrated in Figure 3.1, taken from Cebon, where the effect of tandem axle group spacing on theoretical fatigue damage in a rigid pavement is shown. The figure shows that there is an optimum axle spacing, and using either a wider or more narrow axle spacing will result in increased road damage. Moreover, this optimum axle spacing depends to a large extent on the thickness of the concrete slab.

Figure 3.1: The effect of tandem axle group spacing on theoretical fatigue damage in a rigid pavement (From Cebon, p.301) For pavement design purposes, however, the loads of tandem axles and tri-axles are mostly converted to a number of ‘equivalent standard axle loads’ (Nesal) by summing the contributions of the individual axles [3]. These individual contributions are then calculated using the Load Equivalency Factor described in Section 3.2., resulting in:

N esal =

nr of axles

∑ 1


⎛ Waxle ⎞ ⎜⎜ ⎟⎟ ⎝ Wstandard axle ⎠



Table 3.2: Definitions of different axle combinations Single axle

a single axle with more than 1.8 m spacing from other axles.

Double axle

a configuration of two axles, with more than 1.8 m spacing. (This is not a tandem axle, and the individual axles of a double axle are considered separately.)

Tandem axle

a configuration of two axles, with less than 1.8 m spacing between the axles. (Often the suspension of a tandem axle is such that the load on the tandem axle is shared rather equally between the constituent axles.) The maximum load is dependent on axle spacing and suspension, and is different for motor vehicles or for trailers and semitrailers. (The EC also distinguishes a ‘bogie’, being two axles with shared suspension and less than 1.3 m spacing).

Tri axle

a configuration of three axles, with relatively short longitudinal distance between the axles. (Often the suspension of the tri-axle is such that the load on the tri-axle is shared rather equally between the constituent axles.)

As an example on how different axle configurations are used in regulations, the maximum allowed loads in Sweden are shown in the table below: Table 3.3: The maximum allowed loads (in metric tons) in Sweden for different axle configurations and road classifications (BK1, BK2 and BK3). From [4]. BK 1

BK 2


a) Non driven axle




b) Driven axle




a) Inter-axle distance < 1,0 m




b) 1,0 m ≤ Inter-axle distance < 1,3 m




c) 1,3 m ≤ Inter-axle distance < 1,8 m




d) 1,3 m ≤ Inter-axle distance < 1,8 m,







a) The distance between the outer axles < 2,6 m




a) The distance between the outer axles ≥ 2,6 m




1. Axle load

2. Tandem axle load

and the driven axle has dual tyre fitment and air suspension, or equal suspension, or if the driven axles has dual tyre fitment and the load on each axle does not surpass 9,5 tons e) Inter-axle distance ≥ 1,8 m 3. Tri axle load


3.5 Tyre specific effects The current trend (in Europe) is smaller tyre diameter and higher tyre pressure. A smaller tyre diameter enables lower vehicle floors, which increases the volume that is possible to transport. A higher tyre pressure might have a positive effect on fuel consumption. Also, wide single tyres are beginning to replace the traditional dual tyres which can be explained by a lower weight, reductions in fuel consumption, and a lower cost of tyre wear. Although beneficial for transporters, the effect of these trends might be an increase to road wear since they imply a smaller contact area between a tyre and the road. This area, henceforth called “footprint” is an important road wear factor. The larger the footprint, the less the load distributed on every road area unit. The difference in road wear between single and dual tyres is thus not caused by the differences in tyre types as such. (COST 334, section 4.1) Single tyres are normally used on axles with loads below 8 ton, while dual tyres are the most common for axle loads above 8 ton. However, there exist wide base single tyres exist for axle loads of more than 10 ton. The use of single or dual tyres also depends on the axle formation. The more axles constituting the formation (tandem or tri-axle), the more common is the use of single tyres. The wide base single tires, is more commonly used in Europe. For example, as of 1997, wide-base singles comprised 30 percent of the tires in France and Britain compared to 2 percent in the U.S. [10]. The difference in size between one of the most extreme wide base single tyres and an ordinary dual tyre is shown in Fig. 3.2. There are many different types of wide-base tires available in varying sizes and inflation pressures. In addition to simply enlarging the size of the tire, there have been recent developments in tread and load-bearing technology that allow for lower inflation pressures and even greater surface area than the initial wide-base tires that were introduced in the early 1980s [10].

Figure 3.2: Wide-base Single Tire (445/50R22.5) compared to standard dual tyres (275/80R22.5). (Picture from Ref. [10], with permission from the author) However, although wide base single tyres might increase road damage through its smaller footprint and higher inflation pressure, it improves roll-over stability of the vehicle. This in turn has consequences for suspension design. As is discussed below, suspension stiffness is necessary for roll-over stability but increases road damage. It is therefore at least a theoretical possibility that the increased road damage induced by the change from dual tyres to super single tyres can be compensated for by reducing the spring stiffness. Also, the damping needed to reach the


minimum road damage is about 25 percent lower for wide single tyres than for dual tyres, mainly because of a lower unsprung mass. This improves the possibility to design an optimal suspension. (Cebon p. 453). Another important aspect to take into account when comparing single and dual tyre assemblies is the concept of unequal load sharing of the dual tyres. When comparing dual and single tyre assemblies at equal wheel load, generally the assumption is made that the wheel load is shared equally between both tyres of the dual assembly. However, in practice this might not be true. A number of reasons could cause an unequal load division (‘load imbalance’) between both tyres: 1. differences in vertical stiffness between both tyres, because of •

differences in inflation pressure (mainly due to poor maintenance)

different tyre structure ( due to e.g. different brands)

2. differences in vertical compression between both tyres, because of •

differences in diameter between both tyres

bending of the vehicle axle

transverse unevenness of the pavement surface

These reasons are illustrated in Figure 3.3.

Figure 3.3: Causes unequal load sharing between tyres in a dual tyre assembly (‘load imbalance’). From Ref. [3]. Axle- and tyre configuration also affect road damage in an indirect way, an effect that is denoted lateral wander. In practice, not all wheels will pass at the same lateral position in a road section. Vehicles generally follow a slightly zigzagging course between the bounds of the traffic lane, which is called lateral wander. Therefore, the wheel positions of consecutive vehicles will be transversely distributed over the pavement.


Detailed measurements and analysis of this distribution are reported by Blab [5]. He showed that the probability distribution of the vehicle positions is a Laplace distribution, in stead of the normal distribution that is often assumed. For a certain vehicle width and lateral wheel spacing, the probability distribution of the wheel (centre) positions is a Laplace distribution, too. However, the number of ‘hits’ by a tyre per cm pavement width is approximately normally distributed, due to the summation over various vehicle widths, wheel spacings, dual and single wheels, and various tyre widths. The difference is shown in Figure 3.4.



Figure 3.4: The difference between probability distribution of the wheel positions (a), and the number of hits by a tyre per cm pavement width (b). From Ref. [5]. Lateral wander distributes pavement loading, and hence pavement wear, over a larger area of the pavement. This prolongs the pavement service life. The effects of lateral wander are different for the different distress modes. They also may differ between dual tyres and wide base singles. COST 334 reported that the distress reduction factor of lateral wander on primary rutting compared to non-wandering loading were in the range 0.67 – 0.87, using different road structures and a range of tyres. Generally, the effects of lateral wander for the dual tyres that were tested were all very similar and close to those of a 385 mm wide single tyre. The effect of lateral wander for a 495 mm wide single tyre were smaller (about 30%) than for the other tyres. They also concluded that the beneficial effects of lateral wander for all tyres increase with decreasing pavement thickness.


3.6 Suspension effects As mentioned above (Section 3.3) vertical movements in the vehicle create a dynamic axle load that can be higher as well as lower than the static load. A road-friendly suspension decreases the magnitude of the vertical movements that are triggered by unevenness of the road, which in turn means a lower dynamic axle load, for a given static load The dynamic axle load is affected by the type of suspension on the vehicle and its ability to reduce movements in various frequency ranges. In general, the dynamic load increases with spring stiffness. The dynamic load is also sensitive to the damping ratio, the speed of which the amplitude of movements is reduced. EU (directive 92/7/EEC) defines a road-friendly suspension as a one with a sprung mass frequency no greater than 2 Hz and a damping ratio above 20 percent of critical damping. It is also required that the Coulomb damping ratio does not exceed 50 percent of the viscous damping. From a road wear perspective, the purpose of the suspension is to reduce motions to decrease the dynamic load. But the suspension characteristics have implications for road safety as well so there are certainly important trade offs. Reducing the stiffness in order to decrease the dynamic load also reduces the resistance to roll over. The traditional truck suspension is constructed using spring leaves. The characteristics of this type of suspension vary considerably under different road and driving conditions. The friction between the leaves might result in a locked suspension in case the pavement is smooth and the speed moderate. This is caused by sliding friction between spring leaves and has been found to adversely affect suspension performance. In the locked cases the suspension is stiff and the dampening abilities poor. Newer steel spring suspensions have been designed to remedy this problem by minimizing the contact area between individual leaves. With this construction stiffness is lower compared to the traditional design and a complete lock is not possible. The dampening effect is however reduced considerably why it is necessary to use hydraulic dampers. In recent years, air suspension has been developed. These provide a low stiffness and a smooth deflection characteristic. Air suspensions are used in combination with hydraulic dampers. Hydraulic dampers (shock absorbers) are common in modern trucks in combination both with leaf and air springs. Their force generating characteristics depend on the amplitude and frequency of the imposed motion. A semi-active damper is able to dissipate energy at a continuously, variable and controllable rate. It can be switched off when it is required to feed power into the suspension. (Cebon)


4. Experimental results from the literature 4.1 Overview The experimental results regarding vehicle influence on road deterioration are indeed wide spread. This is likely because of the many different vehicle features contributing to the road wear, which in turn is highly dependent on the kind of road, and the type of damage that is considered, which makes it hard to deduce the effects from a single feature alone. David Cebon made a summary of some of these effects in his book from 1999, (see ref. [1], page 321). The results, shown here in Fig. 5, are based on 19 references from 1965 − 1992, with the majority of the work carried out during the 1980’s. In that summary no distinction between different forms of distress modes, or different pavement thicknesses has been made.

Figure 4.1: Summary of literature on the effects of various vehicle features on road damage. From Ref. [1]. From the chart in Fig. 4.1, Cebon draws the following conclusions: 1. Applying a tandem suspension load to a single axle can be expected to increase road damage by a factor of up to 25 (first bar of chart)3. 2. Replacing dual tyres with wide-base single tyres may increase road damage by a factor of up to 10 (second bar of chart). 3

Cebon points out that this is not a particularly realistic scenario, but the included it for comparison purposes.


3. Unequal static load sharing between axles in a tandem suspension may increase road damage by a factor of up to 3 (third part of chart).

4. The fourth bar summarises the literature on the road-damaging effects of dynamic tyre forces. The average increase in damage caused by dynamic forces, compared to static forces alone is approximately 10% −40% (“mean damage” on the fourth bar of the chart, as calculated by the road stress factor and/or by neglecting spatial repeatability). This is small compared with the effects of tyre type and unequal static load sharing shown in the second and third bars. If instead a high degree of “spatial repeatability” is assumed, the relative increase in peak road damage caused by dynamic forces is in the range 2 − 14 (“peak damage” in the fourth bar of the chart), which is comparable with the effects of tyres and unequal static load sharing. The rest of this chapter compares results from the main references used in this report, with respect to vehicle influence on road deterioration.

4.2 Experimental findings: static axle load As stated in Section 3.2, the concept of number of equivalent standard axles, and the so called fourth power law, has been a highly debated topic. There has been many different reports in the literature regarding the exponent n in the load equivalence equation. This relation, comparing the damage caused by axles of different loads is

N ref Nx

⎛W =⎜ x ⎜W ⎝ ref

⎞ ⎟ ⎟ ⎠



where Wx and Wref are axle loads and Nx and Nref are the corresponding number of load applications. Cebon concludes that for flexible pavements, values of 1.3 – 6 has been reported in the literature, while for composite and rigid pavements, values are thought to be as high as 8 – 33. COST 334 makes a distinction between individual distress modes, and reports that cracking of bituminous layers has a value of 4 − 7, permanent deformation of the subgrade has an exponent of perhaps 3 − 4 and permanent deformation of bituminous layers a value of 1 − 2.

4.3 Experimental findings from using different tyres The COST 334 project, conducted research, in addition to a literature study, to draw conclusions on the effect from tire fitment on pavement wear. Specifically, wide single tires and dual tyres were compared. The results of the project were finalised in 2001, see Ref. [3]. In that project roads were divided into two categories: •

Primary roads: Defined as the network of principal roads in a country or state, generally comprising motorways (autoroutes, autostrade, etc) and other principal roads, state owned or otherwise. This network provides the major links between large urban areas and key national long-distance routes.

Secondary roads: Defined as the network of secondary roads in a country or state, generally comprising those roads owned by state, regional or local authorities, and acting as links between primary routes, but excluding some rural roads.


The road damage from a specific tyre and assembly is described with respect to a reference tyre in terms of Tyre Configuration Factor (TCF). This concept is introduced in that project, and the interpretation is straightforward: if a tyre has a TCF value equal to three, that means that for the same axle load, this tyre is three times as aggressive as the reference tyre. Different formulas for the TCF were derived for different pavement thicknesses and different distress modes. A tyre specific part taking the tread width, contact length and the tyre pressure ratio (with respect to the recommended pressure) into account is combined with a factor taking the tyre fitment into account. This last factor comprises factors for tyre characteristics regarding dynamic force transmissibility, and for potential load imbalance between the tyres of a dual assembly. The TCF formulae are shown below in table 4.1. Table 4.1: The TCF formulae from COST 334. Total factor for translation to real world conditions Pavement Tyre specifications thickness

Dual tyres

Wide base single tyres

Single tyre

Distress mode primary rutting Medium

(width/470) -1.68 * (length/198) -0.85 * (pres. ratio) 0.81 or (width/470)-1.65 * (pres. ratio) 1.42 * (diameter/1059) -1.12





(width/470) -1.68 * (length/198) -0.85 * (pres. ratio) 0.81 1.01 or (width/470) -1.65 * (pres. ratio) 1.42 * (diameter/1059) -1.12



Distress mode secondary rutting Thin

(total width/570) -2.57 * (pres. ratio)1.58





(total width/570) -2.57 * (pres. ratio)1.58





about equal to 1

Distress mode fatigue Thin

(total width/570) -2.88 * (length/198) -3.13 or (total width/570) -2.44 * (diameter/1059) -2.47





(total width/570) -1.36 * (length/198) -1.40 or (total width/570) -1.23 * (diameter/1059) -1.14





about equal to 1

Below TCF values for different tyres and assemblies reported in COST 334 are presented, using a reference tyre of width 235 mm put in dual fitment. In Fig. 4.2 − 4.4 the graphical overviews of the TCF values of the individual tyres are presented. Dual tyres are represented in green, ‘standard’ single tyres in red and wide base single tyres in blue. The TCF values for primary roads are represented by solid bars, the TCF values for secondary roads are striped. Note that for primary roads, only primary rutting is considered, while for secondary roads, it is the average of primary rutting, secondary rutting and fatigue cracking that is used. In most cases the TCF-


values for each of the distress modes considered for secondary roads, are of the same order. The only exception concerns steering axles, where secondary rutting accounts for roughly 60% of the total TCF-value.

Figure 4.2: TCF of common current and possible future tyres for towed axles.

Figure 4.3: TCF of common current and possible future tyres for driven axles.


Figure 4.4: TCF of common current and possible future tyres for steering axles. Based on the presented results, COST 334 makes the following conclusions: •

The values in the graphs show that there is not one unique answer to the question whether the common current and (possible) future wide base singles are better or worse with respect to pavement damage.

Replacement of duals by wide base singles, both on towed or driven axles, generally results in more pavement damage, for the observed range of common current and possible future tyres. This effect is more pronounced on secondary roads.

Replacement of single tyres on steering axles by wide base singles, however, results in a reduction of pavement damage.

Cebon cites several sources, exhibiting a wide span of results (see Cebon p. 321). The earliest reports, from 1965 and 1978, indicate that the pavement damage from wide single tyres are up to 7-10 greater compared to dual tyres. Later work, from 1991 and 1992, report an increased road damage between 1.1 – 4 for wide based single tyres. Another report (by M. Huhtala, VTT), from 1988, concludes that wide based single tyres are likely to cause 3.5 – 7 times more damage than dual tyres, and that the worst conditions are for thinner asphalt layers. That study also reports that a wide-based single tyre is only 1.5 times more damaging than an unevenly inflated dual pair with 500 kPa in one tyre and 1000 kPa in the other. Regarding these studies, Cebon notes that the large pavement damage factors in the studies that he cites comes from the use of the fourth power law applied on measured (or calculated) strains in the road under dual and wide single tyres. Quoting Cebon, “This raises the important question of whether a fourth power is appropriate, or, whether it may bias the results excessively”. Cebon concludes that various experimental and theoretical studies have indicated that single and wide based single tyres can cause up to 10 times more fatigue damage on thin flexible pavements, compared to dual tyres carrying the same static load. Moreover, tyre contact conditions are less important for rutting of thicker flexible pavements for which wide single tyres


are only 1.5 – 2 times more damaging than dual tyres, and that the tyre type has little influence on fatigue damage of rigid pavements. A TFK report from 1989 [9] presents equivalence factors for different tyre configurations, shown in Fig. 4.5.

Figure 4.5: The load equivalents for different tyre configurations and tyre dimensions as a function of axle load on two different asphalt thicknesses: 80 mm (left diagram) and 150 mm (right diagram). A dual fitment with 12R22,5 tyres with axle load 10 tons has been used as a reference and has the value 1. For all of the 5 configurations, three different tyre air pressures are indicated, where the bold line corresponds to recommended air pressure, and the upper and lower line corresponds to +20% and -20% of recommended air pressure respectively. From Ref. [9]. A recent study from 2005 [10] concluded that a wide-base single tire (445/50R22.5) caused similar, if not identical, pavement response as a conventional dual tire assembly. In fact, the two configurations for the three measured responses (asphalt strain, base stress, subgrade stress) produced, statistically, the same results. Regarding the influence from using different tyre pressures: COST 334 reports that the ratio of actual to recommended inflation pressure was shown to be influential for the cases of primary rutting on thick (and probably medium) pavements and secondary rutting on thin and medium pavements. An inflation pressure 10% higher than that recommended for the actual tyre load results in about 15% increase in pavement wear. Cebon reports (see Cebon p. 304-305) that several studies has indicated that fatigue damage due to tensile strain at the bottom a thin asphalt pavements is likely to increase rapidly with average contact pressure, while the inflation pressure has little effect on subgrade rutting. Based on asphalt pavement strain measurements, it has been reported that a 40% increase in tyre pressure would increase fatigue damage by 26%. Also, laboratory measurements on a 225 mm


thick asphalt road surface model have shown that rut depth development was approximately linearly related to the average contact pressure (independent of load). Another study on ‘high’ type pavements found that overinflation of conventional dual tyres by 170 kPa nearly doubles flexible pavement fatigue. Similar overinflation of wide base single tyres was even more critical, increasing fatigue by a factor of four. In contrast, the tyre inflation on rigid pavements had a moderate influence on fatigue.

4.4 Experimental findings regarding suspensions and dynamic loading According to Cebon a quite simple modification of a trailer steel suspension might reduce road damage by about 5 percent, see Figure 4.6, bar 1. First, the spring stiffness is reduced by half. Then rubber blocks are inserted between the spring leaves to reduce inter-leaf friction, that otherwise gives rise to hysteresis. However, this also eliminates the dampening effect of the spring leaves, so hydraulic dampers have to be added to the suspension system. Replacing the standard steel suspension on a tractor/trailer combination by an air suspension might reduce road damage by 5-6 percent, and optimising the suspension, a further reduction of 9% in road damage could be obtained, see Figure 4.6, bar 2. Experiments showed that adding a computerized dampening system reduces road damage with an additional 5-6 percent, see Figure 4.6, bar 3 (Cebon).

Figure 4.6: Comparison of three suspension for a principal road (from Cebon p. 561) The DIVINE project reports on a comparison between air and steel suspensions conducted as an accelerated test on an indoor pavement. In both cases the static load was 49 kN and wide single tyres were used. In brief the test showed that the steel suspension produced a 15 percent increase in road roughness (IRI) and 10 percent more cracking. Rutting was generally low during the test and no difference in mean rut depth between air and steel suspensions could be observed. Looking at the maximum rut depths though, it was concluded that “ if the maximum rut depth in the range 11-12 mm is taken as a critical level then the air suspension would achieve 45-65 percent more load cycles than the steel suspension to produce the same rutting distress”. Cebon summarises the general conclusion about the effects of suspension types on dynamic tyre forces (Cebon, p. 123-124):


All studies found dynamic tyre forces to increase with speed and road roughness

It has been noted that reducing suspension stiffness generally reduces tyre forces

Centrally –pivoted tandem axle suspensions such as ‘walking beams’ and ‘single-point’ suspensions were always found to generate the highest dynamic loads because of their lightly damped pitching modes at around 8-10 Hz. It has been noted, however, that these suspensions can be improved considerably by suitable use of hydraulic dampers.

‘Four spring’ tandem suspensions were generally found to generate smaller dynamic loads than walking beams. Torsion-bar and air suspensions generated the lowest loads.

It has been noted that modern single-spring parabolic suspensions with good hydraulic damping are “not significantly worse” than stiff air suspensions. Moreover, air suspensions without hydraulic dampers could generate significantly higher dynamic loads than leaf spring suspensions.

Triaxle suspensions were found to generate smaller dynamic loads than tandem suspensions in several studies.

It has been reported that varying the axle spacing of an air spring tandem suspension had negligible effect on the dynamic loads, whereas the Dynamic Load Coefficient generated by a four-spring tandem suspension varied considerably with axle spacing, depending on the speed and road roughness.

4.5 A model taking all factors into account Cebon describes a quantity known as the ‘road stress factor’, proposed by Eisenmann in 1975, which uses the assumption that road damage depends on the fourth power of the instantaneous (dynamic) wheel force. The equation for the road stress factor that accounts for the effects of wheel configuration and tyre pressures is written:

Φ =ν (η Iη II Pstat ) where



Φ = the road stress factor for each tyre

ν = the ‘dynamic road stress factor’ (takes suspension type into account) η I = parameter to account for the tyre configuration (single or dual tyres) η II = parameter to account for the tyre contact pressure Pstat = the static (average) tyre force Sometimes an additional factor is included to also account for the type of axle group (single, tandem or triaxle). Cebon concludes that considerable research effort has gone into quantifying these parameters for a variety of suspensions and tyre contact conditions. The road stress factor has also been the subject of considerable criticism (also from VTI [11]). According to Cebon, “The Road Stress Factor approach incorporates all of the uncertainties inherent in the fourth power law, which has itself been the subject of considerable criticism. It has three other highly questionable features: I. It assumes that the strain in the road surface is directly proportional to the instantaneous wheel force and neglects the sensitivity of road surface response to the speed and frequency of the applied loads and to the structural response characteristics of the road.


II. In using the mean value of the damage criterion, it implicitly assumes that road damage is spread randomly over the surface and does not account for any concentration of damage which may occur in the vicinity of particular roughness features. III. It assumes that each suspension system on a vehicle is dynamically independent and does not influence the tyre forces, and hence road damage, generated by other axles. Thus suspensions are compared through analysis of the wheel loads generated by individual axles of axles groups, rather than through analysis of road damage done by the whole vehicle.” The opinion on the use of the road stress factor seems to be split among the researches. Cebon reports that Ullidtz notes that accounting for dynamic loads using a number of equivalent standard axles calculated using a fourth power law (as per the Road Stress Factor), would result in “completely erroneous” results. He also quotes Morris, and according to him the road stress factor is “a plausible rule of thumb that can serve as a bench-mark for comparison with more analytical approaches”. COST 334 used the road stress factor approach to propose a formula for the damage contribution of a single passage of an axle on primary roads. The so called Axle Wear Factor (AWF) is a dimensionless factor relating the damage contribution of a specific tyre at a given axle load and axle configuration to the damage contribution of a single passage of a reference tyre with a reference axle load (10 tons).

⎛P⎞ AWF = TCF ⋅ ⎜ ⎟ ⎝ 10 ⎠ where



TCF = the Tyre Configuration Factor developed in COST 334. The factor depends on the total tread width (2 x single tyre tread width for dual fitment) and the diameter of the tyre, and thus takes the tyre fitment (single or dual) into account. The following formula is recommended: TCF = (tread width/470)-1.65 * (diameter/1059) -1.12 P = Axle load in tons.

The following remarks regarding this formula are made in COST 334:


Only primary roads are considered, so that only primary rutting is taken into account, which implies a power of 2 in the load equivalency factor.

The value of the factor for Axle Configuration is assumed to be equal to unity (1). It is generally accepted (OECD, 1983) that tandem or triple axles with axle spacings below 1.4 m, cause (slightly) more damage that two, or three passages, respectively, compared to a single axle of equivalent loading. For primary rutting, however, no specific information is available, and a factor of unity appears to be reasonable.

The value of the factor for Suspension Configuration is also assumed to be unity (1). Strictly, this value is valid only for those axles having air suspension, but since this is the case for most of the heavy goods vehicles under consideration, the assumption is again reasonable.

The traction effects of the drive axle on the pavement are ignored.

Correction factors for load imbalance and dynamic effects in the TCF formula should be ignored, since they add only about 1% of additional precision to the calculation of TCF.


5 Calculation models used in the Nordic countries Different calculation models have been used in the Nordic countries in order to compare the relative road wear due to heavy transports. In this chapter two of them are described.

5.1 Classification of special heavy transports in Denmark Vejdirektoratet in Denmark is currently using a model to classify special transports with heavy loads, which has been used since 2002. It is described in Ref. [6]. The model, which can be used on the entire Danish road network, is focusing on the relative road damage a heavy transport induced on a road, in relation to the damage produced by a standard heavy vehicle. The relative road wear is specified in the ESAL10 number, where the reference heavy vehicle axle of 10 ton load has ESAL10=1. The parameters that are included in the model for calculating ESAL10 are Axle configuration

Number of axle groups (axles that are separated by more than 1,8m are divided into different groups)

Number axles within each group

Distance between the axles within a group

The wheel load for each axle

Tyre configuration •

Tyre width

Distance between tyres on the same axle (single or dual fitment, or something in between)

Tyre air pressure

Suspension type

The formula is

Ai Bij C i Dij ⎛ pij ⎞ ⎜⎜ ⎟⎟ ESAL10 = ∑∑ mi 5 i =1 j =1 ⎝ ⎠ n




where n = number of axle groups mi = number of axles within group i Ai = Constant that accounts for both the number of axles within group i, and the distance between the axles within group i. There is a distinction between roads with a strong base (where only primary rutting is considered), and those with a weaker base (where also


secondary rutting, a permanent deformation below the pavement, occurs). For the weaker roads, Ai = the number of axles within the group, independent of the inter-axle distance. For stronger roads, it is assumed that a group of axles with a short inter-axle distance is producing less damage to the road, compared to the same group of axles with a larger interaxle distance. Thus, on this kind of roads, Ai is lower than the number of axles. A smaller inter-axle distance leads to a smaller value of the constant. Table 5-1 Ai

Strong road

Weak road

Number of Inter-axle

All inter- axle



distance (m) 1.0






1.05 1.25 1.40 1.55 1.75 2.00


1.50 1.90 2.20 2.50 3.00


1.70 2.35 2.80 3.30 4.00


1.90 2.80 3.40 4.05 5.00


2.00 3.20 4.00 4.75 6.00


2.20 3.60 4.60 5.45 7.00


2.35 4.00 5.15 6.10 8.00

Bij = Constant that takes the tyre fitment on each axle into account. If dual fitment is used (or if the distance between tyres on an axle is less than the tyre width + 8 cm), Bij = 1. If the tyre fitment is single (if the distance between tyres on an axle is more than 2,5x “the tyre width”), Bij is given a number that is larger than one, and which depends on the tyre width. A wider tire leads to a lower value on the constant. If the distance between the tyres falls in between the definitions of single and dual fitment, Bij is supposed to be determined by interpolation between the single and dual values of the constant, taking the distance between tyres into account. The values of this constant for single fitment are: Table 5-2 Tyre width (mm) Bij 256










Ci = Contant that takes the type of suspension into account. The following suspension types are distinguished between:


Table 5-3 Suspension type


Leaf spring


Parabolic spring ? Coil spring Rubber


Hydraulics Air Oil No suspension


Dij = Constant that accounts for the air pressure of the tyres on a specific axle. A differentaion is made between single and dual fitments, and whether primary rutting or deformations below the pavement is considered. Dij is almost linear with respect to the air pressure, as shown in the figure below. The constant Dij 1.8 Primary rutting Subpavement deformation: Single fitment Subpavement deformation: Dual fitment












7 8 Tyre air pressure [bar]



Figure 5.1: The constant that accounts for tyre pressure Pij = The load (in metric tons) on one tyre on a specific axle. Note that the road damage described by ESAL10 is “the road damage per wheel track”. I.e., the number of wheels on the axles are not explicitly taken into account. The number of wheels, are indirectly used in the calculation of ESAL10 , since the wheel load Pij, depends on the number of wheels on the axle, and the number of wheels on an axle may also affect the tyre fitment constant Bij. According to the model, however, two identical vehicles driven side by side on a road produce the same damage to the road as one of the vehicles would do by itself.


5.2 The Swedish Road Administration method of calculating the equivalent number of standard axles In Sweden, the equivalent number of standard axles per heavy vehicle is a crucial parameter for road dimensioning. In ATB VÄG 2005 [12], which is the Swedish Road Administration’s common technical description, containing the demands on construction and maintenance and of roads, the equivalent number of standard axles per heavy vehicle is called the B-factor. The B-factor is the average number for all the heavy traffic using the road. The standard axle (see Fig. 5.2) has a load of 100 kN, and is supposed to have twin mounted wheels with the load evenly distributed. Each wheel is assumed to have a circular contact patch between tyre and road surface, and the contact area is exposed to a load with a inflation pressure of 800 kPa.

Figure 5.2: Schematic picture of the standard axle used in Sweden, specified by ATB VÄG 2005. From Ref. [12].

Historically, since 1994 a factor 1.3 has been used. However, in ATB väg 2005, section C6, methods for determining the B-factors are given: •

To determine the B-factor measurements of gross vehicle weights and axle loads shall be carried out. The measurements must be performed during a period of at least 7 days. The B-factor shall then be calculated from these measurements. These measurements could be performed using the B-WIM (Bridge Weigh In Motion) technique described in VV Publication 2003:165. In that report a number of measurement results are presented which could serve as a support for choosing the B-factor. For calculation method of the ESAL (equivalent number of standard axles) for each heavy vehicle type , ATB VÄG 2003 is referred to, which shows an example on how an axle of 16 tons (apparently not making any difference between single, tandem or triaxles) results in 6.7 standard axles of 10 tons, using the fourth power rule. The corresponding formula of the ESAL for each heavy vehicle type that is recommended by ATB VÄG 2003 can then be written


⎛W ⎞ ESAL = ⎜ ⎟ ⎝ 100 ⎠



where W is the weight of the specific axle in kN. •

If measurements cannot be carried out, ATB VÄG 2005 suggests that four or five of the most common heavy vehicle classes are used, with weights estimated from local experience. Then the fourth power rule is applied on each axle.

In a recent report from the Swedish Road Administration [14], concerning B-WIM measurements during 2004-2005, another way of using the fourth power rule for calculating ESAL is demonstrated. In section 4.5 of that report, as an illustration on the effects of overloading, four examples on how ESAL values should be calculated are shown. No formula is given, but from private communication with Tomas Winnerholt of the Swedish Road Administration, it was clarified that the fourth power rule together with factors taking the axle type into account has been used. More specifially:


i ⎛W ⎞ ESAL = ∑ ⎜ i ⎟ ∗ k i n =1 ⎝ 10 ⎠


number of axles or axle groups

Wi =

axle (group) weight for axle (group) i (ton)

ki =

effect reduction factor for axle (group) i


k = 1 for single axle k = (10/18)4 = 0,0952 for tandem axle k = (10/24)4 = 0,0302 for tri-axle The factors has been chosen with the maximum allowed loads (in metric tons) in Sweden for different axle configurations (se Table 3.3) in mind, so that a single axle of weight 10 ton, or a tandem axle of weight 18 ton, or a triple axle of weight 24 ton, each results in ESAL=1. This is the current approach on how the Swedish Road Administration is calculating ESAL values. It is based entirely on the legal loads and axle distances. E.g., if the interaxle distance is only marginally longer than what has been defined by Swedish regulations as a tandem axle, the axle will be treated as a single axle. It should be noted that this approach, taking the entire weight of a tandem or tri-axles axle to the power of four, is different from the more common method described in Section 3.2, in which loads of tandem axles and tri-axles are converted to an ESAL by summing the contributions of the individual axles. The following examples are shown in Reference [14]:


Figure 5.2.1: 60 tons equal 3.1 ESAL For a configuration as in Figure 5.2.1, the calculation is:





⎛6⎞ ⎛ 18 ⎞ ⎛ 18 ⎞ ⎛ 18 ⎞ ESAL =⎜ ⎟ * 0.0952 + ⎜ ⎟ * 0.0952 + ⎜ ⎟ * 0.0952 + ⎜ ⎟ = 3.1 ⎝ 10 ⎠ ⎝ 10 ⎠ ⎝ 10 ⎠ ⎝ 10 ⎠

Figure 5.2.2: 66.2 tons equal 4.85 ESAL For a configuration as in Figure 5.2.2, the calculation is:





⎛ 8.7 ⎞ ⎛ 20.9 ⎞ ⎛ 21.2 ⎞ ⎛ 15.4 ⎞ ESAL =⎜ ⎟ = 4.85 ⎟ * 0.0952 + ⎜ ⎟ * 0.0952 + ⎜ ⎟ * 0.0952 + ⎜ ⎝ 10 ⎠ ⎝ 10 ⎠ ⎝ 10 ⎠ ⎝ 10 ⎠


Figure 5.2.3: 20 tons equal 2 ESAL

Figure 5.2.4: 20 tons equal 3.1 ESAL

For a configuration as in Figure 5.2.3, the calculation is: 4


⎛ 10 ⎞ ⎛ 10 ⎞ ESAL= ⎜ ⎟ + ⎜ ⎟ = 2 ⎝ 10 ⎠ ⎝ 10 ⎠ For a configuration as in Figure 5.2.4, the calculation is: 4


⎛ 13 ⎞ ⎛ 7 ⎞ ESAL =⎜ ⎟ + ⎜ ⎟ = 3.1 ⎝ 10 ⎠ ⎝ 10 ⎠


6. Acknowledgements The authors would like to thank Leif Sjögren for contributing with material to this report. The members of NVF ‘Fordon och Transporter’ are also thanked for valuable comments and suggenstions.


7. References [1] D. Cebon, “Handbook of Vehicle-Road Interaction”. Swets &Zeilinger Publishers, Lisse, The Netherlands (1999). [2] Dynamic Interaction between Vehicle and Infrastructure Experiment, DIVINE Technical Report, DSTI/DOT/RTR/IR6(98)1/FINAL, OECD (1998). [3] COST 334 – “Effects of Wide Single tyres and dual Tyres” Report, Chapter 4, version 29, November 2001 [4] U. Isacsson, “Interaktion mellan fordon/miljö och väg”, KTH, (2004) [5] R. Blab “Die Fahrspurverteilung als Einflussgröße bei die bemessung des Straßenoberbaus; Mitteilungen des Institutes für Strassenbau und Strassenerhaltung” TU Wien, ISTU, Heft 5; Institut für Strassenbau und Strassenerhaltung TU Wien; 228 pp.; Wien, AT (1995) [6] Jan M. Jansen, Særtransporters vejslid – Klassificering av køretøjer. Rapport nr 269, Vejdirektoratet. 2002 [7] The Handbook of Highway Engineering, CRC Press, Taylor & Francis Group. 2006 [8] Private communication with Leif Sjögren, VTI. [9] TFK rapport 1989:5 Optimalt Däckval för Tunga Fordon, Fältmätningar av Vägpåkänning, Transportekonomi och Vägkostnader. L. Djärf, M. Huhtala, M. Johansson, E. Samuelsson. [10] A. L. Priest, D. H. Timm, and W. E: Barrett, NCAT report 05-03 Auburn University: Mechanistic comparison of wide-base singe vs. standard dual tyre configurations. June 2005 [11] G. Magnusson, H.E. Carlsson, and E. Ohlsson, “The influence of heavy vehicles’ springing characteristics and tyre equipment on the deterioration of hte road’, VTI (Translated by TRRL as WP/V&ED/86/16, 1986), Report Number 270, 1984. [12] ATB VÄG 2005. VV Publication 2005:112. [13] BWIM-mätningar 2002 och 2003 Slutrapport. VV Publication 2003:165 [14] BWIM-mätningar 2004 och 2005 Projektrapport. VV Publication 2006:136


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