1 1. Introduction

Autonomous trucks are programmed to follow a certain predetermined path along the highway lane. Given with a assumption of 100% autonomous trucks using the lane, with current selection of a zero wander mode in which the truck will follow a straight line path without any lateral wander, a group of trucks would pass through the same path all the time resulting in channelized loading. As the channelized loading frequency increases, the pavement would prematurely fail, either due to rutting or fatigue cracking. If the predetermined path is programmed in such a sway that the vehicle can maneuver laterally inside the lane to minimize the loading on the same specific point on the pavement, the risk of channelized loading can be reduced.

Human driven trucks follow a normal distribution of lateral position in the lanes [1]. A conventional truck platoon with consists of 3 to 8 trucks in a group can have detrimental effects on the pavement structure. In case of human driven trucks, around 80% of loading is channelized along the middle of the lane, which corresponds to acceleration in pavements fatigue damage [2]. However, in case of autonomous trucks, the pavement damage can be reduced inside the truck platoon by using a certain lateral wander mode so that the channelized loading is minimized.

A truck platoon affects the pavement structure based on factors such as speed of the trucks inside the platoon, headway of trucks inside the platoon, loading class and axle configurations of trucks inside the platoon. However, the most contributing factors related to truck platoons damage to pavement is the concentration of loading on the same point of the pavement. Higher speeds result in reduced accumulation of strains under the asphalt layer as well as on top of subgrade layer [3]. Occurrence of creep related distresses is minimized at higher speeds. Headway of the trucks is selected to reduce fuel consumption and adequate reaction time for stopping distance. Current headway times used for trucks may favor fuel efficiency and safety, but its effect on pavement damage is compromised.

Loading class and axle configurations can affect the damage difference between different platoons. Modular truck types with loads exceeding 50 Tons can be damaging if used in platoons. Hence, a platoon size can affect the pavement response during its pass. Platoon size should be carefully controlled and limited based on total number of trucks and total accumulated load on the pavement. Distance in consecutive platoons can be increased to give a relief time to pavement when the next platoon arrives. With the use of preprogrammed lateral wander mode, the damage to the pavement from each platoon can be minimized.

In the existing literature, truck platoon analysis has only been conducted based on headway distance calculations. However, the use of different ruck mix types separated by the axle configurations combined with headway distance and interplatoon distance has not been performed yet. Therefore, this research includes the use of number of trucks in the platoon combined with the different axle configurations grouped by their classes in each platoon type. Moreover, the platoon analysis further includes the use of two lateral wander modes for autonomous trucks for a thorough comparison of aforementioned parameters.

This paper has been further divided in four different sections. Section 2 is the literature review section, where the previous research conducted on the impact of platoon size and headway distance has been discussed. The research is this section is further divided into 3 subsections based on the parameter that effects the platoon performance. Parameters such as loading intervals refer to the pavement recovery time, which is crucial for the pavements' longevity. Moreover, each research in the past has presented detailed analysis on headway distance of trucks, which vary with each research. Section 3 presents the detailed methodology, starting with the pavement type used for this research and its material parameters. Since finite element modelling is used, therefore, it is important to select a relevant material model where Prony series coefficients have been used to better understand the viscoelastic response of pavement under loading. Different grouping of axle configurations based on platoon types are included since it affects the selection of best performing scenario with the use of uniform and lateral wander modes. Section 4 presents the results obtained from simulations conducted for the design traffic and various strain profiles in longitudinal and transverse crossections are provided where each scenario is compared against another. This section presents an in depth analysis of profession of strains under traffic loading, which leads to understanding of pavement longevity in terms of rutting and fatigue cracking. In Sect. 5, findings of this research are concluded and further recommendations are provided with experience obtained from this research. Limitations and future research directions are also provided since there is a potential for further enhancement of this research and this research provides a foundation to perform next research with different pavement cross section types and axle configurations.

2 Literature review

In truck platoon, multiple trucks drive at fixed distances between them with the use of LIDARS and wireless communication networks at a constant speed efficiently [4]. Most efficient type of typical platoon matchmaking is a Real time platooning where the trucks find their match with other tracks based on similarly in routes moments before any departure interval, usually in case of stop breaks or starting the journey in the beginning [5]. The most common concept of truck platoons consists of the leading vehicle that is followed by one or more following vehicles and the following vehicles brake, steer and accelerate according to the leading vehicle [5]. Increased efficiency and decreased fuel consumption of up to 4.7% with the use of truck platoons as a result of increased aerodynamics occurs. The concept of truck platooning is very much in conjcution with progression of autonomous trucks in case of phase 3, in which trucks will have 100% autonomy with no human involvement [6].

2.1 Loading intervals

Truck platooning is considered to be beneficial for traffic safety and fuel consumption however, repeated loading with minimum loading intervals can accelerate pavement fatigue. Song et al. [7] analyzed the effect of number of variables, lateral wander and loading interval in a truck platoon using finite element modelling. Simulations were run based on various lateral offset modes for the following trucks in a platoon, along with corresponding fuel savings for each scenario. Results showed that a lower number of trucks is preferred in case of fuel savings with optimum number of trucks reduced to two using lateral offset which decreases the fatigue damage by 30% and fuel consumption by 8%. Al Qadi et al. performed detailed analysis on impacts of truck platoons on pavements by proposing an optimization method for reducing pavement life cycle costs without compromising the fuel savings by a truck platoon. Finite element modelling was used to analyze the loading intervals, lateral wander scenarios to optimize the use of platoons. Results showed that an optimized truck platoon pattern would decrease pavement life cycle costs by 48% compared to conventional channelized loading of human driven truck platoons.

2.2 Effect on pavement response

Melson [8] performed traffic congestion and mechanical impact analysis of truck platoons on transport infrastructure. In the field of mechanical impact analysis using the pavement design software, it was suggested that lateral wander of tires had a significant impact on fatigue propagation and permanent deformation in the pavement structure. Results showed that without considering lateral wander, up to 35% of decrease in fatigue life can occur for a 20 year design period with maximum increase in maintenance costs of 46%. Elwardany et al. [9] investigated the effect of truck platooning on surface wear related to raveling, fatigue damage and permanent deformation using Dutch pavement design strategies. Results showed that with conventional use of traffic lane in the pavement, truck platoons would negatively affect the fatigue life and permanent deformation in the pavement and further optimization strategies are required to mitigate the extensive pavement damage. Marsac et al. [10] conducted optimization analysis by incorporating the lateral wander option for the trucks inside the platoon using pavement design software Viscoroute.

2.3 Truck spacing

Spacing of trucks inside the platoon and space between each platoon is a function of rest period given to the pavement to properly recover in terms of permanent deformation and fatigue damage. Nejad et al. [11] has identified the effect of prolonged rest period on decreased deformation in pavements. Kim and Kim [12] have identified minimum amount of rest period beyond which the permanent deformation may occur. Al Qadi et al. [13] found that with a 10 ft spacing between trucks, around 99.5% of vertical elastic strain is recovered and the recovered strain amount reduces as the spacing gets smaller than 5ft. Jimenez et al. [14] stated that provision of rest periods can allow for applications of loads until failure caused by fatigue. Al Mansoori et al. [15] suggested the use of extended rest period for asphalt mixtures to minimize permanent deformation. Zeiada et al. [16] investigated the effects of rest period and loading waveform patterns on laboratory prepared asphalt specimens on fatigue damage. Results showed that the strains occurring from rest type loading were four times less than that of continuously loading conditions. Table 1 shows the summary of research conducted on truck platoons.

Table 1 Summary of research on truck platoons
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3 Methodology

The research methodology consists of setting out the headway distance ranging from 2 to 5 m with an increment of 1 m in each scenario, coupled with selected platoon types ranging from PT-1 to PT-3 as shown in Fig. 1. A combination of these scenarios for each platoon type with various headway distance values of 2–5 m is made, along with grouping of uniform wander mode and zero wander mode in the Finite Element model. Furthermore, analysis is done in the model, where optimum headway distance and optimum platoon types are identified based on micros trains evaluated. After selection of the optimum headway distance and platoon type, rutting and fatigue cracking analysis is done against uniform wander and zero wander modes for each scenario of headway distance values.

Fig. 1
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Methodology flowchart

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3.1 Pavement details

Conventional asphalt pavement consisting of asphalt layer, base course and subbase course resting on top of subgrade is considered for this analysis. Thickness of subgrade layer is kept at 2 m for modelling in ABAQUS. To accommodate a complete platoon in the model, length of the model is kept at 60 m and width of the model corresponds to a lane width of 3.5 m as shown in Fig. 2. The length of the model allows for analyzing various platoons and headway distances in this research.

Fig. 2
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Pavement details

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For finite element modelling, the elastic parameters are required for analyzing the impact on the pavement structure based on the number of layers, thickness of each layer with their corresponding elastic moduli and Poisson’s ratio values. Elastic modulus is kept at a closer value to the elastic modulus values of the underlying unbound layers for accurate in depth detection of progressions of microstrains through the whole pavement structure. Therefore, the comparative analysis can be conducted efficiently by individually monitoring the impacts of aforementioned parameters. Therefore, validated pavement layer parameters in the form of elastic moduli and Poisson's ratio have been taken from Cheng et al. [17] as shown in Table 2.

Table 2 Pavement layer properties
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3.2 Material model

For determining the linear viscoelastic behavior of asphalt in finite element modelling, Prony series parameters have been used. Values of complex shear modulus obtained from tensile strength tests of asphalt specimen are converted into Prony series coefficients for time dependent viscoelastic behavior of asphalt in finite element modeling. Hence, a generalized Maxwell model is used to establish the Prony series against several Maxwell elements as shown in Fig. 3.

Fig. 3
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Illustration of a generalized Maxwell model

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In Prony series, stress and strain of a linear viscoelastic system are represented based on a power law [18]. The general form of Prony series is shown in Eq. (1) and (2).

$$g\left(t\right)=1-{\sum }_{t=1}^{N}{g}_{i}(1-{e}^{\left(\frac{t}{{\tau }_{i}}\right)})$$
(1)
$$g\left(t\right)=\frac{G(t)}{G(t=0)}$$
(2)

\(g\left(t\right)\) is the ratio of shear modulus at time \(t\), \(G(t)\) is the shear modulus at \(t\) = 0, \(G(t=0)\), \({\tau }_{i}\) and \({g}_{i}\) are prony series coefficients. \(N\) is the number of terms in the Prony series. Relaxation modulus is \(E(t)\) is used to calculate the shear modulus \(G(T)\) as shown in Eq. (4).

$$G\left(T\right)=\frac{E(t)}{2(1+\mu )}$$
(3)

Furthermore, the long term shear moulus \({G}_{\infty }\) and long term shear modulus \({G}_{0}\) at time t = 0 can be covetered into each other by prony series coeffiecients \({g}_{i}\). In the following equation \({g}_{i}\) is the weighted modulus of relaxation time \({t}_{i}\) as shown in Eq. (4) and (5).

$${G}_{\infty }={G}_{0}\left(1-{\sum }_{i=1}^{N}{g}_{i}\right)$$
(4)
$${G}_{0}=\frac{{G}_{\infty }}{1-{\sum }_{i=1}^{N}{g}_{i}}$$
(5)

However, the value of complex shear modulus \({G}_{\infty }\) is calculated using the elastic modulus \({E}_{\infty }\) and Possion’s ratio \(v\) as shown in Eq. (6).

$${G}_{\infty }=\frac{{E}_{\infty }}{2\left(1+v\right)}$$
(6)

In this research, the validated Prony series coefficients form the field samples of asphalt layer have been taken from Deng et al. [19]. Possion’s ratio used in this case is 0.35 and calculated the instantanaous modulus for the elastic modulus of asphalt layer is 6459 MPa as shown in Table 3.

Table 3 Prony series parameters
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3.3 Truck loading configurations

The class-1 truck as shown in Fig. 4 is a A40 European truck with maximum gross weight of 40 tonnes. It is a semitrailer with the attached trailer having tridem axles with single tires. For the tractor head, the steering axle has single axle with single tires and the drive axle has dual tires with single axle. The wheelbase if 7.555 m with center to center spacing of 1.31 m between each axle in the trailer. The steering and drive axle have wheel types of 295/80R22.5 and the trailer axles have tire types of 385/65R22.5. Dimensions, axles wight and configuration are taken from John Aurell et al. [20].

Fig. 4
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Class-1 truck details

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Class-2 truck is a rigid body truck as shown in Fig. 5. It has a maximum gross weight of 26 tonnes. The wheelbase is limited to 5.5 m in this truck, with center to center spacing of dual tires of 1.31 m. The drive axle has 295/80R22.5 type wheel and dual tandem axles also have 295/80R22.5 type wheels.

Fig. 5
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Class-2 truck details

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Class-3 truck is also a rigid boy truck included in the traffic mix as shown in Fig. 6, having two single axles working as drive axles and tandem axles with dual tires in the rear. Maximum gross weight is 34 tonnes having a slightly longer wheelbase of 5.6 m with center to center spacing of rear axle wheels of 1.37 m. the center to center spacing between the front drive axles is 2 m. Class-3 truck types are commonly used for transport of construction materials. The first two drive axles are single axles with 295/80R22.5 tires and rear axles are tandem axles with dual tires 295/80R22.5.

Fig. 6
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Class-3 truck details

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Since a detailed analysis has been conducted for calculating the tire pressure to be used for simulations, therefore the keyword also contains’’tire pressure’’. With various combinations of axle loads and tires types, tire contact pressure has to be calculated under each tire, which depends on tire dimensions, loading on the tire and tire inflation pressure [21]. The size of tire contact are can also vary based on the tire inflation pressure [22]. Tire deflection, therefore, relates to tire contact area, and it has the highest effect on contact area size at lower inflation pressures. Tire deflection is represented Eq. (7).

$$\Delta = 0.008 + 0.001 \times \left( {0.365 + \frac{{170}}{{p_{i} }}} \right) \times G_{k}$$
(7)

where \(\Delta \) is tire deflection (m), \({p}_{i}\)—tire inflation pressure (kPa), \({G}_{k}\)—wheel load (kN). Hendy et al. [23] has previously used the tire deflection to calculate contact area as well as nominal tire contact pressure. Following Eq. (8) shows the calculation of contact area of the tire.

$$A={b}^{0.8} \times {d}^{0.8} \times {\Delta }^{0.4}$$
(8)

The following Eq. (9) is used for calculating nominal tire contact pressure.

$$p=\frac{G}{{b}^{0.8} \times {d}^{0.8} \times {\Delta }^{0.4}}$$
(9)

Where \(A\)—contact area (m2), \(G\)—vehicle mass (kN), \(b\)—width of unloaded wheel tire (m), \(d\)—diameter of unloaded wheel tire (m). Load on each tire in the axle and tire inflation pressure have been used to validate the values of tire contact area and tire contact pressure from Elhamrawy [24]. Since it has been found that the tire contact area pattern is rectangular [25], and overestimation of tensile strain values at bottom of asphalt layer occurs if a circular contact area is used [26], therefore the following equation is taken from [27] for calculation of longitudinal and lateral dimensions. The results obtained from equation above can be plugged into Eq. (10).

$$L=\sqrt{\frac{{A}_{c}}{0.5227}}$$
(10)

where \(L\) is the constant that is used to measure longitudinal and lateral dimensions of contact patch using the values of 0.6 \(L\) and 0.8712 \(L\) respectively and \({A}_{c}\) is the area of tire conact patch calculated from equation. The tire type and its correposing load, tire inflation pressure, tire contact pressure and contact patch dimensions are shown in Tables 4, 5, and 6.

Table 4 Tire pressure and load details for the Class-1 truck
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Table 5 Tire pressure and load details for the Class-2 truck
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Table 6 Tire pressure and load details for the Class-3 truck
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3.4 Platoon types

Number of trucks in a platoon can affect alter the pavement damage. With higher number of trucks in a platoon the time of continuous axle loads increases thereby resulting in earlier damage to the pavement. Song et al. [7] suggested using no more than 4 truck platoons, when compared with the fatigue damage from a 2 truck platoon, a damage of more than 30% occurs when using greater than 4 trucks. Melson et al. [8] studied the effect on transport costs and impact on pavement with various number of trucks in a platoon. Results showed that use of four trucks in a platoon generate the lowest transport related costs. However, the study didn't include the effect of number of trucks in a platoon on the pavement damage. Three different platoon types based on different axle configurations are chosen as shown in the Fig. 7.

Fig. 7
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Platoon types chosen

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Traffic volume has been assumed to be 12 trucks using the tested highway section of 60 Meters. The rigid body trucks contribute to 50% of the traffic mix which leads to 25% of class 2 and 25% of class 3 trucks in the mixes. Three different truck platoons have been organized to study the effect of different axle types in different platoons on pavement performance. First platoon type is a base scenario where only semitrailers are considered in the traffic mix; other scenarios are analyzed with reference to PT-1. Platoon configuration is presented in Table 7.

Table 7 Platoon configuration details
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In case of PT-2, the idea is to isolate the traffic based on rigid body and semi trailers. One passage of a 4 semitrailer truck platoon will do a different amount of damage than one passage of only the rigid body trucks, with the same amount of trucks in the platoon. Furthermore, the damage from all the platoons of PT-2 is accumulated and compared with the damage caused by PT-3, in which trucks are placed inside the platoon with the balance of maximum load of the platoon. For each platoon type, three platoon groups are simulated to evaluate the interplatoon spacing. An ideal PT-3 consists of two semi trailers and two rigid body trucks. The platoon size has been limited to 4 trucks of any configuration type.

Table 8 explains the truck volume assumed for each truck type and number of platoons needed for a specific truck for each truck type. Since in a PT-3 type platoon, a random traffic mix means more truck platoons are needed to cover the entire traffic with assumed traffic of 12 trucks.

Table 8 Truck types in platoons
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3.5 Incorporation of zero wander and uniform wander modes

For the use of zero wander mode, it is assumed that the trucks in the platoon would follow a straight path without any transverse movement with the lane. While performing analysis in FE mode, only the headway distance is changed among the trucks inside the platoon from 2 to 5 m. A typical scenario in case of PT-3 platoon while using a zero wander mode is shown in Fig. 8.

Fig. 8
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Visualization of zero lateral wander mode

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In this research, the uniform wander mode is selected based on the lateral wander of each truck in the platoon along a fixed path. Each truck in the platoon is given a fixed path to follow. Following this method, there is no overlapping of consecutive trucks in the platoon. Therefore, when each truck in the platoon passes through a fixed point on the pavement, repeated loading of trucks in the platoon on the specific point on the pavement are minimized.

In case of uniform wander mode, each truck in the platoon is given a predetermined base path and is allowed to laterally move with respect to that base path as shown in Fig. 9. In case of PT-3 platoon, the leading truck is positioned at exactly in the center of the lane with 1 m distance from the edge of the pavement to either edge of its outermost tires. For the second truck in the platoon which in this case is a class-2 truck, 0.5 m distance is provided from the left edge of the pavement and 20 cm for the third truck.

Fig. 9
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Visualization of uniform lateral wander mode

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3.6 Finite element model details

The 3D model has a length of 60 m to accommodate the platoons and trucks along the longitudinal direction, a width of 3.5 m and depth of 2.8 m with a greater thickness value given to the soil layer. The bottom of the model is simulated as elastic foundation in terms of friction characteristics to simulate higher thickness of natural soil layer underneath. The model consists of 8 node linear brick elements with reduced integration and hourglass control CPE8R. The model consists of 33,251 elements with element size of 220 for increased accuracy and reduced computation time as shown in Fig. 10.

Fig. 10
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3D model mesh

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The interaction between the pavement layers is kept as normal surface-to-surface contact with hard and frictionless characteristics. For the boundary conditions, the bottom of the model is simulated as an elastic foundation, along the X axis, horizontal movements along X axis are not allowed and along Z axis, horizontal movement along Z are not allowed. Vertical movements are allowed in both planes of symmetry as shown in Fig. 11.

Fig. 11
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Loading and boundary conditions for the model

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4 Results and discussion

For a design life of 15 years with 1.4 million ESALs, simulations are conducted with the loading application performed by dload subroutine. The stress and train values at various components and intervals in them model are then gathered for analysis. The distribution of strain values can be observed in Fig. 12. As observed a higher concentration of stresses is occurring along the rear trailer axles of the Class-1 truck and later it occurs between the Class-1 trucks with its second pass and the Class-3 truck.

Fig. 12
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S (mises) as observed form the simulations in uniform wander mode

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Figure 13 shows the stress profile generated under each passage of all the trucks in a PT-3 platoon. Usually, the higher concentration of stresses occur at rear axles of Class-1 truck and well as front axles of Class-2 trucks due to higher axle loading and shorter wheelbase. Furthermore, the steering axle of the second platoon’s truck can be seen at the end of the model.

Fig. 13
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Observed S(22) after the simulations in uniform wander mode

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Figure 14 shows the pattern of stresses induced in the pavement as a result of zero wander mode. In case of zero wander mode, channelized loading occurs and under axle loads of higher magnitudes in case of drive axle of class-2 truck and rear axles of class-3 truck, higher stress concentration occurs. Moreover, the rear trailer axles of class-1 truck also exhibit higher stress concentration during its second passes. In this scenario, a headway distance of 2 m is provided which is not sufficient for the pavement to recover before the next truck passes through the same point, thereby inducing excessive stresses in the pavement.

Fig. 14
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S(mises) as observed in zero wander mode

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4.1 Equivalent single axle load determination

Since the traffic mix contains variety of axle groups and axle loading, it is necessary to convert them into an equivalent single axle load (ESAL). An ESAL is a single standardized load application and causes an amount of damage to the pavement structure equivalent to one pass of a dual axle load of 80 kN at tire pressure of 758 kPa [28]. Different trucks are categorized based on the number of axle in each truck. Class-1 truck belongs to the axle semitrailer group of 5 Axles, Class-2 truck belongs to the 3 Axle group and Class-3 truck belongs to the 4 Axle group. Hence, each of this axle group have an equivalent ESAL amount termed as load factor. Following Eq. (11) is used to calculate the ESAL value, which is the load factor for each particular truck.

$$ESAL={\left(\frac{{W}_{1}}{{W}_{2}}\right)}^{4}$$
(11)

where \({W}_{1}\) is the load on the designated axle or axle group and \({W}_{2}\) is the load on the standard axle or axle group. Load factors for each truck type in the traffic mix are taken from [28] and shown in Table 9.

Table 9 Load Equivalency Factors for truck types
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As observed from the table above, the Class-3 truck yields the highest number of ESALs per truck due to higher axle load of 205.94 kN on its drive axle and load of 127.49 kN on its steering axle group. Least amount of ESALs per truck occur under the trailer axles of Class-1 truck having designated axle load of 222.61 kN which is divided by the equivalent single ESAL load of 200 kN for tridem axle group. The formula for calculating total ESALs in construction years is shown in Eq. (12).

$$ESALs\,in\,construction\,year=AADT\,(Lane) \times Load\,Factor \times 3.65$$
(12)

Furthermore, the total ESALs for each truck category based on the percentage of shared traffic volume in terms of construction year annual average daily traffic (AADT) is shown in Table 10.

Table 10 ESALs for traffic mix
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Following Eq. (13) is used to calculate the total design ESALs for the pavement lifetime.

$$Total\,design\,ESALs = total\,construciton\,year\,ESALs \times \frac{{(1+{i}_{B to D})}^{n}-1}{{i}_{B to D}}$$
(13)

where \(n\) is base year of construction and \({i}_{B to D}\) is growth rate from base year to final year of design period. For the total pavement design life of 15 years and annual growth rate of 3.5%, the total number of design ESALs calculated are 1.4 million ESALs. This traffic volume has been used for calculation of horizontal tensile strain and vertical compressive strain values.

Analysis of Microstrain Values.

Observed strain component values from ABAQUS have been normalized to equivalent damage values of an 80 kN axle load for each truck type. The strains are loacted in longitudinal directions and the values are generated under the wheel path from the tire footprint patch. Maximum magnitude of values can be observed in the following paragraph..The observed microstrains under the heaviest axle group for each truck type in case of zero wander mode are shown in Fig. 15.

Fig. 15
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Vertical Strains under all platoon groups

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As observed, the highest accumulation of vertical strain magnitudes occur under the Class-1 truck due to channelized loading when using the zero wander mode, in this case 186 microns of strain is accumulated under the Class-1 truck category type, for Class-2 trucks since the axle weight as well as percentage of annual truck traffic is lower than that of Class-1, therefore, the equivalent strain magnitude is only limited to 145 microns. Class-3 type truck however has a larger axle load resulting in larger load factor but due to less share with annual average daily traffic, the accumulation of vertical strains is only limited to 155 microns.

Horizontal strain profiles for the class-2 truck resulting from uniform wander mode and zero wander mode are shown in Fig. 16. Values are observed under a transverse profile under the center of each wheel type. In case of zero wander mode maximum, strain magnitude reaches the value of 160 microns when cumulative equivalent single axle load is used for the class-2 truck. In case of a uniform wander mode, since a separate central path is provided to the second truck in PT-3, hence the peak is skewed towards the left part at 95 microns. The difference of about 65 microns exists between the two lateral wander modes.

Fig. 16
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Class-1 truck strain values with zero wander and uniform wander mode

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However, when the uniform wander mode is used with a separate path provided to the 3rd truck in platoon with a distance of 0.5 m between the pavement edge and right most wheel as shown in Fig. 17, the resulting horizontal strain acting on the asphalt layer is much lower with magnitude of 130 microns. A slight increase is observed in the strain values for the truck with the uniform wander mode, it is due to the fact that a slight overlap of truck tires exists between different predetermined paths of trucks in the platoon due to limited pavement width available of 3.5 m. However, this increment is negligible when the pavement recovery time and the effect of headway distance are considered.

Fig. 17
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Class-1 truck Second Pass strain values with zero wander and uniform wander mode

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For the PT-3, class-3 truck is the fourth truck in the platoon. Horizontal strain values are shown resulting from the cumulative equivalent single axle load calculated for this truck type. In case of the zero wander mode, horizontal strains reach the peak value of 206 microns during total annual passes while using the equivalent single axle load from this truck type as shown in Fig. 18. The peak horizontal strain reaches 110 microns. Due to higher axle load on the front part of the truck and shorter wheelbase than the class-1 truck, the decrease in strains at uniform wander mode is only limited to 20 microns when compared to that of the class-1 truck.

Fig. 18
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Class-4 truck strain values with zero wander and uniform wander mode

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Furthermore, the strains under different headway distances used for PT-3 platoons are compared in case of zero wander mode. Figure 18 compares the horizontal strains under the equivalent single axle load of class-1 truck and class-2 truck under various headway distances from the total annual truck passes. The headway distance of 2 m yields the horizontal tensile strains of 150 microns and the accumulated strain decreases to 138 microns with the headway distance of 5 m Hence, a reduction in 12 microns occur if more recovery time to pavement is given with headway increment of 3 m to the base headway distance of 2 m.

Figure 19 compares headway distances ranging from 2 to 5 m with an increment of 1 m in three scenarios. From first and second truck the maximum Microstrains are observed at 150 microns, for the second and third truck, due to higher loading and axle weight magnitudes, the maximum strain values are at 209 microns at 2 m of heyday distance and values decrease by 12 microns at headway distance of 5 m to 197 microns.

Fig. 19
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Strains for various headway distance values between first and second truck

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In case of the third and fourth trucks' headway distance, the difference between strain values at headway distances of 2 m and 5 m is at 11 microns. It is observed that an average decrease in microstrains of 2.5 microns exists with 1 m increment in headway distance upto 5 m, however the increment is non-linear in nature, and it depends on elastic recovery, axle configurations and loading frequency of trucks in the platoon.

Figure 20 compares the resulting microstrains at various headway distance values between the four trucks in platoon pt-1. In case of the PT-1 scenario, higher accumulation of strains start under the second truck with headway distance of 2 m at 210 microns and the microstrains reduce to 203 microns at the headway distance of 5 m. the situation gets severe in terms of increased microstrains values for the third and fourth trucks in the platoon, where the headway distance of 2 m yields the strains of 248 microns and strain magnitude decreases to 235 microns with the headway distance of 5 m between third and fourth trucks.

Fig. 20
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Strains for various headway distance values between second and third truck

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Horizontal tensile strain values in case of PT-2 platoon are shown in Fig. 21. It can be observed that the highest magnitude of micorstrains exists under the front truck in the platoon when 2 m headway distance is used in case of a zero wander mode at 225 microns, which is 24 microns higher than that of PT-3. Furthermore, with as with increase in headway distance to 5 m, the decrease in microstrains under the fourth truck occurs at 213 microns, the magnitude at this point is still higher by 17 microns when compared to the PT-3 platoon.

Fig. 21
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Strains for various headway distance values between third and fourth truck

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The PT-3 type platoon yields the lowest accumulation of strains when compared against PT-2 and PT-3 platoons at various headway distances ranging from 2 to 5 m as shown in Fig. 22. Highest microstrains in each platoon type exists under the last truck in the platoon due to effect of channelized loading when a zero wander mode is used. The decrease in microstrains due to increase of headway distance of 5 m is limited in case of PT-1 platoon to 7 microns and in case of PT-2 to 10 microns, the decrease is much higher in case of PT-3 platoon by 12 microns.

Fig. 22
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Strains for various platoon types and headway distance values

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The difference of 24 microns exists between PT-2 and PT-3 platoons under the fourth truck, and the difference of 33 microns exists between PT-3 and PT-1 under the fourth truck. Hence, the PT-3 type platoon exhibits the least accumulation of strains when the effect of channelized loading and elastic recovery of pavement is considered with increase in headway distance. It is recommended to use the random truck mix in an equally distributed loading frequency, thereby increasing the elastic recovery of the pavement.

Vertical strains of a series of PT-3 trucks passing through a specific point on the model are shown in Fig. 23. It can be observed that the platoon starts with the class-1 trucks exhibiting a strain of 113 microns on its drive axle, and the strains gradually increase due to added tire pressure and axle load values for fifth wheel and trailer axles. In case of trailer axles, maximum load is exerted on the middle wheel of the trailer at strain value of 290 microns with remaining two axles showing the strain values of 255 microns each.

Fig. 23
figure 23

Longitudinal strain profile for zero wander mode of PT-3 platoon

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The next truck in the platoon is a class-2 truck with its drive axle coming in at 17 m into the platoon. Due to higher axle load of this truck as compared to the class-1 truck for the steering axle, strain values of around 140 microns are shown at this point. The strain values increase as the higher load is exerted, resulting in strains 180 microns under each dual tire assembly. The third truck in this case is again a class-1 truck making is second pass with its drive axle making the pass at 26 m in the model. Since 2 m headway distance is given, a very little time is available for the pavement to fully recover, hence the accumulation of strains increase 1.2 times at the drive axle to 135 microns.

Furthermore, a gradual increase in microstrains is observed under the fifth wheel and trailer axles, with the middle trailer axle exhibiting the highest strain value of 320 microns. The last truck in this four truck platoon is a class-3 truck with a higher axle load on its front axles as compared to class-1 and class-2 type trucks, arriving at 41 m in the model. Therefore, an ideal recovery distance of 8 m is recommended between each platoon.

In case of a uniform wander mode, with a specified dedicated path given to each truck in the platoon, the PT-3 is shown with the headway distance of 2 m in Fig. 24. Class-1 truck leads the platoon with microstrains of 113 microns under its steering axle. The strain values gradually increase to 130 microns under the drive axle of the truck, highest microstrains under class-1 truck are observed under its middle trailer axles with peak value of 190 microns and 160 microns under remaining two trailer axles. Class1- truck is then followed by the class-2 truck at 18 m in the model. Due to higher accumulation of axle load and small wheelbase, a higher amount of microstrains appear under the steering axle with value of 115 microns, exhibiting a 5% increase in strains compared to the steering axle of class-1 truck.

Fig. 24
figure 24

Longitudinal Strain profile of PT-3 platoon under uniform wander mode

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4.2 Pavement distress analysis

With the equivalent strain values obtained from simulations, the pavement failure modes such as rutting and fatigue cracking have been calculated based on the 15-year pavement lifetime consists of 1.4 million ESALs applications. Number of repetitions to failure for fatigue cracking have been calculated using the Asphalt Institute model, as shown in Eq. (14), (15) and (16) [29].

$${N}_{f}=C \times 0.0796 \times {\varepsilon }_{h}^{-3.291} \times {E}^{-0.854}$$
(14)
$$C={10}^{M}$$
(15)
$$M=4.84 \times \left(\frac{{v}_{b}}{{v}_{v}+{v}_{b}}-0.69\right)$$
(16)

where \({N}_{f}\) is the fatigue life (design repitions to failure), \({\varepsilon }_{h}\) is the horizontal tensile strain at bottom of asphalt layer, \(E\) is the dynamic modulus of asphalt concrete in MPa, \({v}_{v}\) is the percent air voids in total mix and \({v}_{b}\) is the percent binder volume. The data for percent air voids and percent binder volume has been taken from Cheng et al. [30].

For evaluation of rutting, Per Ullidtz Eq. (17) is used.

$${N}_{f}=\frac{1}{R} \times 3.069 \times {10}^{10} \times {\left(\frac{E}{{E}_{0}}\right)}^{3.26b} \times {{\varepsilon }_{v}}^{-3.26}$$
(17)

where \({N}_{f}\) is the number of load repititons to failure, \(R\) is the regional factor of value 1.75, \(E\) is the dymanic modulus of structural layer in MPa, \({E}_{0}\) is the adjusted reference elastic modulus of 158 MPa, \(b\) is 1.16 if \(E<{E}_{0}\), otherwise value of \(b\) is 1, and \({\varepsilon }_{v}\) is vertical compressive strain on the top of layer. Moreover, for evaluation of rut depth based on corresponding number of reptitions to failure, following Eq. (18) is used.

$${\mathrm{d}}_{\mathrm{p}}=25\mathrm{mm} \times {\left[\frac{N}{{10}^{6}} \times {\left(\frac{{\varepsilon }_{v}}{1230 microns}\right)}^{7.14}\right]}^{0.5}$$
(18)

where, \({\mathrm{d}}_{\mathrm{p}}\) is the rut depth in mm, \(N\) is the number of reptitions to failure for rutting and \({\varepsilon }_{v}\) is the vertical compressive strain on the top of layer. Rutting and fatigue cracking predictions based on number of loading repititons to failure and rut depth as a of functional failure of pavement are further calculated.

Decrease in fatigue life in number of years for uniform wander and zero wander modes along with various headway distance of 2–5 m for the selected optimum PT-3 platoon are shown in Fig. 25, the decrease in fatigue life in number of years is only 6 months in case of a uniform wander mode at 2 m and at the same scenario for zero wander mode, decrease in fatigue life reaches to 2.4 years, thereby causing am accelerated decrease in pavement life as a result of channelized loading with very little elastic recovery time available to the pavement.

Fig. 25
figure 25

Decrease in fatigue life under various headway distance values and lateral wander modes

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Moreover, it can be observed that a gradual decrease in reduction of fatigue life of pavement occurs as the headway distance in case of zero wander is increased to 5 m. a difference of almost 1 year of reduction in fatigue life exists between zero wander and uniform wander modes at headway distance of 5 m.

Figure 26 shows the percentage decrease in fatigue life under uniform and zero wander modes with various headway distances ranging from 2 to 5 m. In case of a uniform wander mode., the difference in decrease in fatigue life is only 0.8 percent when owing from headway distance of 2 to 5 m while in case of zero wander modes, the difference between headway distance of 2 m and 5 m is 20%, thereby exhibiting a significant reduction in decrease in fatigue life if headway distance is increased.

Fig. 26
figure 26

Decrease in number of passes and fatigue life in percentage under various headway distance values and lateral wander modes

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Moreover, at headway distance of 5 m, in case of uniform wander mode, the decrease in fatigue life is 40% less than that of zero wander mode. Hence, when a uniform wander mode is used along with separate paths assigned to each truck in the platoon, the fatigue life of almost 1.2 years can be gained.

Figure 27 compares the number passes required to reach rut depth of 6 mm, against uniform wander and zero wander modes, along with headway distance ranging from 2 to 5 m. The least number of passes are exhibited by the zero wander mode at only 239,875 passes, corresponding to acceleration in rutting by 2.6 years out of 15 years design life of the pavement.Thereby, the acceleration of rutting propagation is only limited to 6 months when 5 m headway distance is used. Hence, It is recommended to use the headway distance of 3 m with uniform wander mode to accommodate higher highway capacity.

Fig. 27
figure 27

Number of passes to reach rut depth value of 6 mm under various lateral wander modes and headway distance values

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Rut depth at the end of service life of pavement after 15 years at 1.4 million ESALs for trucks in a PT-3 platoon is shown in Fig. 28. In case of headway distance of 2 m while using a zero wander scenario, the rut depth reaches 13.3 mm which is 38% higher than the rut depth for a uniform wander mode while using 2 m headway distance. In case of a 5 m headway distance of zero wander mode, the magnitude of rut depth still stays at damaging magnitude of 12.2 mm, hence channelized loading in case of zero wander mode has a severe effect on rutting progression in the pavement. It is suggested to use the headway distance of 3 m when a uniform wander mode is used.

Fig. 28
figure 28

Rut depth at 1.4 million ESALs under various headway distance values and lateral wander modes

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5 Conclusions and Recommendations

In this research, the effect of headway distance and grouping of trucks based on their axle configurations on platoon formation has been analyzed in combination with the use of zero wander mode and uniform wander mode. Since, headway distance can influence the pavement elastic recovery when the loads pass through the specific point on the pavement, the resulting strain accumulations in terms of vertical compressive strains and longitudinal tensile strains have been obtained through finite element modeling.

A 3D FE model has been used to simulate the effect of three different types of platoons based on the category of trucks inside each platoon. The platoon truck size is limited to only 4 trucks and each platoon is simulated along with variable headway distances of 2 m to 5 m with 1 m increment. Furthermore, the effects of lateral wander modes beginning with the zero wander mode and uniform wander mode have been analyzed. In case of uniform wander mode, each truck in the platoon is given a predetermined path to follow along with the uniform wander mode applied through the dload subroutine used in ABAQUS.

Effect of headway distance on accumulation of strains, is highly critical and headway distance of less than 3 m causes excessive damage to the pavement under repeated loading cycles in case of zero wander mode. In case of using the uniform wander mode, headway distance has a less significant effect on the development of damaging strains since there is only a slight overlap of wheel paths for all the trucks in the platoon. PT-3 platoon yields the least amount of accumulative strains among other platoons. The use of pavement failure prediction models for rutting and fatigue racking indicate that zero wander mode can cause premature failure of the pavement, however if the uniform wander mode is used in combination with the use of PT-3 platoon, pavement life can be increased.

It is recommended to design the truck platoons based on the classes of truck being used on the highways. Since in this research three different classes of trucks are considered, therefore the use of truck mix where high axle loading is used, it is recommended to include the truck type in the traffic mix with the lowest axle load in subsequent intervals for adequate pavement recovery time. Moreover, it is recommended to calculate the optimized headway distance when the platoon size increases or the axle configurations of trucks in the traffic mix change. However, in this scenario, the best performing platoon type consists of 4 trucks and a specified interplatoon distance of 10 m is provided between the successive platoons. Furthermore, the pavement response can be further increased by using cement treated base course without increasing the pavement structural layer thickness.

In terms of limitations, in this research the effect of temperature variations and freeze thaw cycles have not been considered. Therefore, this research excludes the environmental impacts that may alter the progression of strains and occurrence of rutting and fatigue cracking. Moreover, based on assumptions, only 3 different types of truck axle configurations have been used due to a higher percentage occupied by these vehicle classes. Nevertheless, inclusion of further axle configuration will further enhance the comparative analysis which will be performed in the future work along with the inclusion of temperature variations in the pavement structure.

  1. 1.

    Rigid boy trucks also induce considerable amount of stresses in the pavement resulting in damaging strains with 75% damage as class-1 truck.

  2. 2.

    With the increase in the wheelbase to 2 m, the magnitude of stresses exerted by rigid body trucks in the pavement can be reduced by 30%.

  3. 3.

    With the use of rigid body trucks, the platoon length can however be optimized to allow for larger headway distance of upto 5 m, resulting in more recovery time for the pavement.

  4. 4.

    The use of PT-1 drastically increase the strains by 60% due to very minimal relaxation time and excessive repetitions of same loads type.

  5. 5.

    In case of the use of PT-1, it is recommended to increase the headway distance of 2 m to 5 m, that results in increase fatigue life and rutting performance of pavement to up to 1.6 years.

  6. 6.

    Whenever possible, it is recommended to use the PT-3, in that case, the repetitions of loading along the same magnitude is reduced along in conjunction with the uniform wander mode.

  7. 7.

    An ideal headway distance for a PT-3 is 4 m for a zero wander mode, where it reduces the pavement damage in terms of fatigue to 8 months, the distance can however be increased based on traffic volume of the highway.

  8. 8.

    Spacing between truck platoons have a minimal effect on pavement damage when the spacing is 10 m or more for traffic speed of 90 km/h.

  9. 9.

    Interplatoon distance in case of a uniform wander mode has no significant impact on pavement elastic recovery since a minute section of pavement is loaded repeatedly buy each truck in the platoon.

  10. 10.

    Accumulated microstrains in case of a uniform wander mode decrease by 45% under each axle of the following truck when compared against zero wander mode.

  11. 11.

    A heady distance in case of uniform wander mode can be reduced to 2.5 m, since the headway distance has a little effect on the pavement elastic recovery from permanent deformation.

  12. 12.

    With a decreased heady distance of each truck in the platoon and reduced interplatoon distance, highway capacity can be further increased for operating speeds of 90 km/h.

  13. 13.

    Interplatoon distance of 5 m is suggested while using the uniform wander mode. in this research, selection of random platoon type pt-3 is suitable for the use of uniform wander mode, due to less accumulation of strains and variable loading frequencies due to different axle configurations, it is recommended to use a random platoon PT-3 mixed with equally distributed trucks based on their axle orientations.

  14. 14.

    Use of either pt-1 and pt-2, can lead to higher accumulation of strains both in uniform wander mode and zero wander mode, due to same loading frequencies of axles.

  15. 15.

    With increase in wheelbase by 0.7 m for class-2 and class-3 trucks, the strain values under the axles can be reduced by 16%.

  16. 16.

    A class 1 truck has an advantage over the other types due to its longer wheelbase and higher number of axles, regardless of the highest maximum gross weight of 40 T.

  17. 17.

    The use of wide base tire for a drive axle of both class-2 and class-3 trucks is recommended since it can reduce the accumulation of permanent strains under drive axles by 35%.

  18. 18.

    With the use of pt-2 platoon, microstrains increase by 24 microns at headway distance of 2 m between the first two trucks in the platoon and micro strains increase by 17 microns in case of PT-2 platoon with heady distance of 5 m.

  19. 19.

    It is suggested to use the PT-3 type platoon with headway distance of 4 m while using a uniform wander mode.

  20. 20.

    The use of uniform wander mode is suggested because the headway distance increment from 2 to 5 m has minute effect on increased strain values due to channelized loading, however, a small amount of wheel path overlap exists from all the four trucks in PT-3 platoon.

  21. 21.

    Fatigue life decreases by 40% in case of using a zero wander mode at headway distance of 5 m when compared to uniform wander mode.

  22. 22.

    Zero wander mode, decrease the pavement life by 1.2 years.

  23. 23.

    In case of zero wander mode, the fatigue life increases by 13% when moving from headway distance of 2 m to 5 m.

  24. 24.

    Acceleration of propagation of rutting reaches 2.6 years to reach rut depth of 6 mm when the zero wander mode is used.

  25. 25.

    Uniform wander mode delays the rutting progression by 1.6 years when compared against zero wander mode at optimum headway distance of 3 m.

  26. 26.

    At the end of service life of the pavement, the rut depth in case of zero wander mode is 38% higher than that of uniform wander mode at headway distance of 2 m.

  27. 27.

    Due to slight overlapping of wheel; paths in case of uniform wander mode, a minute decrease in rut depth occurs if higher headway distance of 5 m is used, however, it is recommended to use the headway distance of 3 m for better highway capacity.