Adding an extra tire to the standard axle to reduce pavement damage due to overload

The present work grants a study of technical development under a differentiated aspect where an extra tire was added to the standard double axle recommended by the Brazilian traffic calculation norms. The number N generated a triple axle, and a comparative study was made relating the balance load standardized in Brazilian balance laws for each type of axis and the damage generated on the pavement, measuring the results on a pavement chosen as a model, usually used on Brazilian highways. We verified through computer software, which uses the methodology of the theory of finite elements, supervised by the inspection bodies of the National Department of Transport infrastructure, proving if a larger amount of cargo generates the same damage to the pavement without jeopardizing its useful life, which was initially designed to last ten years.


Introduction
The concept of road pavement means a structure constituted on is a structure built on the surface obtained by earthmoving services with the primary function of providing the user with safety and comfort, achieved with the maximum E = 2 (1 + m) qVs 2 (Eq. 1) Kim et al. (2018) observed that the effect of different configurations of regular contact stresses on the performance of grooves of soft and rigid and Crushed Graduated Gravel layers in the Finite Elements model, based on a real structure of the generated pavement and the asphaltic concrete layer simulated as a viscoplastic viscoelastic material system. Therefore, the present study had the purpose of verifying the pavement of Brazilian road projects, with pre-established and constant dimensions, varying the number of tires used, and we verified the pressure applied to the pavement, used by the standard methodology, and confirmed the effect on the layers through the fatigue equations standardized by the DNIT (2006).

Material and Methods
For meeting the objective, we used the deduction method with qualitative and quantitative approaches (Pereira et al., 2018). The standards agreed and accepted by the projects of the National Department of Transport Infrastructure-DNIT and its state representatives according to the Paving Manual -IPR -719 (2006)

Methods of calculating the N number and its variables
The number "N" is calculated using Equation 1.
where, N = number of requests equivalent to the default axis; P= project period; VDM= average daily traffic volume; FV= vehicle factor; FR = regional climate factor; D= percentage of commercial vehicles in the most requested range; d= percentage of vehicles per direction.
Defined the project period of 10 years, according to the guidelines of the Department of Highways of the State of São Paulo (DER/SP) the determination of the N number consists, initially, in the definition of the traffic volumes of each type of vehicle and its projection of growth.
The second stage of calculation is the vehicle factor (VF) definition, which allows the determination of the number of axles equivalent to the standard axle from the volume of vehicles with a specific configuration of axles and loads that travel during the design period. The vehicle factor is calculated from Equation 2.
where FE= axis factor; HR= load equivalence factor.
The maximum loads by axle type defined in the Balance Law and the Brazilian Traffic Code (Law No. 9.053.de 23/09/1997resolution no. 12 of 02/06/1998) correspond to 6.0 tf on the single front axle, and 10.0 TF, 17.0 TF, and 25.5 TF for single axles, double tandem, and triple tandem rear, respectively.
The factors of equivalence to the standard load of 8.2 tf are determined analytically, through two calculation methods, the United States Army Corps of Engineers (USACE) and the American Association of State Highway and Transportation Officials (AASHTO, 1972), the first recommended by der/sp and the second for mechanistic evaluation purposes. The procedure of dimensioning the Department of Highways of the State of São Paulo considered variations in the humidity of the pavement's Development, v. 10, n. 1, e39710111852, 2021 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v10i1.11852 constituent materials during the various seasons (which translates into variations in the materials' support capacity). The equivalent number of requests of the standard axis (or traffic parameter) "N" is multiplied by a coefficient "FR" called Regional Factor, which, in the AASHTO (1993) experimental track, ranged from 0.2 (occasions when low moisture content prevails) to 5.0 (occasions when the materials are practically saturated).
In Brazil, there are no experimental elements for such determination, but according to the recommendations of the Department of Highways of the State of São Paulo, one can adopt: FR = 1.0

Verification of pavement structures through the theory of elasticity
Vehicle loads generate stresses and deformations inside the pavement structure. These stresses and deformations are a function of the magnitude of the loading, the resilient modules and thicknesses of the pavement constituent layers, and the subgrade support capacity. Therefore, the displacements and active deformations that originate inside the loaded pavement were determined for later comparison with the values of displacements and permissible deformations that are a function of the type of material used in the pavement structure. To determine the internal efforts requesting, deformations, and displacements of the flexible layer structure, the Elsym5 (ElasticLayered System)computational program was used, which considers constant elastic characteristics for each layer of the pavement structure. The parameters used for the calculation were: Standard 80 kN single shaft load, represented by 4 x 20 kN; Tire/layer contact pressure of 5.6 kgf/cm²; ASPHALT Resilience Module (Coating) of 35.000 kgf/cm²; Simple Graded Gravel resilience module of 3.000 kgf/cm²; Macadam resilience module of 2.500 kgf/cm²; 700 kgf/cm2 subgrade resilience module for CBR=7% where ASPHALT= Hot Machined Bituminous Concrete; kN= kilo Newton; CBR= California Bearing Ratio;kgf/ cm²= kilogram strength per square centimetre. The displacements and internal deformations of the structure were determined in its critical locations, i.e., at the top of the asphaltic concrete layer (vertical displacement), in the lower fiber of the asphaltic concrete layer (horizontal tensile deformation), and at the top of the subgrade (vertical compression deformation). Fatigue equations 3, 4, and 5 were used to determine permissible efforts. Vertical displacement on the layer surface -deflection -D0 10 -2 (mm). PRO 11 -DNER Model (DNER, 1979).
Vertical compression deformation at the top of the subgrade layer is V 10 -4 (cm/cm), (Dormon & Metcalf, 1965). The values obtained by the software used in the fatigue equations represented above for each layer, and the N number of requests from the common axis for the design period found.
In the present study, aiming to optimize freight and load distribution on the pavement, we consider another tire added to the standard axle and using the existing parameters. A load simulation was rotated and verified through the finite element theory and fatigue equations recommended by DER/SP and DNIT, which are the results at the top of the layer, in its useful life and load increment possibilities.

Results
Tables 1 and 2 show the output data applied to the fatigue equations. The results compared to the values obtained the standard axis considered for the 10-year project according to Brazilian standards' requirements. The amount was compatible with initial overloads of 5% added, and the program rerun until the 50% for comparison purposes only. Checking the Overall Results Standard Axle table for deflection in the ASPHALT layer, where the DER/SP PRO-11 equation used equation 3, the value of N considered for the standard axis of 8.2 t, of 7,55 x 107 was found in the Triple Axle table when adding the amount of 15% load.
For the ASPHALT layer's traction, the Federal Highway Association equation used the original N for the standard axis was found only between 40 and 45% of load increase. For the deflection at the top of the subgrade, where the Shell equation (1978) and Dormon & Metcalf (1965) used, the original N for the standard axis found only between 35 and 40% of load increase.
In the first reading of the pavement, using the triple tire, there is a tolerance up to 15% of overload; for the second reading, a tolerance is between 40 and 45% of overload, and in the last layer in the subgrade, the tolerance is between 35 and 40 % overload more than initially projected with double running for ten years of design.  In the first column, Tables 1 and 2 represent the percentage of load increased concerning the standard axis of 8200 kg represented in the second column. In the third column of Table 1, column two's value is divided by tires resulting in 2050 kg for each, whereas in Table 2, the value of the standard axle was divided by 6 because a wheel was added on each side of the standard axle double.
Deflection is the deformation in the pavement's top layer when the Elsym5 software reads the axle load's tension.
Columns h and v show the readings of the Elsym5 software for the tensile stress in the bottom layer of the CBUQ, and the deformation is shown at the top of the subgrade, respectively. The columns of variation in useful life represent a comparison to the 10-year life of the initial project, always being the standard axis considered zero variation and being compared to the load increase and triple rollover in Table 2. Finally, in the Damage column, 1 divided by the previous column's damage was shown to elucidate the variation.  These results showed an increase of 43.22% number N, generating the same damage to the project's pavement. Additionally, we can verify, as an example, that the triple axle accepts 15% more overhead at the top of the asphalt layer to generate the same damage to the pavement in 10 years when compared to the standard double axle of design.

Discussion
In this research, some factors were considered that led to the relevance of the results. In Brazil, road transport represents more than 70% of the total vehicle and becomes the most important means of supply and cargo movement in the country. Taking an economic view, we see the need to reduce costs, both in the maintenance and conservation of highways and in the value of freight itself. The study verified the importance of resultant tensions applied in the pavement through the loads imposed by the commercial vehicles' weight. Dey et al. (2014) mention that for trucks with loads above the legal weight limits, DOTs issue special licenses. With specific control of the scale load, the maintenance processes of bridges and pavements can drop significantly and would require less frequent maintenance and rehabilitation. Transport control policies and alternative ways have been looking more efficiently for revenue sources to maintain the infrastructure. Because of the damage caused by overweight trucks and recover the costs of the accelerated deterioration, it is necessary to quantify the damage to bridges and pavements attributed to overweight trucks. Based on the damage estimate, damage costs for overweight trucks are estimated for the most common recovery fee typesadditional damage costs above the legal limit up to the maximum overweight limit. Pais et al. (2013) present a study on the impact of overloaded vehicles on road pavements' performance, studying the truck factor for different vehicle types when applied to a set of pavements, including five different asphalt layers thicknesses and five other subgrade stiffness modules. The presented results allowed us to conclude that heavy vehicles do not operate with the maximum load defined by law. On average, and depending on the shaft's position, each axle varies from 20 to 90% of the full legal load. However, for classes F4 and H6, the number of cars overloaded varied from 40-60%. The presence of overloaded vehicles can increase costs by more than 100% compared to the same cars' price with legal loads.
Different distribution patterns were observed between overweight and unweighted traffic in truck classes and axle load spectra . The reduction in pavement life was used to normalize the effect of an overweight truck in different conditions. In general, it shows that a 1% increase in overweight trucks can cause a 1.8% reduction in pavement life. The M-E analysis proved to be a valid approach to quantify the impact of overweight trucks on pavement damage at the network level by comparing the expected pavement life from the M-E analysis and field-estimated performance data.
Another study using SAFEM (Finite Elements) for predicting the asphalt pavement structural responses under static loads (Liu et al., 2015) proposes the use of MATLAB-based software. A comparison with ABAQUS verified the accuracy of the program. Pavement responses to a static load predicted by SAFEM and ABAQUS are in excellent agreement. Furthermore, the computational time of the SAFEM is much shorter than that of the ABAQUS. To further reduce the computational time, the infinite elements are coupled with the finite elements in the SAFEM. As a result, the pavement model's scale at the infinite domain controlled a suitable level, and computational time reduced without decreasing its accuracy.
For further investigation, the SAFEM allows dynamic analysis and various material properties, such as viscoelasticity for asphalt and nonlinear elasticity, for the pavement subbase. Furthermore, the regulation of the minimum amount of the finite elements required to use in the finite-infinite element coupling analysis should be determined by the theoretical research and large numbers of case studies.
The world economic scenario demands increasingly require cost optimization and technical adequacy to achieve better results, aiming at a surplus in the cost/profit ratio of the trade balance. There was a need to reinvent mechanisms already considered established in the market and studies for more favorable adaptations to new demands in this context. In the commercial vehicle, the market found a structure that has been used for cargo transport for years. It was verified the possibility of a new study of load distribution on the pavement through the pressure exerted by tires, which, by extension, would benefit the amount of cargo to be transported by the same truck in the same freight generating the same damage on the pavement of the typical structure used in the current standard of balance load.
The viscoplastic stress is located at the bottom of the asphalt concrete layer when the BGS layer is not compacted. The region location moves to the middle of the asphalt concrete when the BGS layer is rigid. These simulations revealed that the structure of steel-concrete layers depends heavily on the properties of the BGS layer. The configuration of the stress contact.
Therefore, future studies will focus on how the asphaltic concrete layer's regular performance is altered by the variation of Graded Gravel and subgrade layer properties.

Conclusions
The following conclusions can be drawn from the simulations in the present study: -Groove depth in the asphalt concrete layer under everyday realistic contact stresses is about 1.5 times greater than the groove's center under standard pressure evenly distributed.
-The distribution of stress should depend on the transverse location with its maximum in the center transverse direction of the contact area to ensure the groove's maximum depth in the contact area's center.
-The magnitude of the routine depth in the asphaltic concrete layer is usually inversely proportional to the stiffness of the BGS Layer.
The implementation of a standardized tire and already established double axle, forming a triple tire, proved to be quite efficient in two main points, (1) in the technical scope, it generates an increase in the permissible load to be transported on the triple axle, generating the same damage as standard double axle; and (2) in the economic view, we will have a greater load capacity at the same freight value.
For further study, we suggest an economic survey on freight cargo and fuel consumption in the real scenario of cargo transportation on Brazilian highways to check the impact of the proposed changes on the environment.