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The representation in the three-dimensional space of the physical model symbolized by the application of the pairing of the wheels described by 2 disks with a radius of 0.125 m and a 0.375 m spacing has the advantage of more accurately simulating the loading. In most cases, the assumption of a uniform distribution of loading on the circular surface is considered. In order to determine the effect of dual wheels, this research proposes a new approach to the distribution of vertical contact stress in three-dimensional space with loading on the circular surface. This allowed evaluating the maximum deformation on the space described by the dual wheels. The results showed that vertical deformation is maximum at the center of each circular surface. The distribution of the vertical contact stress is non-uniform on the circular footprint and has a significant influence on the deformation of the pavement at the level of the bituminous layer. The impact assessment of the twinning reveals that the dual wheels load causes less damage than that of a single wheel. These results are obtained by means of a numerical simulation under Cast3M with a gravitational lateritic pavement.

The impact assessment of the twinning reveals that the dual wheels load causes less damage than that of a single wheel pavement design methods; it is generally assumed that the contact pressure is static and equal to the inflation pressure [

The present research aims to propose a new approach to the distribution of the vertical contact stress in three-dimensional space with the loading on the circular surface. In addition, an analysis of the evolution of the deformation as a function of depth will be used to better understand the distribution. The implementation of this one will make it possible to quantify the maximum deformation and to pronounce on the effect of the dual wheels. The studies conducted as part of this work are essentially based on a numerical simulation using the Cast3M finite element calculation coding.

In this paper, we present some results from modeling to evaluate the influence of two parameters: axle configuration impact and vertical stress distribution. The results of the simulation, which will be discussed regarding the distribution of the vertical contact stress, also make it possible to study the impact of twinning.

Factors taken into account in the traffic analysis are essentially the axle load, the axle configuration and the number of axle applications [

Traffic loads are applied to roadways by means of tires. These tires may consist of single or dual wheels. Most axle configurations are used (single axle, tandem axle and tridem axle).

Single axle: isolated axle (single wheel or dual wheels) whose axis is more than 2m distant from any axle of the vehicle.

Tandem axle: axle belonging to a group of two axles whose distance from the axles is less than 2 m.

Tridem axle: axle belonging to a group of three axles whose distance from the axes is less than 2 m.

The number and spacing of axles are the determining factors for the transmission of loads to the pavement. The increase in the number of axles reduces the load transmitted to the pavement at equal load [

The distribution of contact pressures depends mainly on the type of tire, the load applied and the inflation pressure. In 1989, [

To take into account the non-linearity of the foundation and base layers, and to evaluate the impact of the overload, [

Based on the work of [

The modeling of a structure leads, in general, to be interested in several aspects of which the most usual is the geometry and its discretization. The modeling is based on a 3D structure of flexible pavement, consisting of a surface layer made of 80 mm thick bituminous materials, a lateritic gravelly basecoat treated with 2% cement of 250 mm thickness, a laterite gravelly foundation layer of 250 mm thickness and a platform of infinite thickness. The simulations were performed considering the hypothesis of the non-linearity of the base layer and that of the foundation, while the bituminous layer and the platform have a linear behavior. The input parameters obtained by [

The construction of the finite element model under Cast3M is done in this study using elements at 8 knots (cub8) on a quarter of the pavement. The carriageway is loaded with a half-axle with two (2) dual wheels spaced 37.5 cm apart and a single wheel with a radius of 12.5 cm. The charges will be applied to finely meshed fingerprints located at the surface layer. The description of this geometry has been adopted by [

The loading of a half-axle is equal to 65 KN. This load will be distributed and applied to the two finely meshed fingerprints located at the surface layer. For the one wheel one, it is the totality of this load that is applied. For the boundary conditions, the horizontal displacements are blocked in the transverse directions and the vertical and horizontal displacements are blocked in the lower part of the platform.

The images of the 3D mesh of each structure are given in

Layers of roadway | Thickness (m) | Linear model | Parameters of Uzan nonlinear model | |||
---|---|---|---|---|---|---|

υ () | E (MPa) | k_{1} (KPa) | k_{2} () | k_{3 }() | ||

Bituminous Base 2% Raw foundation Platform | 0.08 0.250 0.250 10 | 0.35 0.25 0.25 0.25 | 1300 84 62 30 | - 279,074 837,276 - | - 0.65 0.13 - | - -0.56 -0.33 - |

The modeling first focuses on the study of the distribution of the vertical stress and the impact of the configuration of the axles on the pavements. In the context of this simulation, the distribution of the vertical contact stress is studied by considering two (2) loading cases of a half-axle equal to 65 KN. For a one-wheel load, it is the totality of this load that is applied. The evaluation of the deformation will take place at the center of the circular imprint and also on a point of the circle (edge). For dual wheels, this load will be distributed over the two (2) circular impressions. The evolution of deformation over three (3) points (center, edge and plumb) will be examined as shown in

The impact of the axle configuration on the pavements is evaluated by considering a single and a dual wheel axle. The loading of a half-axle used is equal to 65 KN. The roadway is loaded with a semi-axle with dual wheels spaced 37.5 cm and a single wheel radius equal to 12.5 cm.

For this, we will represent the deformation at each layer of the roadway to better understand the distribution of the vertical stress.

The deformations obtained at each layer, for the single wheel, are presented in

The results obtained in the two (2) loading cases show that the evolution of the deformations in the center of the impression differs from that of the edge of the impression. Deformation is substantially greater at the center of the footprint than at the edge for all layers of the roadway except the platform. For each loading case studied here, the difference between the vertical deformation at the center and that at the edge is very considerable at the level of the bituminous layer. It decreases according to the depth of the layer at the level of the roadway. This may be due to the fact that the effect of the load decreases with the depth and distance of the area requested. However, it is important to note that the opposite trend is observed at the bottom of the foundation layer to a certain depth of the platform. This may be related to several factors (material properties, interface

phenomenon, etc.) that are not covered in this study.

At the platform level, the evolution of the deformation on the different points considered remains the same for the two loadings (single wheel and dual wheels). For dual wheels, the evolution of the deformation obtained at the edge of the footprint is confused with that obtained at the level of the equilibrium of the twinning. It should also be noted that, with the dual wheels, the deformations obtained at the edge of the footprint is slightly higher than those obtained in the center at the level of the foundation layer at a certain depth.

Overall, with the load cases studied here, it can be concluded that the vertical contact stress is non-uniform on the circular footprint and has a significant influence on the deformation of the pavement at the level of the bituminous layer. This deformation is maximum in the center of the circular imprint where the vertical stress is maximum. The distribution of the vertical contact stress has no influence on the platform. These results show that it is possible to determine non-uniform distributions of the vertical contact stress for modeling to evaluate their effect.

In other words, the results obtained with the semi-axle with dual wheels are of particular interest for the size of roadways. The stresses induced in the structure by the load are maximum in the center of each circular imprint but not in the center of gravity of the half-axle (or in line with the twinning). Figures 5(a)-(d) give the deformations obtained for each layer of the roadway with the single wheel.

The deformations obtained with the dual wheels at the different layers of the roadway are presented in Figures 6(a)-(d).

The effect of wheel twinning has been evaluated under the center of a dual wheel in comparison with the center of a single wheel. Figures 7(a)-(d) show the results. The deformations obtained at the center of a dual wheel are lower than

those obtained at the center of a single wheel. At the level of the bituminous layer, the difference between the deformations caused by the type of loading is high. This difference decreases as we get closer to the platform. The configuration of the load participates in the transmission of the load at the level of the roadway. The dual wheels reduce the transmission of the load at the level of the road where a reduction of the deformation.

These results are in agreement with those of [

The purpose of this study was to determine the effect of dual wheels on lateritic pavements to understand the variation in the state of stress and deformation during the passage of traffic loads. The analysis of the results obtained made it possible to determine the distribution of the vertical contact stress on the circular impression of a single wheel and on the two discs of dual wheels, the pairing of which is described with the aid of two discs 0.125 m of radius, spacing 0.375 m. The study of this distribution allowed evaluating the maximum vertical deformation for each case of loading. This deformation is maximum in the center of the circular imprint where the vertical stress is maximum. Therefore, the vertical contact stress is non-uniform on the circular footprint and has a significant influence on the deformation of the pavement at the level of the bituminous layer. This non-uniformity has been shown by [

Thiam, B.B., Samb, F. and Dione, A. (2018) Taking into Account the Effect of Dual Wheels on the Behavior of Lateritic Gravelly Pavements. Geomaterials, 8, 27-37. https://doi.org/10.4236/gm.2018.83003