Keywords: road, viscoelastic material, moving load, multilayer.

As the usual soils are unable to support traffic loads, roads are designed as a multilayer structure to get lower stresses at the level of the supporting soil and to allow the traffic and the parking of vehicles. The calculation of French roads uses the Burmister multilayer elastic model [1]. This model is implemented in numerous software like ALIZE from LCPC described in [2]. Supposing that each layer has an elastic behaviour, it gives by semi-analytical calculations relatively good stress and strain fields for roads with high lorry traffics. On the contrary, to study soft roads with small traffics or with high temperature gradients, it is necessary to take into account the viscoelastic behaviour of asphalt materials.

In this paper, a model for a semi-infinite multilayer structure taking into account the thermo-viscoelastic Huet-Sayegh [3,4] constitutive relation is presented. The proposed method consists in using a double Fourier transform to set the problem in the domain of horizontal wavenumbers. Then the problem is solved analytically along the depth in each layer as a sum of six waves depending on six unknown parameters. Continuity conditions on the displacement and stress vectors are written at each interface between neighbouring layers. Conditions of vanishing waves at infinity and equilibrium with the load on the ground surface lead to a complete system whose solution gives all the unknown waves parameters in the layers. The solution in the moving load reference system is then got by a double inverse Fourier transform. Finally one can calculate the displacements and the stresses in different positions in the road according to the intensity of the load, the temperature or the speed of the vehicles.

The results have been validated by comparing with an analytical solution developed by Chabot and Piau [5] for an infinite half-space and with finite element results from the CVCR (Calcul Visco-élastique sous Charge Roulante) from Heck et al. [6] in the case of structures made of several layers on a half-space elastic layer. Several results are also presented to show the influence of the velocity of the source and the influence of the temperature. Usually the displacement is larger when the velocity is lower. The temperature is found to have a more important effect than the velocity. The displacement is larger when the temperature increases, as the asphalt is weaker in this case. The proposed model allows estimating these effects, which can increase the displacement until 50% compared to purely elastic solutions. On the contrary the influence of the velocity or of the temperature is very low on the stresses inside the structure.

The proposed method is mainly interesting by its high speed compared to the finite element approach and however it is still able to calculate a viscoelastic multilayer structure. Software called VISCOROUTE (French name for viscoroad) based on this modelling is under development. Its main use will be the analysis of damages in aeronautic platforms.

1

D.M. Burmister, "The theory of stresses and displacements in layered systems and applications of the design of airport run ways", Proceedings of the Highway Research Board, 23, 126-148, 1943.

2

P. Autret, A. Baucheron de Boissoudy, J.P. Marchand, 1982, "ALIZE III Practice" Proc. 5th int. Conf. Structural Design of Asphalt Pavements, 174-191, Delft, 1982.

3

C. Huet, "Etude par une méthode d'impédance du comportement viscoélastique des matériaux hydrocarboné", PhD thesis, Faculté des sciences de Paris, 1963.

4

G. Sayegh, "Variation des modules de quelques bitumes purs et bétons bitumineux", Conférence au Groupe Français de Rhéologie, 51-74, 1963.

5

A. Chabot, J.M. Piau, "Calcul semi-analytique d'un massif viscoélastique soumis à une charge roulante rectangulaire", 1ère Conférence Internationale Albert Caquot, October, Paris, 2001.

6

V. Heck, J.M. Piau, J.C. Gramsammer, J.P. Kerzreho, H. Odéon, "Thermo-visco-elastic modelling of pavements behaviour and comparison with experimental data from LCPC test track", 5th Conference on Bearing Capacity of Roads and Airfields, Trondheim, Norway, 1998.

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