Keywords: dynamic, semi-analytical model, finite element method, falling weight deflectometer, flexible pavement, Rayleigh damping, viscosity, non-destructive testing.

The study of a bituminous pavement represents an important stage to the diagnosis as well as the repair of road structures. Indeed, the lifespan of these structures is difficult to estimate accurately with elastic and static models because vehicles cause a dynamic response. Moreover, in these multi-layered structures, the first layer has a viscoelastic behavior implying the stiffness dependence on temperature and frequency.

Two methods for the solution of the dynamic equation are used in this paper. In the first method, the authors propose a two-dimensional axisymmetric semi-analytical approach to study the displacements induced by a transient load in a multilayered structure [1,2]. The model includes either hysteretic, Rayleigh or viscoelastic damping. The theoretical approach uses a Helmholtz decomposition for the displacements. Moreover, a Fourier transform on the time variable and a Hankel transform on the surface radial variable is introduced to obtain displacements in the frequency-wavenumber domain. Transformed displacements are expressed in terms of an incident and reflected waves in each layer and in terms of incident wave in the half-space. A matrix conditioning technique is implemented to avoid numerical problems due to exponential terms. Boundary conditions are also established with matrix formulation to link the stresses at each interface to the displacement vector. Transformed displacements are then obtained numerically. Besides, inverse fast Fourier transform is performed to obtain the displacements in the time. The inverse Hankel transform is performed with the Filon method. In the second method, a coupled finite element-absorbing boundary model is used. The solution of the dynamic problem is performed using Newmark's explicit algorithm based on the central finite difference method. Two types of damping are studied. First, Rayleigh damping is taken into account in the platform, which implies a diminution in amplitude according to the distance and a weak dephasing. Then, viscoelastic damping in the bituminous structure shows a dephasing which depends only on the viscosity value.

A comparison between the various models and measurements using a falling weight deflectometer (FWD) [3] on an instrumented pavement [4] is introduced. Nine sensors used by the FWD on the structure make it possible to obtain information on wave propagation arrival times, basin of deflections, reflexions at rigid layers and the apparent stiffness of the various layers and their evolution. Further works will be based on the numerical model for which results are close to the real behavior of the pavement and will be used in a process of inverse analysis and lead to the estimation of the state of the pavement's degradation.

1

A. Mesgouez, G. Lefeuve-Mesgouez, "Study of transient poroviscoelastic soil motions by semi-analytical and numerical approaches", Soil Dyn Earthquake Eng, 29(2), 245-248, 2009. doi:10.1016/j.soildyn.2008.02.002

2

G. Lefeuve-Mesgouez, A. Mesgouez, "Ground vibration due to a high-speed moving harmonic rectangular load on a poroviscoelastic half-space", Int. Journal of Solids and Structures, 45(11-12), 3353-3374, 2008. doi:10.1016/j.ijsolstr.2008.01.026

3

B. Picoux, K. El Ayadi, C. Petit, "Dynamic response of a flexible pavement submitted by impulsive loading", Soil Dynamics and Earthquake Engineering, 29(5), 845-854, 2009. doi:10.1016/j.soildyn.2008.09.001

4

A. Phelipot-Mardelé, B. Picoux, A. Millien, C. Petit, "Stratégie, conception et construction d'une chaussée expérimentale pour le diagnostic d'une structure comportant des défauts", Geodim'08, April 2008.

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