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Modélisation à l'échelle du réseau de conduits des propriétés acoustiques d'un matériau poreux : application aux enrobés drainants

Abstract : We propose, on a microscopic scale, a model that predicts the acoustical characteristics of porous road. The Biot theory shows that the skeleton can be considered as rigid, so we limit our study to propagation of waves in the pores. For materials containing pores of uniform cross section, we need only three parameters to characterise physically the porous medium (classical model). These parameters are porosity, tortuosity and flow resistivity. For more complex materials, and specially for porous road, the discontinuity of the granular composition induces a disorder in size and shape of the pore distribution. The shape influence being poor, we approximate the pore as a series of straight uniform tubes with constant area over the length of each section. We generalise the deterministic approach established by Stinson and Champoux for arbitrary materials with two different shape factors to describe the viscous and thermal effects. We introduce the random distribution in a different way. For each elementary section we associate a transfer matrix which links the pressures and velocities on both edges of the tube. A global transfer matrix is calculated for the pore by the product of elementary matrices. At low frequencies, this matrix depends on macroscopic parameters as in the classical model. When the frequency increases, we need other parameters characterising the pore size distribution. This formulation allows us to relate the pore geometry to the physical parameters. By this way, we propose new theoretical formulations for these quantities and for the additional parameters. The surface impedance is obtained by a homogenisation method, with an integral formulation. Thus, we can take into account different kind of pores in a discrete model, where the problem is formulated also in terms of transfer matrices. The results are illustrated for the classical, the generalised and the discrete models with numerical simulations for different kind of porous media.
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Othman Belhoucine Drissi. Modélisation à l'échelle du réseau de conduits des propriétés acoustiques d'un matériau poreux : application aux enrobés drainants. Acoustique [physics.class-ph]. Ecole Nationale des Ponts et Chaussées, 1997. Français. ⟨tel-00529387⟩

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