The interaction of airborne sound with the porous ground: The theoretical formulation

Abstract

The surface of the ground is modeled as that of an air-filled poroelastic soil layer of known thickness overlying a semi-infinite nonporous elastic substrate. Using a modified form of the Biot–Stoll differential equations for wave propagation in fluid-saturated porous media, propagation constants for the two possible dilatational waves and the shear wave in the poroelastic layer are determined. The dilatational waves are identified as a fast wave, moving predominately in the solid frame, and a slow wave, moving predominately in the pore air. The elastic moduli in the substrate are assumed to be those of the solid grains of which the poroelastic soil layer is composed. Intergranular friction in the soil and substrate is assumed to be negligible. Boundary conditions at the air–soil interface and at the porous soil–substrate interface are applied to determine, numerically, the displacement amplitudes of the allowed wave motions. From the incident and reflected amplitudes at the air–soil interface, the normalized ground surface impedance is calculated as a function of angle of incidence and of frequency. In this paper, the response of the pore fluid and frame to airborne acoustic waves is considered and those ideas will be pursued in a later publication. The predicted impedance at normal incidence is compared with measurements of the impedance of a sandy soil for which measurements of the various parameters required by the theory are also available. The predictions of impedance are found to be in tolerable agreement both with measured data and with predictions of a simpler model of the surface as that of a rigid porous semi-infinite homogeneous medium. Calculations of the surface impedance as a function of angle of incidence suggest that the porous medium is locally reacting.