Acoustic granular materials with pore size distribution close to log-normal

Abstract

The water suction method is used to determine the parameters of the pore size distribution of a representative selection of loose and consolidated granular materials. It is shown that the experimentally determined pore size distribution in granular materials is often close to log-normal. The low- and high-frequency asymptotic behavior of the Biot viscosity correction function for media with log-normal pore size distribution is investigated and used to develop a simple rational approximation. This approximation is used to predict accurately the acoustic characteristic impedance and propagation constant for this class of materials. Unlike many available theoretical models for the acoustic properties of porous media which involve empirical shape factors, the proposed approximation is based entirely on four routinely measurable nonacoustic parameters: the porosity, flow resistivity, tortuosity, and the standard deviation of the pore size. The theoretical predictions for the acoustic surface impedance and absorption coefficient of loose and consolidated granulates are compared against the experimental results. A good agreement is obtained throughout the considered frequency range. [The authors are grateful to the Engineering and Physical Sciences Research Council (EPSRC) in the UK (Grant GR/L54905) for the support of this work. The authors would like to thank Dr. P. Leclaire for his help with the water suction experiments.]