Percus–Yevick radial distribution function calculation for a water-saturated granular medium

• We develop a numerical algorithm to calculate the Percus-Yevick radial distribution function with a high volume fraction.
• Our algorithm is composed of combining the analytic method and the filtered Fourier transform method.
• We show that our method provides better results up to long distance for the high volume fraction.
• The proposed method is useful for calculating the effective mechanical property of porous medium like ocean sediment.

This paper presents a practical technique to evaluate the Percus–Yevick (PY) radial distribution function (RDF) for a water-saturated granular medium with a high volume fraction of grains. This is based on the weighted average of the PY RDF׳s recursive formula (Goodwin et al., 1992) and the PY integral equation׳s numerical solution using the filtered fast Fourier transform. In a highly dense medium, the combination of both models produces more accurate and stable results. The error analysis for the volume fraction of scatterers and the distance is given for validation. Finally, using the proposed PY RDF result, we solve an acoustic multiple-scattering equation with quasi-crystalline approximation (QCA) to obtain the effective bulk modulus and attenuation of the water-saturated granular medium, and confirm that our method provides a reasonable result.