Simulation of sound propagation and calculation of its velocity in spherical and superellipsoidal particle systems

Abstract

Discrete element method is used to simulate sound propagation in spherical and superellipsoidal particle systems and calculate the sound velocities under different boundary and stress conditions. Compressional and shear wave velocities at different axial and confining pressures for a conventional triaxial compressed spherical particle system under cylindrical boundary condition are calculated through time-of-flight method and analyzed using stiffness, effective medium theory (EMT), and granular solid hydrodynamics (GSH) theory. Results obtained through the time-of-flight method for a system under fixed boundary condition are consistent with the existing experimental results. The system stiffness calculated by branch vector and contact force can explain the variation of sound velocity with axial stress and confining pressure. For compressional velocities, the simulation results of spherical particle system at different axial stresses under isotropic compression in radial direction are consistent with the theoretical results provided by EMT and GSH theories. Compared with compressional velocities, shear velocities predicted by EMT are bigger than experiments, and shear modulus of theories improving upon EMT gives velocities in accordance with experiment. Moreover, the sound velocities of spherical and superellipsoidal particle systems are calculated under the same boundary and normal stress conditions to investigate the influence of particle shape on the sound velocity. The difference between compressional wave velocities in spherical and superellipsoidal particle systems is evident and is qualitatively explained from the perspective of anisotropy of contact force distribution in the system. The proposed methods of sound propagation simulation and sound velocity calculation can be used to investigate the elastic wave propagation in particle system, and can obtain the microscopic quantities that are difficult to obtain experimentally and theoretically. They can provide references for the study of EMT and GSH theories and further discuss the influence of shape-induced anisotropy on sound velocity.