Influence of particle packing structure on sound velocity

The anisotropy in the particle systems of different packing structures affects the sound velocity. The acoustic propagation process in four kinds of packing structures (denoted as S45, H60, S90, and D) of two-dimensional granular system is simulated by the discrete element method. The velocity v_tof obtained by the time of flight method and the velocity v_c obtained from the stiffness tensor of the system are compared. Different sound velocities reflect various packing structures and force distributions within the system. The compression wave velocities of H60 and S90 are nearly the same, and transmit faster than that of D packing structure, while the sound velocity of S45 is the smallest. The shear wave velocities of S45 and H60 are nearly the same, and transmit faster than that of D packing structure. The compression wave velocity is sensitive to the volume fraction of the structure, however, the shear wave velocity is more sensitive to the geometrical structure itself. As the normal stress p is larger than 1 MPa, v_tof and v_c are almost equal, and the stiffness tensors of various structures explain the difference of sound velocities. When the normal stress is less than 1 MPa, with the coordination number unchanged, the law v_tof∝ p^1/4 still exists. This demonstrates that apart from different power laws between force and deformation as well as the change of the coordination number under different stresses, there are other complicated causes of v_tof∝ p^1/4, and an explanation of the deviation from v_tof∝ p^1/6 is given from the perspective of dissipation.