Experimental and numerical investigation of elastic wave dispersion and attenuation induced by coal particle damping

Abstract The collision of skeletal matrix particles in dry coal plays a crucial role in the dispersion and attenuation of elastic waves. Using a low-frequency testing system, acoustic velocity dispersion and energy attenuation experiments were performed across a frequency range of 1–250 Hz on two types of dry primary structure coal with varying metamorphic degrees, along with a 3D-printed model. Meanwhile, a discrete element numerical model was developed, incorporating damping particles and different gradations, based on the theory of rock particle damping, to simulate inter-particle collision behavior. The results indicate that rock dispersion and attenuation are affected by tangential damping, normal damping, and particle size distribution. Tangential damping contributes approximately three to four times more to these effects than normal damping. Notably, these effects are minimal when the damping coefficient is zero, and as the damping coefficient increases and particle distribution becomes more heterogeneous, the P-wave velocity decreases while dispersion and attenuation are significantly enhanced. Moreover, both the elastic wave velocity and attenuation coefficient exhibit pronounced frequency dependence in dry coal and 3D-printed models. Low-rank coal, with a broader particle size distribution and a more disordered, looser packing, demonstrates stronger dispersion and attenuation. In contrast, the polylactic acid (PLA) model fabricated by fused deposition modeling shows weaker dispersion and attenuation compared to the photosensitive resin model. This study provides crucial insights into the dispersion and attenuation mechanisms of primary structure coal, optimizing parameters such as particle elastic modulus, damping, and uniformity to improve understanding of the seismic acoustic response of dry coal.