Geometric and material attenuation of surface acoustic modes in granular media

Granular materials can be used in laboratory-scale physical models to simulate and study seismic wave propagation in various unconsolidated, porous heterogeneous media. This is due to the diverse available grain configurations, in terms of their shape, size and mechanical parameters, which enable the physical and geological modelling of various complex substrates. In this work, an unconsolidated granular medium, made of silica microbeads, featuring a gravity-induced power-law stiffness profile is experimentally tested in a laboratory setting. The objective is to investigate the attenuation mechanisms of vertically polarized seismic waves traveling at the surface of unconsolidated substrates that are characterized by power-law rigidity profiles. Both geometric spreading and material damping due to skeletal dissipation are considered. The understanding of these two attenuation mechanisms is crucial in seismology for properly determining the seismic site response. An electromagnetic shaker is employed to excite the granular medium between 300 and 550 Hz, generating linear modes that are localized near the surface. A densely sampled section is recorded at the surface using a laser vibrometer. The explicit solution of the geometric attenuation law of Rayleigh-like waves in layered media is employed to calculate the geometric spreading function of the vertically polarized surface modes within the granular material. In accordance with recent studies, the dynamics of these small-amplitude multimodal linear waves can be analysed by considering the granular medium as perfectly continuous and elastic. By performing a nonlinear regression analysis on particle displacements, extracted from experimental velocity data, we determine the frequency-dependent attenuation coefficients, which account for the material damping. The findings of this work show that laboratory-scale physical models can be used to study the geometric spreading of vertically polarized seismic waves induced by the soil inhomogeneity and characterize the material damping of the medium.