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Energy dissipation during wave propagation in fragmented\udgeomaterials can be caused by independent movement of fragments leading to\udenergy loss on their impact. By considering a pair of impacting fragments at\udtimes much greater than the period of their oscillations, we show that at a\udlarge timescale, the dynamics of the pair can be described by a linear\udviscous model with damping coefficients expressed through the restitution\udcoefficient representing energy loss on impact. Wave propagation in\udfragmented geomaterials is also considered at the large timescale assuming\udthat the wavelengths are much larger than the fragment sizes such that the\udattenuation associated with wave scattering on the fragment interfaces can be\udneglected. These assumptions lead to the Kelvin–Voigt model of damping\udduring wave propagation, which allows the determination of a dispersion\udrelationship. As the attenuation and dispersion are not related to the rate\uddependence of rock deformation, but rather to the interaction of fragments,\udthe increased energy dispersion at low frequencies can be seen as an\udindication of the fragmented nature of the geomaterial and the capacity of\udthe fragments for independent movement

Continuum model of wave propagation in fragmented media: linear damping approximation