  The block medium is modeled by a discrete-periodic spatial lattice of masses
connected by elastic springs and viscous dampers. To describe the viscoelastic
behavior of the interblock layers, a rheological model of internal friction
with two Maxwell elements and one Voigt element with the quality factor of the
material as the determining parameter is proposed. Numerical experiments show
that, within the framework of this interlayer model, it is possible to select
the viscosity and stiffness of the Maxwell and Voigt elements so that the
quality factor of the material differs from the given constant value by no more
than 5%. In the one-dimensional case, within the framework of the proposed
model, the influence of the quality factor on the dispersion properties of a
block medium is studied and it is shown that the greatest effect of the quality
factor on the dispersion is observed in the low-frequency part of the spectrum.
In the three-dimensional case, within the framework of the proposed model, some
geomechanical problems are numerically studied for a block half-space under the
action of a surface concentrated vertical load. Namely, the attenuation of the
velocity amplitudes of surface blocks was studied depending on the Q-factor
under step action and under the action of a Gaussian pulse. In addition, we
study a layer on the surface of a half-space under the action of a concentrated
vertical impulse load in the case when both the layer and the half-space are
block media but have different properties.
