  In this article the physics of horizontally polarized shear waves travelling
across a locally resonant metasurface in an unconsolidated granular medium is
experimentally and numerically explored. The metasurface is comprised of an
arrangement of sub-wavelength horizontal mechanical resonators embedded in
silica microbeads. The metasurface supports a frequency-tailorable attenuation
zone induced by the translational mode of the resonators. The experimental and
numerical findings reveal that the metasurface not only backscatters part of
the energy, but also redirects the wavefront underneath the resonators leading
to a considerable amplitude attenuation at the surface level, when all the
resonators have similar resonant frequency. A more complex picture emerges when
using resonators arranged in a so-called graded design, e.g., with a resonant
frequency increasing/decreasing throughout the metasurface. Unlike Love waves
propagating in a bi-layer medium, shear waves localized at the surface of our
metasurface are not converted into bulk waves. Although a detachment from the
surface occurs, the depth-dependent velocity profile of the granular medium
prevents the mode-conversion, steering again the horizontally polarized shear
waves towards the surface. The outcomes of our experimental and numerical
studies allow for understanding the dynamics of wave propagation in resonant
metamaterials embedded in vertically inhomogeneous soils and, therefore, are
essential for improving the design of engineered devices for ground vibration
and seismic wave containment.
