Forests as a natural seismic metabarrier: analysis of interaction between trees and Rayleigh waves

The present thesis describes a sensitivity analysis over design parameters carried out through finite element simulations on seismic metamaterials, locally resonant structures able to affect the propagation of waves passing through them. Locally resonant metamaterials represent a particular type of resonant scattering, which is very powerful mean for stopping (bandgaps) and redirecting elastic waves at different length scales. This work, carried out at the Imperial College London, is inserted as part of the the METAFORET project, a large-scale wave experiment, which aims to demonstrate the effectiveness of metamaterials in geophysics. In particular, this project proved that a dense forest of tree can behave as a natural seismic metamaterial for Rayleigh surface waves. Thus creating anomalous dispersion curves and bandgap, frequency regions where the wave propagation is forbidden. These regions are associated with compressional and flexural resonances of the trees. Therefore I studied the same phenomena with time-domain numerical simulations, implemented in MATLAB. In particular, the simulation is performed with the spectral element method, a popular and efficient formulation of the finite element method that provides a numerical solution of partial differential equations. I analyzed the interaction between seismic metamaterials and the Rayleigh waves in one-dimensional and two-dimensional domain, neglecting the horizontal component to maintain the physical and numerical complexity low. This method is really efficient to conduct a sensitivity analysis, in order to identify which parameters influence the behavior of metamaterials and drive benchmarks.