Forest trees as a natural metamaterial for surface wave attenuation in stratified soils

Abstract

Forest trees have been shown to act as a natural metamaterial to attenuate elastic waves. However, the existing studies assumed that forest trees are located on homogeneous soils and did not consider the soil stratification that widely exists in natural strata. This study investigates the forest trees as a natural metamaterial to manipulate the propagation of elastic waves in stratified soils. A semi-analytical method is proposed to calculate the dynamic responses of a layered half-space coupled with arbitrary number of trees. A close-form Green’s function for a harmonic line load on a layered half-space is derived by the thin layer method, and subsequently used to determine the multiple scattered wavefield induced by forest trees as surface oscillators. The attenuation performance of forest trees on stratified soils is systematically investigated. Trees with a graded array of heights can provide a wide attenuation zone at frequencies below 80 Hz. Since the higher surface wave modes in a layered half-space can propagate forward without being affected by trees, the attenuation efficiency of trees on stratified soils is significantly lower than that of trees on corresponding homogeneous soils. The performance uncertainty induced by the randomness of the height, sizes, and spacing of trees is subsequently investigated through a Monte Carlo simulation. The forest trees can still obtain a significant attenuation efficiency at frequencies below 80 Hz even the randomness of tree properties being considered. The randomness in height and radius leads to significant uncertainty in attenuation performance, while the randomness in spacing results in reasonable uncertainty.