Characterization of heterogenous soils using surface waves: Homogenization and numerical modelling

Seismic surface waves are well-adapted to study the elastic parameters, and hence the mechanical properties, of soils. The aim herein is to evaluate whether Rayleigh waves in heterogeneous soils may be used to estimate average elastic parameters and to determine how these parameters are influenced by heterogeneities. The heterogeneous medium, underlain by a homogeneous half-space, is considered as a homogeneous matrix with one or several types of randomly distributed inclusions (with a normal distribution) in the matrix. Seismic waves generated by surface loads and propagating in this medium were calculated using the finite element method (FEM) and then compared with single- and multiple-scattering homogenization methods. For the FEM calculation, special care was taken to reduce numerical dispersion through the use of elements smaller than 1/20 of the dominant wavelength. The group and phase velocity dispersion curves were measured and inverted in order to obtain the effective shear wave velocity of the heterogeneous medium. The results show a clear dependence of the wave velocity with respect to the nature, concentration, and size of the inclusions. The dependence with respect to the nature and concentration of inclusions coincides with that obtained from a multiple-scattering homogenization method up to an inclusion concentration of approximately 50%.