Scattering Of Surface Waves At Anisotropic Wave Barriers

Abstract

In this paper we consider the screening effectiveness of an infilled trench for isolation from near-surface ground-transmitted vibrations. The infilled trench is modeled by a vertical anisotropic layer embedded into an isotropic half-space. To study surface wave scattering at the layer we employ the Green’s function technique. The narrow anisotropic layer is modeled by a matrix operator which relates displacement and stress fields at the left-hand side and right-hand side of the layer. The matrix operator is obtained using Taylor’s series decomposition. To represent the field inside the thick layer we apply forward-backward decomposition of the field and calculate forward and backward scattering coefficients of the layer. The results of calculations for the anisotropic layers are compared with similar calculations for various isotropic layers. INTRODUCTION Isolation of buildings and machine foundations from ground-transmitted vibrations by installation of wave barriers has been attempted many times and has met with various degrees of success. In the last three decades various experimental, numerical and analytical techniques have been applied to study surface wave propagation across different kinds of barriers or deep trenches [ e.g., Woods (1968), Richart et al. (1970)) Segol et al. (1978), Leung et al. (1990), Ahmad and Al-Hussaini (1991)) Lee and Its (1995)]. These investigations confirmed the effectiveness of deep narrow open trenches for reducing the amplitude of the transmitted surface wave. However, keeping the deep trenches open can cause some problems from the engineering point of view. Therefore, infilled trenches have also been investigated. The screening effectiveness of an infilled trench depends on the host medium and filling materials, on the dimensions of the trench (in a wavelength scale), and on the angle of the wave incidence. Aboudi (1973), Biagi et al. (1990), L eung et al. (1990) and Lee and Its (1995) showed the advantage of low shear velocity barriers compared to high velocity ones for near normal angles of incidence. On the other hand, screen parameters of high velocity barriers increase significantly for large angles. These results suggest the use of a composite barrier which behaves as a low velocity barrier for small angles of incidence and as a high velocity one for big angles. A three layer composite barrier was studied by Its and Lee (1993a). The inner low velocity layers were modeled by non welded boundary conditions,