The simulation of 3D elastic scattering produced by thin rigid inclusions using the traction boundary element method

Abstract

A mixed formulation that uses both the traction boundary element method (TBEM) and the boundary element method (BEM) is proposed to compute the three-dimensional (3D) propagation of elastic waves scattered by two-dimensional (2D) thin rigid inclusions. Although the conventional direct BEM has limitations when dealing with thin-body problems, this model overcomes that difficulty. It is formulated in the frequency domain and, taking into account the 2-1/2D configuration of the problem, can be expressed in terms of waves with varying wavenumbers in the z direction, k z . The elastic medium is homogeneous and unbounded and it should be noted that no restrictions are imposed on the geometry and orientation of the internal crack.

Some theoretical and numerical observations on scattering of Rayleigh waves in media containing shallow rectangular cavities

“…The cavity is characterized by analyzing the changes in the wave pattern in the time and/or the frequency domains caused by the waves scattered from cavities (Ganji et al, 1997;NasseriMoghaddam et al, 2007;Park et al, 1998Park et al, , 1999. Since the analysis of scattering wave field is important to the characterization of cavities, many analytical and numerical studies have been conducted on the wave scattering produced by different types of cavities and inclusions with different stiffness contrast from the surrounding soils (António and Tadeu, 2001;Boström and Kristensson, 1983;Campman, 2005;Campman et al, 2005;Ganji et al, 1997;Gelis et al, 2005;Höllinger and Ziegler, 1979;Nasseri-Moghaddam et al, 2007;Riyanti, 2005;Tadeu et al, 1996Tadeu et al, , 2002Tadeu et al, , 2006Wijk, 2003). These studies are helpful in developing appropriate inversion algorithms for characterization of cavities or subterranean inclusions from the collected data (Campman, 2005;Campman et al, 2005;Riyanti, 2005).…”

“…There are several methods to get the Green's functions in a homogeneous or layered half space (António and Tadeu, 2001;Campman, 2005;Campman et al, 2005;Kausel, 1999;Riyanti, 2005;Tadeu et al, 1996Tadeu et al, , 2002Tadeu et al, , 2006. Among these expressions, the discrete analytical expressions of the Green's functions obtained by the thin layer method are attractive (Kausel, 1999).…”

Coupling the BEM/TBEM and the MFS for the numerical simulation of acoustic wave propagation and transient conduction heat transfer

“…The resulting hypersingular kernels were computed analytically by defining the dynamic equilibrium of semi-cylinders above the boundary elements that discretize the crack. Following that, Tadeu et al [5] proposed a combined (or dual) BEM/TBEM formulation able to solve the case of fluid-filled thin inclusions placed in an unbounded medium, and in [6] they applied the same numerical techniques to the case of elastic scattering produced by thin rigid inclusions.…”

Forward modelling the multiply scattered 2.5-D teleseismicPwaves accelerated by the multilevel fast multipole method

“…Wu et al 2000; Xie & Wu 2001), boundary element method (e.g. Vai et al 1999; Tadeu et al 2006) and those distinctly defined methods (e.g. Faccioli et al 1997; Fu & Bouchon 2004; Haines et al 2004; Gao & Zhang 2006).…”