3D seismic response of a limited valley via BEM using 2.5D analytical Green's functions for an infinite free-rigid layer

Abstract

This paper presents analytical solutions for computing the 3D displacements in a flat solid elastic stratum bounded by a rigid base, when it is subjected to spatially sinusoidal harmonic line loads. These functions are also used as Greens functions in a boundary element method code that simulates the seismic wave propagation in a confined or semi-confined 2D valley, avoiding the discretization of the free and rigid horizontal boundaries.The models developed are then used to simulate wave propagation within a rigid stratum and valleys with different dimensions and geometries, when struck by a spatially sinusoidal harmonic vertical line load. Simulations are performed in the frequency domain, for varying spatial wave numbers in the axial direction of the valley. Time results are obtained by means of inverse Fourier transforms, to help understand how the geometry of the valley may affect the variation of the displacement field. q

Wave propagation in the presence of empty cracks in an elastic medium

“…3 in a cross-sectional 2D view. The crack is located inside an unbounded elastic medium, which has a mass density of 2140 kg/m 3 First, the displacement jumps along that crack, obtained by the TBEM model, are compared with the displacements at the top and bottom of the same crack, given by the TBEM + BEM model, for a specific frequency and spatial wavenumber. Afterwards, a set of 3D snapshots taken from computer animations at different time instants, makes the analysis of the TBEM time-dependent results easier.…”

“…This corresponds to reducing (by one) the problem's dimension, since in twodimensional (2D) problems only the line boundary of the domain is discretized and in three-dimensional (3D) problems only the surface of the domain needs to be discretized. Other advantages of the BEM include the automatic verification of the far-field conditions in unbounded or layered media, the way it can easily handle irregular geometries and the precision achieved, without the discretization of the interior domains [3,34,40].…”

2.5D elastic wave propagation in non-homogeneous media coupling the BEM and MLPG methods

“…Yang and Hung [22] analyzed visco-elastic bodies subjected to moving loads by means of a 2.5D finite and infinite element approach. A 2.5D BEM approach was also applied to layered elastic and acoustic formations by Tadeu and Antonio [23] and to seismic analyses [24]. An overview of the structural response to moving loads analyzed by finite element and boundary element schemes is given by Andersen et al [25].…”

Wave Propagation Due to an Embedded Seismic Source in a Graded Half-Plane with Relief Peculiarities Part I: Mechanical Model and Computational Technique

“…Guan et al [39] presented a transient Green's function, caused by suddenly applied line load in an isotropic and homogeneous half-space. Antonio and Tadeu [40] presented analytical solutions for computing the 3D displacements in a flat elastic stratum bounded by a rigid base, when it is subjected to spatially sinusoidal harmonic line loads. These functions are also used as Green's functions in a BIEM code that simulates the seismic wave propagation in a confined or semi-confined 2D valley, avoiding the discretization of the free and rigid horizontal boundaries.…”