Free-Field (Elastic or Poroelastic) Half-Space Zero-Stress or Related Boundary Conditions

Abstract eng:
The boundary-valued problem for solving for waves scattered and diffracted from surface and sub-surface topographies have attracted much attention to earthquake and structural engineers and strong-motion seismologists since the last century. It is of importance in the design, construction and analysis of earthquake resistant surface and sub-surface structures in seismic active areas that are vulnerable to near field or far field strong-motion earthquakes. The half-space medium can be elastic, or poroelastic and fluid saturated, the later case has attracted much new research in recent years. The presence of a surface or sub-surface topography, like the case of a surface canyon, valley, canal or structural foundations, or an underground cavity, tunnel or pipe, will result in scattered and diffracted waves being generated. Combined with the free-field input waves, they will together satisfy the appropriate stress and/or displacement boundary conditions at the surface of the topography present in the model. For those problems where analytical solutions are preferred in the studies, this often involves a topography that is either: circular, elliptic, spherical or parabolic in shape. This is because in those coordinate systems, the scattered waves are expressible in terms of orthogonal wave functions, and the surface of the topography often allows the orthogonal boundary conditions to be applied, so that the wave coefficients can be analytically defined. However, the presence of the half-space boundary makes the problem much more complicated. The scattered wave functions are no longer orthogonal on the flat half-space surface, and the zero-stress or related boundary conditions are no longer simple nor straight forward to apply. This paper will examine the available numerical and approximate methods that have been attempted or proposed, and the direction all future research is taking us to solve this part of the problem.

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