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Propagation of shock waves at the surface of heterogeneous soil grounds
Author(s) -
Holzlöhner U.,
Auersch L.
Publication year - 1984
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.1610080105
Subject(s) - shear modulus , half space , mechanics , rayleigh wave , wave propagation , geotechnical engineering , shear (geology) , dispersion (optics) , surface wave , shock wave , physics , mathematics , geometry , materials science , geology , optics , composite material
Abstract The paper deals with the propagation of shock waves at the surface of soils. Heterogeneity and damping are introduced into analytical half‐space solutions. The suggested model explains two phenomena, often observed with shock propagation in actual soils, that differ from the behaviour of the homogeneous half‐space: the pronounced decay of the disturbances with distance and the elongation of the disturbance into a train of waves. The effects of heterogeneity and damping are discussed quantitatively. The response of footings on heterogeneous soils has been investigated by several authors. Awojobi 4 considered the Gibson soil in which the shear modulus increases linearly with depth. Luco 5 and Gazetas and Roesset 6 investigated a multi‐layered soil, the shear modulus being constant within each layer. Gazetas 7 , using a technique suggested by Gupta 8 extended this method to layers with linearly varying shear modulus. Little work is available on the propagation of waves in heterogeneous bodies. Some results concerning the modes and the mode shapes in heterogeneous soils were reported by Ewing, Jardetzky and Press 9 and Bath. 10 The modes have to be superposed in an appropriate way to obtain the displacement field at the surface. This has been approximately achieved by the finite element formulations of Lysmer, 11 , Lysmer and Waas 12 and Waas. 13 Auersch 14 applied this method to a homogeneous layer on a rigid base. He found some dispersion of the Rayleigh wave within a narrow frequency range. Finite elements combined with discrete Laplace transforms, however, consume much computer time. Rao and Goda 15 and Rao 16 calculated surface vibrations of a half‐space with exponentially varying shear modulus and density. Their method is similar to Lamb'S 1 procedure for the homogeneous half‐space. Only one mode–the Rayleigh wave–occurs in their heterogeneous half‐space. The examples show the considerable effect of heterogeneity on wave propagation. In the present paper, more general variations of the shear modulus are considered.