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Cone models for a soil layer on a flexible rock half‐space
Author(s) -
Wolf John P.,
Meek Jethro W.
Publication year - 1993
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290220302
Subject(s) - half space , reflection (computer programming) , stiffness , layer (electronics) , amplitude , refraction , cone (formal languages) , reflection coefficient , geology , range (aeronautics) , geotechnical engineering , frequency domain , optics , geometry , mechanics , physics , materials science , mathematical analysis , mathematics , structural engineering , engineering , computer science , algorithm , composite material , programming language
A modified truncated cone model is used to calculate approximately the dynamic response of a disk on the surface of a soil layer resting on flexible rock. The procedure is analogous to that for a layer on rigid rock, the only modification being that the reflection coefficient —α at the layer–rock interface is no longer equal to −1. The modified value of α can be determined straightforwardly by considering one‐dimensional wave propagation along the cone. The low‐ and high‐frequency limits lead to a frequency‐independent α, which allows the dynamic analysis to be performed directly in the familiar time domain. This cone represents a wave pattern with amplitude decay and also incorporates the reflection at the free surface and the reflection‐refraction at the layer–rock interface. The results for the static stiffness of the disk are highly accurate for a wide range of geometrical and material properties of the layer and the rock. For the dynamic stiffness the agreement with the exact solution is satisfactory.