Nonexistence of Solution for Horizontally Rigid Half-Space
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 137, Issue 4
Abstract
The Westergaard expressions for stresses and displacements in a half-space of Westergaard material are shown to be invalid because the vertical shear stress does not vanish at the plane boundary of the half-space. The same inadequacy is discovered in the solution for a horizontally rigid cross-anisotropic half-space deduced from Michell’s expressions. A surprising conclusion is drawn, namely, that there is currently no exact elastic solution for the stresses and displacements in a horizontally rigid cross-anisotropic half-space. The Westergaard theory should cease to be regarded as an exact elastic solution for a problem of the theory of elasticity.
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Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 137 • Issue 4 • April 2011
Pages: 430 - 434
Copyright
© 2011 American Society of Civil Engineers.
History
Received: May 10, 2010
Accepted: Sep 12, 2010
Published online: Sep 18, 2010
Published in print: Apr 1, 2011
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