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The properties of anisotropic conical failure surfaces in relation to the Mohr–Coulomb criterion
Author(s) -
Griffiths D. V.,
Prevost J. H.
Publication year - 1988
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.1610120504
Subject(s) - conical surface , singularity , mohr–coulomb theory , diagonal , extension (predicate logic) , gravitational singularity , geometry , wedge (geometry) , anisotropy , principal stress , mathematics , coulomb , stress space , friction angle , surface (topology) , mathematical analysis , physics , geotechnical engineering , geology , constitutive equation , finite element method , optics , cauchy stress tensor , quantum mechanics , computer science , thermodynamics , programming language , electron
An earlier publication 1 considered the properties of circular conical failure surfaces whose axes coincide with the space diagonal in principal stress space. The present work uses a similar approach to analyse conical surfaces that are offset from the space diagonal. It is shown that cones fitted to the Mohr–Coulomb surface in triaxial compression contain a potential singularity. The occurrence and location of the singularity depends on the Mohr–Coulomb friction angle to which the surface is fitted in triaxial extension. It is shown that for a cone fitted to the same friction angle in both triaxial extension and compression, singular conditions occur when that angle reaches \documentclass{article}\pagestyle{empty}\begin{document}$ \sin ^{ - 1} \left({\sqrt 7 - 2} \right)\left({ = 40.22^\circ } \right) $\end{document} . Even cones fitted to smaller friction angles give significant overestimations of material strength for certain stress paths.