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Kinematics of axisymmetric vertical slopes at collapse
Author(s) -
Drescher A.
Publication year - 1986
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.1610100407
Subject(s) - classification of discontinuities , rotational symmetry , kinematics , mathematics , stability (learning theory) , upper and lower bounds , geometry , classical mechanics , mechanics , mathematical analysis , physics , computer science , machine learning
This paper discusses the kinematic admissibility of axisymmetric velocity fields for the upper bound stability analysis of slopes surrounding cylindrical openings in frictional materials. The governing kinematic equations for two corner regimes of the Mohr–Coulomb yield condition are analysed. Although the equations can be solved by the method of characteristics, the characteristics and the characteristic relations for each regime differ significantly, for the Haar–von Karman regime the characteristics are non‐orthogonal and strong discontinuities are admissible, whereas for the other regime the characteristics are orthogonal and strong discontinuities must be excluded. Examples of simple velocity fields and the corresponding stability numbers are, given and compared with the partial collapse mechanisms. The solutions are verified against certain inequalities which must be satisfied for kinematical admissibility of axisymmetric velocity fields.