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Cylindrical cavities and classical rat‐hole theory occurring in bulk materials
Author(s) -
Hill James M.,
Cox Grant M.
Publication year - 2000
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 - 10.1002/1096-9853(200010)24:12<971::aid-nag107>3.0.co;2-g
Subject(s) - internal friction , exact solutions in general relativity , basis (linear algebra) , mathematics , differential equation , friction angle , mathematical analysis , mechanics , physics , geometry , materials science , geotechnical engineering , geology , composite material
The phenomenon of stable cylindrical cavities known as rat‐holes in stockpiles and hoppers is well known but is not properly understood, and existing theory is unsatisfactory, in that it is believed not to properly incorporate actual material properties. Here the classical rat‐hole theory of Jenike and his coworkers is re‐examined, with a view to examining the validity of the so‐called ‘stable rat‐hole equation’, which is widely used in practice. For certain plastic regimes, new exact analytical solutions are determined for two special values of the angle of internal friction. One of the exact results may be used as the basis of an approximate solution valid for small angles of internal friction. Further, these exact and approximate solutions are compared with a full numerical solution of the governing differential equations. One of the approximations used by Jenike and his coworkers is shown to be invalid. Copyright © 2000 John Wiley & Sons, Ltd.