# Free surface problems for static Coulomb-Mohr granular solids

McCue, Scott W. & Hill, James M.
(2005)
Free surface problems for static Coulomb-Mohr granular solids.
*Mathematics and Mechanics of Solids*, *10*(6), pp. 651-672.

## Abstract

This paper is concerned with some plane strain and axially symmetric free surface problems which arise in the study of static granular solids that satisfy the Coulomb-Mohr yield condition. Such problems are inherently nonlinear, and hence difficult to attack analytically. Given a Coulomb friction condition holds on a solid boundary, it is shown that the angle a free surface is allowed to attach to the boundary is dependent only on the angle of wall friction, assuming the stresses are all continuous at the attachment point, and assuming also that the coefficient of cohesion is nonzero. As a model problem, the formation of stable cohesive arches in hoppers is considered. This undesirable phenomena is an obstacle to flow, and occurs when the hopper outlet is too small. Typically, engineers are concerned with predicting the critical outlet size for a given hopper and granular solid, so that for hoppers with outlets larger than this critical value, arching cannot occur. This is a topic of considerable practical interest, with most accepted engineering methods being conservative in nature. Here, the governing equations in two limiting cases (small cohesion and high angle of internal friction) are considered directly. No information on the critical outlet size is found; however solutions for the shape of the free boundary (the arch) are presented, for both plane and axially symmetric geometries.

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ID Code: | 40055 |
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Item Type: | Journal Article |

Keywords: | granular materials, cohesive arching, free surface problems, Coulomb-Mohr yield condition |

DOI: | 10.1177/1081286505036423 |

ISSN: | 1081-2865 |

Subjects: | Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Theoretical and Applied Mechanics (010207) |

Divisions: | Past > QUT Faculties & Divisions > Faculty of Science and Technology Past > Schools > Mathematical Sciences |

Copyright Owner: | Copyright 2005 SAGE Publications |

Deposited On: | 14 Feb 2011 23:19 |

Last Modified: | 15 Feb 2011 06:19 |

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