## Statics and Kinematics of Granular MaterialsThis book outlines the basic science underlying the prediction of stress and velocity distributions in granular materials. The nature of a rigid-plastic material is discussed and a comparison is made between the Coulomb and conical (extended Von Mises) models. The methods of measuring material properties are described and an interpretation of the experimental results is considered in the context of the Critical State Theory. Exercises and solutions are provided that will be particularly useful for the reader. |

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### Contents

1 Introduction | 1 |

2 The analysis of stress and strain rate | 7 |

3 The ideal Coulomb material | 21 |

4 Coulombs method of wedges | 47 |

5 The method of differential slices | 84 |

6 Determination of physical properties | 127 |

7 Exact stress analyses | 163 |

8 Velocity distributions | 243 |

9 The Conical yield function | 277 |

10 The prediction of mass flow rate | 292 |

Set problems chapters 210 | 329 |

Appendices | 338 |

346 | |

349 | |

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### Common terms and phrases

active failure analysis angle of friction angle of internal angle of repose angle of wall assumed asymptote boundary conditions bulk density calculation centre-line co-ordinates coefﬁcient cohesionless material conﬁned conical hopper consider constant Coulomb material cylindrical bunker deﬁned by equation deﬁnition denote depth deviatoric diameter discharge discontinuity evaluate Figure ﬁll ﬁnd ﬁrst ﬂow rule ﬂuid force given by equation gives granular materials hence horizontal incipient yield inclined internal friction Janssen’s Jenike log-normal distribution major principal stress mass ﬂow rate method of characteristics method of wedges Mohr’s circle normal stress obtained occur oriﬁce particle predicted proﬁles radial stress ﬁeld radius retaining wall shear strain shear stress shown in ﬁgure sign convention slip plane slip surface slope solution speciﬁc strain rate stress distribution stress parameters sufﬁcient surcharge top surface voidage Walker’s wall friction wall stress x-face x-plane yield function zero