Kinematics of axisymmetric vertical slopes at collapse

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.