Roof stability in flat-ceiling deep rock cavities and tunnels

Three-dimensional stability of roofs in deep flat-ceiling cavities is analyzed. The stability number, factor of safety, and required supporting stress are used as measures of roof stability. Despite the simplicity of the flat roof geometry, the three-dimensional stability analysis presents some complexities owed to the shape of the failure surface geometry in the collapse mechanism. The failure mode assumes a rock block moving downward into the cavity, and the study aims to recognize the most critical shape of the failing block. Three specific block shapes are described in some detail, but more have been analyzed. Blocks defined by a special case of a 4th order conical surface (quartic) on a rectangular base, and a 2nd order elliptic surface (quadric) are found to be the most critical in the stability analysis. The kinematic approach of limit analysis was used, with the rock strength governed by the Hoek-Brown failure criterion. The parametric form of the Hoek-Brown function was employed. Interestingly, an absence of diagonal symmetries in the most critical failure mechanisms was observed in roof collapse of square-ceiling cavities. Computational results in terms of dimensionless measures of stability are presented in charts and tables.