Planar Slope Failure in Heavily Jointed Rock: Tension Cracks and Nonlinear Strength

Abstract

This work proposes the calculation of the factor of safety for a strongly jointed rock mass in the case of plane failure with a tensile crack whose exact position or depth is not known but is expected to exist. This calculation is performed by applying the non-linear failure criteria of the Focus Procedure of Úcar and Hoek–Brown’s and implementing the necessary formulae in a spreadsheet. The aim is to provide a simple, cost-effective, and easy-to-use procedure that is useful in the early stages of a project or as a starting point for more detailed investigations. Besides slope geometry and strength parameters, the required parameters are the RMR of the rock mass or its mi, depending on the criterion used. The proposed procedure allows for the estimation of the factor of safety, the position and depth of the tensile crack, and the inclination of the failure plane in the most unfavorable case, with reasonable accuracy, using an iterative process with the conventional tools available in common spreadsheet programs. An example is provided in which an accuracy of 86–96% for the factor of safety is obtained.