Global sensitivity analysis for transformation of Hoek-Brown failure criterion for rock mass

Abstract

A variety of engineering activities require reliable evaluation of rock strength. For instance, the stability of rock slopes depends on structural geology of rock massif in which the slope is excavated. Hoek-Brown (HB) failure criterion applied in rock design practice introduces factors based on the properties of jointed rock. The non-linear finite element safety calculation is conveniently used for calculation safety the factor of slope stability. The Mohr-Coulomb (MC) failure (strength) criterion for soil is widely applied in geotechnical design. Therefore, the appropriate transformation from HB to the equivalent MC, employing angle of shearing resistance φ and cohesion c, is necessary. This article studies the effect of jointed rock massif properties on the transformed MC parameters by using Sobol’s global sensitivity analysis (SSA) and HB transformation equations. Statistical parameters needed for the evaluation of sensitivity analysis are processed using classical statistical methods upon the emulation of Latin Hypercube Sampling simulation methods. Developed and adapted by authors techniques are illustrated by processing real rock investigation data from survey of the trachyte massif located in the Czech Republic. The first and higher order effects of random inputs are identified using SSA. It is illustrated that the effects of inputs on the MC parameters varies significantly depending on the discontinuity distribution and height of the slope.

Keywords

• sensitivity analysis
• reliability
• statistical analysis
• Latin hypercube sampling
• jointed rock
• rock sample