Influence of Hoek-Brown linearization and input cross-correlation in slope Probability of Failure Calculation

When Hoek-Brown failure-criterion (H-B) is selected, their parameters are determined as the ones that better fit data; therefore, depends on the method of fitting, the experimental error and statistical sufficiency of data. If these uncertainties are considered, H-B parameters are random variables. On the other hand, in slope stability analyses, is common to linearize the H-B criterion to estimate equivalent friction angle, ф_e, and cohesion, c_e, which generate a non-lineal relation between ф_e and c_e. In this paper, we examine the effect of this linearization in probabilistic analyses that use a Mohr-Coulomb criterion when the input data are random H-B parameters. We study the uncertainty propagation from H-B parameters to ф_e and c_e. Additionally, because linearization cross-correlate ф_e and c_e, we analyze the effect of the correlation ρ_фc in Factor of Safety (FS) and Probability of Failure (PoF) results, finally because also H-B parameters can be correlated we examine the effects on FS and PoF.