Revisiting statistical correlation between Mohr-Coulomb shear strength parameters of Hoek-Brown rock masses

Mohr-Coulomb shear strength parameters (i.e. cohesion c and friction angle ϕ) have been widely applied to analyses and designs of rock engineering (such as tunnels, underground caverns, and rock slopes), and they are statistically correlated. Such a correlation plays a vital role in the reliability and risk assessment of rock engineering, and is often quantified by their correlation coefficient ρ_{c ϕ}. Observations on ρ_{c ϕ} for intact rocks and rock masses are, however, conflicted, indicating that the ρ_{c ϕ} is negative for intact rocks while positive for rock masses. Reasons for such a confliction are unrevealed, posing difficulties in determining a proper ρ_{c ϕ} value for reliability and risk assessment of rock engineering. This study revisits the statistical correlation between c and ϕ of rock masses based on Hoek-Brown (H-B) failure criterion and triaxial test data of intact rocks. The rock masses, whose c and ϕ are derived from H-B failure criterion using triaxial test data of intact rocks, are referred to as “H-B rock masses”. Various uncertainties affecting ρ_{c ϕ} of H-B rock masses are first identified, and their effects on ρ_{c ϕ} are systematically explored. It is shown that the positive correlation between c and ϕ of H-B rock masses is attributed to the simultaneous decrease in c and ϕ with the decrease of Geological Strength Index of rock masses and the increase in lumped uncertainty in triaxial test data of intact rocks. Nevertheless, the negative correlation between c and ϕ of intact rocks is due to the decomposition of a certain shear strength of intact rocks into cohesion and friction parts. The increase in one part leads to the decrease in the other part so as to obtain the same shear strength of a given type of intact rock. The generalized H-B failure criterion allows exploring the correlation between c and ϕ of intact rocks and rock masses under a unified framework.