Statistical analysis of some main geomechanical formulations evaluated with the Kaniadakis exponential law

The following paper reviews four well-known geomechanical equations, i.e. the elastic modulus of the rock mass as function of the Rock Mass Rating (RMR) system, the relation between Rock Quality Designation (RQD) and spacing distribution of the natural discontinuities in the rock mass, the distribution of the discontinuity spacing along a straight line for a rock mass and the intact rock strength in function of the specimen diameter by using a power-law flat tails equation based on the theory of Kaniadakis. The results show that by using novel formulations, the experimental data are better approximated by the power-law flat tails statistical approach, which shows a trend similar to ordinary exponential for a certain part of the interval of variability of x; the tails, however, follow the power law for extreme values of x. It was, therefore, possible to obtain new formulations able to better represent some fundamental aspects of geomechanics.