Weibull distribution parameters of rock strength based on multi-fractal characteristics of rock damage

According to the standpoint of multi-fractal, three-dimensional multi-fractal spectra which can indicate the complexity of the micro-crack distribution in damaged rock are calculated and plotted. By introducing a relative fractal dimension value which can reveal inhomogeneity and anisotropy of damaged rock material and considering the singularity values of multi-fractal spectra, a quantitative method for actual damage state of the rock is derived. In addition, based on the representation of Mohr-Coulomb criterion and the characteristics of Weibull random distribution of rock strength, the change laws of Weibull parameters on diffreent multi-fractal parameters are studied by introducing a fractal parameter into the constitutive model and considering the uniaxial stress-strain test curve of rock. The results show that for the same rock in different damage states, the Weibull parameters change according to certain rules, and the distribution of micro-cracks in damaged rock has different influences on the post-peak strength of rock. The test results may further improve the statistical damage constitutive model of rock.