Statistical Characterization of the Mechanical Parameters of Intact Rock Under Triaxial Compression: An Experimental Proof of the Jinping Marble

We investigated the statistical characteristics and probability distribution of the mechanical parameters of natural rock using triaxial compression tests. Twenty cores of Jinping marble were tested under each different levels of confining stress (i.e., 5, 10, 20, 30, and 40 MPa). From these full stress–strain data, we summarized the numerical characteristics and determined the probability distribution form of several important mechanical parameters, including deformational parameters, characteristic strength, characteristic strains, and failure angle. The statistical proofs relating to the mechanical parameters of rock presented new information about the marble’s probabilistic distribution characteristics. The normal and log-normal distributions were appropriate for describing random strengths of rock; the coefficients of variation of the peak strengths had no relationship to the confining stress; the only acceptable random distribution for both Young’s elastic modulus and Poisson’s ratio was the log-normal function; and the cohesive strength had a different probability distribution pattern than the frictional angle. The triaxial tests and statistical analysis also provided experimental evidence for deciding the minimum reliable number of experimental sample and for picking appropriate parameter distributions to use in reliability calculations for rock engineering.