Probabilistic analysis of shear strength of intact rock in triaxial compression: a case study of Jinping II project

•Triaxial compression tests of marble from Jinping II project were conducted.•Marble shear strengths from triaxial tests were obtained.•Maximum entropy distributions of cohesive strength and angle of friction. Triaxial compression testing can yield realistic simulations of in-situ rock properties in underground excavation. This paper presents laboratory triaxial compression tests for marble from Jinping II hydropower station project, southwestern China. The test results were used to determine shear strength parameters (i.e., angles of internal friction and cohesive strengths) of the marble. Prominent uncertainties were found among the shear strength parameters. Modelling and quantifying these uncertainties in rock properties are initial, critical steps in probabilistic analysis and design of rock engineering. However, disagreement exists among researchers about which probability distribution should be used to characterize the rock angle of internal friction and the cohesive strength. This paper proposes an alternative universal form of probability distributions for these shear strength parameters, i.e., maximum entropy probability density functions. The entropy distributions are obtained from maximum entropy method, a combination of maximum entropy principle and a second order Akaike information criterion. The maximum entropy principle is used to determine a probability density function that maximizes Shannon’s entropy subjected to constraints in terms of sample integral moments. The second order Akaike information criterion can provide strong consistent and unbiased estimate for Kullback-Leibler entropy, and thus the most unbiased and objective probability density distribution with optimum order can be determined from an available sample. Kolmogorov-Smirnov test is used to establish the maximum entropy probability distributions, which are compared with conventional normal and lognormal probability distributions to illustrate the advantages.