Prediction model for sandstone strength based on Weibull distribution of micro-element strength and power-law distribution of crack length

Abstract

It is of the great significance to construct the strength prediction model that considers the influence of the macro and micro defects in the rock in an overall manner to ensure the construction of smart mines and the safety of underground personnel and equipment. Based on the Weibull distribution of rock micro-element strength and the power-law distribution of crack length and the discrete element calculation model, the prediction model for strength of damaged rock specimens were established by numerical simulation and theoretical derivation respectively. Then the rationality of the model was verified by the calculated results. The results show that: 1) The weibull distribution of the micro-element strength and the power-law distribution of the crack length in the PFC2D calculation model are realized by programming, and the quantitative corresponding relationship between the macro, micro and micro damage in the rock and the corresponding distribution parameters is analyzed. 2) 400 sandstone specimens with macro, micro and micro damage are numerically established and loaded to achieve statistical analysis of the relationship between micro element strength, pre-crack information and rock strength. According to the simulation results, the four-dimensional space scatter points of uniaxial compressive strength of sandstone specimens are constructed, and the flow law of compressive strength of sandstone specimens under the influence of multiple damage parameters is obtained. 3) Combined with Mori Tanaka method and rock damage probability distribution theory, a 12 parameter rock strength prediction model is established. The model can both describe the influence of the micro-element strength and macroscopic crack information on the rock strength, and the model calculation results are highly consistent with the simulated results, with the correlation coefficient up to 0.991.