Research on the relationship between macroscopic and mesoscopic mechanical parameters of limestone based on Hertz Mindlin with bonding model

Abstract

The mesoscopic parameters of numerical simulation cannot be directly obtained from laboratory test, and it is necessary to calibrate the parameters by comparing the numerical simulation results with the experimental results. To quickly and reasonably determine the mesoscopic parameters of limestone, a unique variable principle is used to comprehensively analyze the quantitative relationship between mesoscopic and macroscopic parameters. The results show that: The elastic modulus is positively correlated with the shear and normal stiffness per unit area. The compressive strength increases linearly with the increase of normal and shear stiffness per unit area, and it has a power function growth relation to critical normal stress and shear stress. The cohesion is mainly affected by critical normal and shear stress. With an increase of the critical normal and shear stress, the cohesion decreases. The normal stiffness per unit area, shear stiffness per unit area, critical shear stress, and critical normal stress have little influence on the internal friction angle. But there is a linear relationship between the internal friction angle and shear stiffness per unit area, and the internal friction angle is linearly related to the critical shear stress. Considering the interaction of multiple parameters, the correlation criterion and empirical formula between the mesoscopic parameters and rock mechanical parameters in the Hertz–Mindlin with Bonding contact model are proposed. The peak load, elastic modulus, and stress–strain curve variation law obtained by laboratory test and numerical simulation are close to each other, which indicates the correlation criterion can accurately simulate the mechanical properties of limestone.