Rock Macro–Meso Parameter Calibration and Optimization Based on Improved BP Algorithm and Response Surface Method in PFC 3D

Abstract

In order to obtain the calibration law of rock macro and meso parameters under three-dimensional conditions, based on the parallel bond model, starting with the basic theory of PFC and the qualitative relationship between macro and meso parameters, an orthogonal experimental scheme is designed. An improved BP algorithm is proposed, which has a function with gradient factor, adaptive Nesterov momentum method, and adaptive learning rate for the lightweight analysis of meso parameters. The sensitivity between macro and meso parameters is quantified, and the key meso parameters are screened out. Based on the lightweight model, the correlation and influence mechanisms between macro and meso parameters are analyzed. It was found that the elastic modulus increases linearly with the increase in equivalent modulus. The parallel bond stiffness ratio can inhibit the growth of the elastic modulus, and the elastic modulus decreases greatly when the stiffness is relatively high. There is a linear relationship between Poisson’s ratio and stiffness ratio, and the increase in the friction coefficient will cause the nonlinear decrease in it. The strength parameters have an incentive effect on the peak strength. When the tensile and shear strengths of the parallel bond are at a high level, the combination has the most significant effect on the increase in the peak strength. The internal friction angle mainly has a certain influence on the postpeak strength of the rock, because it has a control effect on the particle sliding on both sides of the shear zone when the sample is loaded after the peak. Based on the central composite experimental design and response surface method, a nonlinear model of macro–meso parameters described by multiple subresponse surfaces is obtained. Finally, the mathematical model of parameter calibration is established, and the optimal solution of rock meso parameters is obtained by using optimization techniques. Through the example verification, it was found that the numerical experiment and laboratory test results are close in the stress characteristics, stress evolution, and failure mode of the sample, which proves the effectiveness and reliability of the calibration method. The research results have a certain reference value for PFC parameter calibration.