Interaction effects and an optimization study of the microparameters of the flat-joint model using the Plackett-Burman design and response surface methodology

摘要

In view of the large number of microparameters of the flat-joint model (FJM) and the inefficiency of the calibration process, this paper uses the Plackett-Burman (PB) design, response surface methodology (RSM), and optimization techniques to calibrate the FJM3D. The values of each lower and upper bound in the PB design are selected based on the relationship between 10 microparameters and the UCS, BTS, UCS/BTS, elastic modulus E, Poisson's ratio upsilon, Hoek-Brown strength parameter m(i), average coordination number (CN), and crack initiation stress sigma (ci). Then, the PB design is used in the sensitivity analysis to screen out the three most influential factors for each response for the central composite design (CCD). The three microparameters most influencing E are the effective modulus Empb, the ratio of the normal to shear stiffness KnKs, and the installation gap ratio Gapr; the three microparameters most influencing upsilon are KnKs, the mean bond cohesion strength Coh, and Empb; the three microparameters most influencing UCS are Coh, Gapr, and the mean bond tensile strength Mbts; and the three microparameters most influencing BTS are Mbts, KnKs, and the residual friction angle Rfa. CCD analysis reveals that there are interaction effects between the FJM3D microparameters and the real effect of each microparameter differs at different levels of other microparameters. The linear and nonlinear equations obtained by fitting the PB design and the CCD design are applied as constraints to the optimization problem, and the problem of obtaining the best set of FJM3D microparameters is solved. The optimal sets were successfully matched for a variety of rock types from both the FJM3D simulations and experiments, and Lac du Bonnet granite was used as an example to compare the strength, deformation characteristics, and rock failure modes. This method can be used as a new way to quickly calibrate the microparameters of the FJM3D.