Stochastic inversion method for dynamic constitutive model of rock materials based on improved DREAM

Abstract

Abstract The difference in dynamic mechanical properties of different rock samples leads to a random process of deformation and stress. Uncertainties exist in the parameters of the rock material dynamic constitutive model. Unlike traditional inversion analysis methods, this paper treats model parameters as random variables. Bayesian theory and Differential Evolution Adaptive Metropolis algorithm (DREAM) are used to accurately quantify the uncertainty of the dynamic constitutive model parameters. The error function of the DREAM algorithm is divided into prediction error and model error to mitigate the effect of parameter compensation and improve the prediction ability. Peak stress error term is added to the DREAM prediction error to increase the peak stress fitting accuracy. Experiments of shock compression under freezing and high temperature cooling damage are presented to illustrate the proposed method. Different optimization algorithms such as Genetic Algorithm and Ant Colony Optimization are used to compare the accuracy of inversion parameters. The results show that the obtained peak stress fitting accuracy of the dynamic constitutive model is significantly improved. The 95% confidence interval considering model errors almost completely covers the experimental observations, indicating that the parameter probability distribution interval can accurately cover the true value while reflecting the model uncertainty. Using inversion parameters to predict other working conditions, 95% confidence interval considering model errors has high coverage. Thus, stochastic inversion method can accurately fit and predict the deformation and failure law of rock under impact load.