A deep CNN-based constitutive model for describing of statics characteristics of rock materials

The inhomogeneity, discontinuity, and elastoplasticity of the rock mass affect the deformation and failure of rock, and it is difficult to describe the stress–strain relationship of the rock mass by traditional constitutive models with a certain mathematical models. In order to address the complex problems caused by multiple variables, firstly, 77 rock specimens were collected from overburden of the working face 1012001 in Yuanzigou coal mine, China. Triaxial compression tests were carried out on these samples, and 673,632 data samples were output. Secondly, based on deep convolutional neural networks (CNN), a CNN-based rock constitutive model (CNNCM) was proposed. The structure and hyperparameters of deep CNN include M, ρ, Ed, υd, σz, and σy, as the input features, ɛz as the output features;Conv2D layers ×4; Max pooling2D layers×4; Dense layers ×4; learning rate_0.001; Epoch_ 200; Batch size_1024; Total params: 160801. Comparing the test results of eleven rock samples with the predicted results of CNNCM, the scope of MAPE and R2 from 0.52–1.94% and 0.999870–0.999988, which indicates the proposed CNNCM has good performance. The sensibility and correlation of physical parameters were analyzed, and the results show that the correlation of stress, Ed, υd, and ɛz is strong. Finally, considering the availability and simplicity of CNNCM, a new CNNCM is proposed though replacing the Ed and υd with E and υ, and different input features. The predictive performance of the trained CNNCMs(#6 and #2) is also performs well although the predicted results are worse than CNNCM #0. The different CNNCMs show that E has a great influence on the results and the rank of importance of other five features is E >σy >υ >M >ρ. This study proposes a machine learning method to describe the stress–strain relationship in the process of the rock failure.