Deep learning-based AI constitutive modeling for sandstone and mudstone under cyclic loading conditions

Rocks undergoing repeated loading and unloading over an extended period, such as due to earthquakes, human excavation, and blasting, may result in the gradual accumulation of stress and deformation within the rock mass, eventually reaching an unstable state. In this study, a CNN-CCM is proposed to address the mechanical behavior. The structure and hyperparameters of CNN-CCM include Conv2D layers x 5; Max pooling2D layers x 4; Dense layers x 4; learning rate=0.001; Epoch=50; Batch size=64; Dropout=0.5. Training and validation data for deep learning include 71 rock samples and 122,152 data points. The AI Rock Constitutive Model learned by CNN-CCM can predict strain values(e1) using Mass (M), Axial stress (o1), Density (p), Cyclic number (N), Confining pressure (o3), and Young's modulus (E). Five evaluation indicators R2, MAPE, RMSE, MSE, and MAE yield respective values of 0.929, 16.44%, 0.954, 0.913, and 0.542, illustrating good predictive performance and generalization ability of model. Finally, interpreting the AI Rock Constitutive Model using the SHAP explaining method reveals that feature importance follows the order N > M > o1 > E > p > o3.Positive SHAP values indicate positive effects on predicting strain e1 for N, M, o1, and o3, while negative SHAP values have negative effects. For E, a positive value has a negative effect on predicting strain e1, consistent with the influence patterns of conventional physical rock constitutive equations. The present study offers a novel approach to the investigation of the mechanical constitutive model of rocks under cyclic loading and unloading conditions.