Geomechanics and Engineering

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

  • Luyuan Wu (School of Civil Engineering and Architecture, Henan University) ;
  • Meng Li (School of Civil Engineering and Architecture, Henan University) ;
  • Jianwei Zhang (School of Civil Engineering and Architecture, Henan University) ;
  • Zifa Wang (School of Civil Engineering and Architecture, Henan University) ;
  • Xiaohui Yang (Henan Provincial Engineering Research Center for Artificial Intelligence Theory and Algorithm, Henan University) ;
  • Hanliang Bian (School of Civil Engineering and Architecture, Henan University)
  • Received : 2023.10.13
  • Accepted : 2024.03.10
  • Published : 2024.04.10
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Abstract

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 × 5; Max pooling2D layers × 4; Dense layers × 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(ε1) using Mass (M), Axial stress (σ1), Density (ρ), Cyclic number (N), Confining pressure (σ3), 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 > σ1 > E > ρ > σ3.Positive SHAP values indicate positive effects on predicting strain ε1 for N, M, σ1, and σ3, while negative SHAP values have negative effects. For E, a positive value has a negative effect on predicting strain ε1, 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.

Keywords

Acknowledgement

All authors contributed to the study conception and design. This work is supported by Henan Natural Science Foundation Youth Fund Project (No.232300421331), Joint fund of the technical R&D program of Henan Province(225200810005),Key Scientific Research Projects of Colleges and Universities in Henan Province (No.23A440005) and Postdoctoral Research Grant in Henan Province (No.202103049), China Postdoctoral Science Foundation (2023M741009).

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