Deep-learning surrogate models for the stability of a wide rectangular tunnel

The stability of a wide rectangular tunnel in spatially variable soils is investigated using deep-learning surrogate models combined with a mixed formulation of limit analysis. The mixed formulation is employed to perform stochastic simulations of tunnels in spatially random soils, generating the data to train the surrogate models. Two types of deep-learning models are tested: Fully Connected Neural Networks (FCNs) and Convolutional Neural Networks (CNNs). To enhance model performance, the study introduces two novel encoding techniques to enhance the identification of tunnel regions in the input data. The first, Mask-FCN, directly incorporates spatial information into the model by adding a binary mask layer to distinguish tunnel regions from the surrounding soil. The second, Grad-FCN, modifies training gradients to indirectly highlight these differences. Additionally, a Mask-CNN model is developed, leveraging spatial filtering to better capture local patterns and correlations. Our results show that the surrogate models, trained on data from stochastic reliability analyses, demonstrate robustness and accuracy across various evaluation metrics. The encoding neural networks outperform the baseline model in accuracy and overall regression performance on training datasets. Importantly, both encoding networks achieve acceptable accuracy on unseen datasets with new tunnel geometric features, a task the baseline model fails to accomplish. The FCN-based encoding neural network achieves prediction capabilities comparable to ordinary CNNs, while the CNN-based encoding neural network delivers high prediction accuracy for unknown datasets with new tunnel geometric characteristics. The study concludes that the generated surrogate models offer a computationally efficient alternative for predicting tunnel stability in spatially variable soils.