Deep learning-based evaluation of factor of safety with confidence interval for tunnel deformation in spatially variable soil

The random finite difference method (RFDM) is a popular approach to quantitatively evaluate the influence of inherent spatial variability of soil on the deformation of embedded tunnels. However, the high computational cost is an ongoing challenge for its application in complex scenarios. To address this limitation, a deep learning-based method for efficient prediction of tunnel deformation in spatially variable soil is proposed. The proposed method uses one-dimensional convolutional neural network (CNN) to identify the pattern between random field input and factor of safety of tunnel deformation output. The mean squared error and correlation coefficient of the CNN model applied to the newly untrained dataset was less than 0.02 and larger than 0.96, respectively. It means that the trained CNN model can replace RFDM analysis for Monte Carlo simulations with a small but sufficient number of random field samples (about 40 samples for each case in this study). It is well known that the machine learning or deep learning model has a common limitation that the confidence of predicted result is unknown and only a deterministic outcome is given. This calls for an approach to gauge the model's confidence interval. It is achieved by applying dropout to all layers of the original model to retrain the model and using the dropout technique when performing inference. The excellent agreement between the CNN model prediction and the RFDM calculated results demonstrated that the proposed deep learning-based method has potential for tunnel performance analysis in spatially variable soils.