An Efficient Method for Reliability Analysis of High-Speed Railway Tunnel Convergence in Spatially Variable Soil Based on a Deep Convolutional Neural Network

A novel deep learning method based on the two-dimensional convolutional neural network (2D-CNN) was proposed to predict the horizontal and vertical convergences of high-speed railway tunnels considering the spatial variability of soil Young’s modulus. The input and output of the neural network were the soil Young’s modulus random field and tunnel convergence, respectively. The coefficient of determination (R²) and the relative error of the predicted results were determined to evaluate the prediction performance and extrapolating ability of the proposed CNN model. The prediction accuracy increased with increasing scale of fluctuation (SOF) from 10 to 60 m as the R² increased. Two prediction data sets with 10,000 samples (per set) were generated to illustrate the model, where the R² values were greater than 0.99. Also, the relative errors of the limit values of 90% and 99% exceeding the probability between the CNN-predicted and random finite difference method (RFDM)-calculated convergences were within 0.64%. The computational efficiency was significantly improved by 2,371 times with satisfactory accuracy. The trained CNN model showed excellent extrapolation ability in solving cases with an anisotropic random field and variation of COV. Results indicated that the proposed CNN model is a promising surrogate of RFDM with Monte Carlo simulations to analyze tunnel convergence considering soil Young’s modulus in an isotropic random field.

The spatial variability of soil parameters is commonly believed to have a significant influence in assessing tunnel reliability. Traditional probabilistic analysis of tunnel deformation was generally conducted by time-inefficient random finite-element/difference methods with Monte Carlo simulations. Recently, machine learning methods are vastly applied in geotechnical engineering with the rapid development of computational techniques, aiming to improve calculation efficiency. This study develops a two-dimensional convolutional neural network-based model to predict tunnel convergence with consideration of soil spatial variability. The input and output of the surrogate model are the soil Young’s modulus random field and tunnel convergence, respectively. The coefficient of determination, mean square error, and relative error are used to evaluate the prediction performance. The surrogate model is trained by isotropic random field data sets and performs excellent extrapolation ability on the data sets of the anisotropic random field. It suggests that the proposed model can conduct a probabilistic analysis of tunnel convergence in spatially variable soil with high accuracy.