Probabilistic analysis of tunnel convergence in spatially variable soil based on Gaussian process regression

Traditional probabilistic analysis of tunnel convergence in spatially variable soil typically involves using the random finite difference method, which is computationally intensive. In this study, we propose an efficient machine learning method based on the Gaussian Process Regression (GPR) model for predicting the horizontal and vertical convergences of a high-speed railway tunnel. In the proposed approach, the soil Young's modulus random field is simplified from a 2D matrix to a 1D vector, which serves as the input of the GPR model. Considering the prior knowledge about the probability distribution of the tunnel convergence, the horizontal and vertical convergences are transformed into two random variables that can be predicted effectively by the GPR model. Notably, the developed GPR model requires only 1.97% of the computational cost to achieve similar prediction accuracy as the 2D-convolutional neural network model. A training dataset comprising 1400 samples can deliver satisfactory prediction performance of the surrogate model under a certain scale of fluctuation (SOF). Moreover, selecting 700 samples from each random field optimally composes a mixed dataset for training the GPR model. The findings of this study suggest that the trained GPR model provides excellent performance for the probabilistic analysis of the tunnel convergences considering the spatially variable soil Young's modulus.