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.

Interpreting random fields through the U-Net architecture for failure mechanism and deformation predictions of geosystems

The representation of spatial variation of soil properties in the form of random fields permits advanced probabilistic assessment of slope stability.In many studies,the safety margin of the system is typically characterized by the term“probability of failure(Pfailure)”.As the intensity and spatial distribution of soil properties vary in different random field realizations,the failure mechanism and deformation field of a slope can vary as well.Not only can the location of the failure surfaces vary,but the mode of failure also changes.Such information is equally valuable to engineering practitioners.In this paper,two slope examples that are modified from a real case study are presented.The first example pertains to the stability analysis of a multi-layer-slope while the second example deals with the serviceability analysis of a multi-layer c-φslope.In addition,due to the large number of simulations needed to reveal the full picture of the failure mechanism,Convolutional Neural Networks(CNNs)that adopt a U-Net architecture is proposed to offer a soft computing strategy to facilitate the investigation.The spatial distribution of the failure surfaces,the statistics of the sliding volume,and the statistics of the deformation field are presented.The results also show that the proposed deep-learning model is effective in predicting the failure mechanism and deformation field of slopes in spatially variable soils;therefore encouraging probabilistic study of slopes in practical scenarios.