Coupling isogeometric analysis with deep learning for stability evaluation of rectangular tunnels

Abstract

The problem considered in this paper is for the stability evaluation of a rectangular tunnel in undrained clay during lining process. The approach adopted involved the use of isogeometric analysis (IGA) and the upper bound limit analysis formulation for the stability analysis. For the geometrical representation, B-spline basis functions are used to generate a set of B-spline surfaces that define the boundary of the soil domain, allowing for the exact representation of the tunnel geometry. The upper bound limit analysis is then formulated as a second-order cone program (SOCP), which can be solved by using a numerical optimization algorithm. The accuracy and reliability of the proposed method are validated by comparing the results with those published in previous studies. Furthermore, a large dataset is generated by randomly varying the input parameters, and a deep learning model is trained to learn the dataset. The deep learning model is trained using the mean squared error (MSE) metric, which yields an MSE as small as 10−6, indicating the high accuracy and precision of the proposed approach. Feature analysis and Partial Dependence Plots (PDPs) were used to gain insights into physical behavior by identifying important variables and understanding their individual and collective effects. In conclusion, the coupling of IGA and upper bound limit analysis provides a comprehensive and reliable solution to the stability of rectangular tunnels. The results obtained from this approach are accurate and can be achieved with reduced computational cost, making it an attractive approach for practical engineering applications. This approach can be used as a basis for future research on tunnel and tunnel stability analysis and may be extended to other types of soil structures under complex geometries.