As urbanization accelerates, the demand for efficient underground infrastructure has grown, with rectangular tunnels gaining prominence due to their enhanced space utilization and construction efficiency. However, ensuring the stability of shallow rectangular tunnel faces in undrained clays presents significant challenges due to complex soil behaviors, including anisotropy and non-homogeneity. This study addresses these challenges by developing a novel failure mechanism within the kinematic approach of limit analysis, integrating soil arching effects alongside anisotropic and non-homogeneous undrained shear strength. The mechanism's analytical solutions are rigorously validated against finite element simulations using PLAXIS 3D and existing models, demonstrating superior accuracy. Key findings show that the proposed model improves predictive performance for critical support pressure, with relative differences as low as 5% for wide rectangular tunnels compared to numerical simulations. Results reveal that limit support pressure decreases with increasing non-homogeneity ratios and rises with higher anisotropy factors. However, both effects diminish in wider tunnels, where increasing width in soils with high non-homogeneity and low anisotropy factors significantly enhances stability. Practical implications of this study are substantial, offering design formulas and dimensionless coefficients for estimating critical face pressures in shallow rectangular tunnels. These tools enable engineers to account for soil anisotropy and non-homogeneity, optimizing design and ensuring safety in urban environments. Furthermore, the proposed model's applicability extends to circular tunnels, where it offers comparable accuracy. This study bridges a critical gap in understanding the stability of rectangular tunnels, providing a robust framework for tackling the challenges of modern urban construction.

The focus of the study is to examine the undrained behavior of twin circular tunnels in anisotropic and nonhomogeneous clays. To consider the effect of anisotropic soil, the popular anisotropic undrained shear (AUS) failure criteria are adopted in the study while the nonhomogeneous behavior is represented by linearly increasing strength with depth. Using Broms and Bennermarks' stability number, this study investigates the dependence of the undrained stability number N on four dimensionless input parameters, namely the isotropic ratio (re), the undrained shear strength gradient (rho D/suTC0), the cover depth ratio (C/D), and the spacing ratio (S/D). The effects of these four design parameters on the failure mechanism are also examined graphically. After being verified with previously published works, the comprehensive 1080 numerical results are then utilized as the dataset to create several machine learning models, including artificial neural network (ANN), support vector machine (SVM), and multivariate adaptive regression splines (MARS). The evaluating process by optimizing hyper-parameters reveals that the MARS model is a top competitor, providing considerable regression accuracy with a simple predictive function. The sensitivity analysis has also uncovered that both rho D/suTC0 and C/D have significant influences on the undrained stability number N, while comparing to re and S/D. The present study would provide many practical insights to the problem of twin circular tunnels in anisotropic and nonhomogeneous clays.