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.

Seismic activity on a tunnel damages the tunnel support systems. The extent of the tunnel damage depends on the soil type, the magnitude of the earthquake acceleration, and the tunnel cover depth. Hence, analyzing the stress induced by the seismic event from the surrounding ground on the tunnel facilitates a safe tunnel design. Based on the pseudostatic method, this study examined the seismic stability of square and rectangular tunnels placed in cohesive-frictional soil. The tunnel collapse load was found using the lower-bound theorem of limit analysis in combination with the finite-element method. From the distribution of stresses along the periphery, the normal stress at each tunnel node was calculated, and the maximum of stresses was reported as the support pressure. Thus, the systems safeguarding the tunnel against devastating lateral earthquake forces are expected to offer the ultimate resistance equal to the maximum normal stress on the tunnel periphery. With the increase in tunnel cover depth, aspect ratio, seismic acceleration coefficients, and a decrease in soil cohesion and friction angle, the support pressure was noted to enhance. The distribution of normal stresses around the tunnel periphery depends on the tunnel geometry, the soil's shear strength parameters, and the magnitude of earthquake acceleration. For a square tunnel, the magnitude of stress was maximum on the walls, followed by the roof and base, implying that collapse will be more prone from the side walls. However, the rectangular tunnels are noted to be susceptible to collapse from the roof, followed by walls and base.