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.

This study aims to investigate the effects of antislide piles and cohesion anisotropy on seismic displacements of three-dimensional (3D) layered slopes. A discrete mechanism generated by the point-to-point technique is employed as the deterministic model, and the particle swarm optimization algorithm is used to determine the least upper-bound solutions. By combining the pseudostatic approach and Newmark's method, the yield acceleration coefficients ky and earthquake-induced displacements of two-layer slopes are further analyzed in varying positions of strong/weak layers, ratios of layer strength, reinforcement locations of piles, and anisotropy coefficients of cohesion. The results indicate that for the seismic slopes (strength ratio Sr = 1.5), displacement can be reduced by an order of magnitude after pile reinforcement; considering the anisotropy results in higher safety evaluations, typically, there is generally about a 65% reduction in the seismic displacement of Sr = 1.5 slopes when coefficient kc decreases from 1 to 0.7; the optimal pile locations in anisotropic slopes may be further away from the slope toe; the presence of a strong layer at the bottom of the slope is more conducive to slope stability than in the top, but it also makes the slope stability more sensitive to changes in layer strength ratio; the destabilizing/stabilizing effect of the weak/strong layer at the slope bottom is most pronounced at low values of its proportion; switching the strong layer from the bottom to the top, the maximum values of ky experience a 25%-40% reduction, while this percentage would be magnified when calculating its impact on displacement. Moreover, different from single-layer slopes, layer heterogeneity may also result in nonuniqueness in the optimal pile locations.