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 investigates the stability of multilayer shield tunnels beneath high-speed railway bases, with a particular focus on the influence of dynamic loads induced by high-speed rail vibrations and shield thrust. A self-designed scale test apparatus was employed to simulate the effects of these dynamic loads on tunnel soil stability, face integrity, formation stress, deformation, and settlement. The experimental setup was specifically designed to accurately replicate the deformation characteristics of the tunnel face and surrounding strata under the combined influence of shield tunneling and high-speed rail loads. The reliability of the experimental results was validated through comparison with numerical simulations performed using FLAC3D software. The study underscores the effectiveness of integrating physical model tests with numerical simulations to predict the failure characteristics and ultimate support forces of tunnel faces under dynamic loading conditions. The findings provide novel insights into the deformation and failure mechanisms of tunnel faces during shield excavation, particularly under the influence of high-speed rail loads. This research establishes a robust methodological framework for assessing tunnel face stability and offers valuable guidance for the design and construction of shield tunnels in analogous geological and operational contexts.

When a shield tunnel is excavated in water-rich strata with soft upper and hard lower layers, the failure mode of the tunnel face may shift from an overall failure mode to a partial failure mode. To address this issue, three-dimensional discrete failure mechanisms for both partial and overall failure modes are established on the basis of the upper bound theorem and spatial discretization techniques. The influence of pore water pressure is also considered, leading to the development of a method for calculating the critical support force of tunnel faces in such strata, while taking into account both failure modes and the effects of groundwater. Through parameter analysis, factors such as the tunnel diameter, proportion of soft soil, stratum cohesion, and pore water pressure coefficient significantly influence the tunnel face failure mode. A comprehensive critical support force, which takes both partial and overall failure modes into account, is proposed. The parameter analysis reveals that this comprehensive critical support force exhibits complex variations under the influence of multiple parameters. At the same time, a method is proposed to determine the upper and lower bounds of the ultimate support force, based on the calculation results under no seepage and free seepage conditions at the excavation face. The entire method provides a valuable reference for the stability analysis of tunnel faces in water-rich strata with soft upper and hard lower layers.

When tunnelling in difficult ground conditions, shield machine would inevitably produce significant ground loss and vibration, which may disturb the ground ahead of the tunnel face. In this paper, discrete element models calibrated by model tests were established to investigate the response of tunnel face under the coupling effects of unloading and cutterhead vibrations. The results show that the friction angle reduction under cyclic loading and vibration attenuation in the sandy ground are significant and can be estimated by the fitted exponential functions. Under cutterhead vibration, the tunnel face stability is undermined and the limit support pressure (LSP) increases to 1.4 times as that in the static case with the growth of frequency and amplitude. Meanwhile, the loosening zone becomes wider and the arching effect is weakened with the reduction of peak horizontal stress and the increase of vertical stress above the tunnel. Based on the numerical results, a pseudo-static method was introduced into the limit equilibrium analysis of the wedge-prism model for calculating the LSP under vibration. With an error rate less than 5.2%, the proposed analytical method is well validated. Further analytical calculation reveals that the LSP would increase with the growth of vibration amplitude, vibration frequency and covered depth but decrease with the increase of friction angle. This study can not only lay a solid foundation for the further investigation of ground loss, ground water and soft-hard heterogeneous ground under cutterhead vibration, but also provide meaningful references for the control of environmental disturbance in practice.

The traditional deterministic analysis for tunnel face stability neglects the uncertainties of geotechnical parameters, while the simplified reliability analysis which models the potential uncertainties by means of random variables usually fails to account for soil spatial variability. To overcome these limitations, this study proposes an efficient framework for conducting reliability analysis and reliability-based design (RBD) of tunnel face stability in spatially variable soil strata. The three-dimensional (3D) rotational failure mechanism of the tunnel face is extended to account for the soil spatial variability, and a probabilistic framework is established by coupling the extended mechanism with the improved Hasofer-LindRackwits-Fiessler recursive algorithm (iHLRF) as well as its inverse analysis formulation. The proposed framework allows for rapid and precise reliability analysis and RBD of tunnel face stability. To demonstrate the feasibility and efficacy of the proposed framework, an illustrative case of tunnelling in frictional soils is presented, where the soil's cohesion and friction angle are modelled as two anisotropic cross-correlated lognormal random fields. The results show that the proposed method can accurately estimate the failure probability (or reliability index) regarding the tunnel face stability and can efficiently determine the required supporting pressure for a target reliability index with soil spatial variability being taken into account. Furthermore, this study reveals the impact of various factors on the support pressure, including coefficient of variation, cross-correlation between cohesion and friction angle, as well as autocorrelation distance of spatially variable soil strata. The results also demonstrate the feasibility of using the forward and/or inverse first-order reliability method (FORM) in high-dimensional stochastic problems. It is hoped that this study may provide a practical and reliable framework for determining the stability of tunnels in complex soil strata. (c) 2024 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Face passive failure can severely damage existing structures and underground utilities during shallow shield tunneling, especially in coastal backfill sand. In this work, a series of laboratory model tests were developed and conducted to investigate such failure, for tunnels located at burial depth ratios for which C/D = 0.5, 0.8, 1, and 1.3. Support pressures, the evolution of failure processes, the failure modes, and the distribution of velocity fields were examined through model tests and numerical analyses. The support pressure in the tests first rose rapidly to the elastic limit and then gradually increased to the maximum value in all cases. The maximum support pressure decreased slightly in cases where C/D = 0.8, 1, and 1.3, but the rebound was insignificant where C/D = 0.5. In addition, the configuration of the failure mode with C/D = 0.5 showed a wedge-shaped arch, which was determined by the outcropping shear failure. The configuration of failure modes was composed of an arch and the inverted trapezoid when C/D = 0.8, 1, and 1.3, in which the mode was divided into lower and upper failure zones.