In recent years, some cities have adopted a new type of tunnel termed quasi-rectangular tunnel (QRT). Compared with the common double-line single-circle tunnel, the QRT has a smaller cross- and narrower spacing. Existing researches about QRTs mainly focus on their mechanical properties, with a lack of research on the influence of vibration and resulting noise on the surrounding environment. The vibration and structure-borne noise in the building along the subway line are adverse to human health when trains pass through the QRT. In this paper, the characteristics of vibration generated by train operation in the QRT and the propagation law in the soil are analyzed based on the finite element method-infinite element method (FEM-IEM) model. Combined with the monitoring data, vibration and indoor secondary structure-borne noise and their annoyance degrees in a 7-storey residential building 18m away from the line are also predicted and evaluated. Results show that during the ground vibration, indoor vibration and structure-borne noise of buildings along the line are mainly concentrated in the frequency band around 40Hz. The vibration and structure-borne noise of the first floor all exceed the night limit specified by an industry standard. The annoyance caused by vibration on the first floor is 0.96, which makes people feel very annoyed, while the annoyance caused by noise is 0.251, which makes people feel slightly annoyed. The research results highlight the effects of railway-induced vibrations in QRT on the building along the subway line, emphasizing their importance in the development of rail transit with QRT. The estimated vibration and noise levels, along with the degrees of annoyance, can be effectively utilized during the design and construction processes of both QRT and buildings to mitigate negative impacts on human comfort and health.

Subway tunnels with rectangular cross-sections in soil layers are susceptible to damage from fault dislocations, particularly when multiple faults are involved. The interaction between tunnel structures and multiple fault displacements can lead to significant stress and cumulative damage. The focus of this study is to investigate the mechanical behavior of a rectangular subway tunnel under the influence of multiple normal fault dislocations using validated numerical simulations. By analyzing the cumulative damage effects and the impact range from these fault displacements, the study proposes defense strategies and mitigation measures to enhance tunnel safety. The results show that tension damage occurs at the tunnel crown in the footwall and the invert in the hanging wall, and tension-bending-shear damage was observed at the tunnel sidewalls at the fault. Compared to horseshoe-shaped tunnels, rectangular tunnels exhibit a more uneven stress distribution across section, with tensile stress up to 5 times higher. Simultaneous displacements of multiple faults result in high tensile stress, especially at the crown and invert, while sequential fault dislocations cause progressive damage in these areas, shifting the stress to the sidewalls with a 50% reduction. The cumulative plastic strain from sequential displacements is three times greater than that from simultaneous displacements. In areas with closely spaced faults, overlapping damage zones can occur. To mitigate these effects, anti-fault measures such as deformation joints and enlarged tunnel cross-sections are recommended, along with enhanced waterproofing solutions, including waterstop strips and embedded grouting pipes. These findings offer valuable insights into ensuring the safety of tunnels in fault-prone regions and provide practical strategies for mitigating fault-induced damage.

The focus of this contribution is to develop an improved 2.5-dimensional (2.5D) FE (finite element)-BE (boundary element) method for a tunnel structure-transversely isotropic saturated soil system subject to underground moving train loads. In the proposed model, the rectangular tunnel invert, the lining, and the region of interest within the soil continuum use the 2.5D FE method. The remaining region of half space is replaced with a viscous spring boundary along the lateral sides and boundary element along the bottom. The theory of acoustic propagation in saturated media is extended to include transversely isotropy, viscoelasticity and boundary elements. An existing case is calculated using the enhanced model, and the results are compared with the previous literature to validate the accuracy and reliability of the proposed method. A parametric analysis is further conducted, and the factors considered in the analysis of ground-borne vibrations induced by trains meeting in the rectangular tunnel include the soil permeability, the groundwater level, and the depth of the tunnel. Numerical comparisons show that the saturated soil above the tunnel moderates the displacement undulation caused by quasistatic axle loads of the train, but this is not the case if the load has a non-zero excitation frequency. Moving train loads with excitation produce larger excess pore water pressure amplitude than do the quasi-static loads over a wide range along the travelling direction. The effect of meeting trains depends on the running speeds of both lines in opposite directions to some extent. Other conclusions useful to practical engineers are contained in the parametric study.

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.

Conducting soil stability assessments around tunnels has always been a concern. However, most existing studies have regarded soil as an isotropic and homogeneous material. To overcome this limitation, within the framework of upper bound theory, this paper proposes a novel rotational-translational failure mechanism where the velocity discontinuity surfaces are derived numerically. This theoretical mechanism includes two cases according to the positions of the velocity discontinuity surfaces. An analytical solution for pore water pressure is obtained using the conformal mapping method, which involves solving the two-dimensional (2D) Laplace equation and considering the soil and shotcrete permeability. Then, upper bound expressions for the limit supporting pressure are derived by computing work equations with and without pore water pressure. Comparisons with previous work and numerical results illustrate that the presented approach offers improvements and could be applicable for stability analyses of shallow rectangular tunnels in anisotropic and nonhomogeneous soils. Finally, this paper discusses the effects of the anisotropy and nonhomogeneity of soil properties on the normalized limit supporting pressure and the collapsing domains of rectangular tunnels with different geometric shapes. In addition, the impact of pore water pressure on the changed water levels is assessed. The results demonstrate that for rectangular tunnels that are excavated in water-bearing zones, the width-to-height ratio plays a significant role in the stability of the surrounding soils.

In underground space technology, the issue of tunnel stability is a fundamental concern that significantly causes catastrophe. Owing to sedimentation and deposition processes, the strengths of clays are anisotropic, where the magnitudes of undrained shear strengths in the vertical and horizontal directions are different. The anisotropic undrained shear (AUS) model is effective at considering the anisotropy of clayey soils when analyzing geotechnical stability issues. This study aims to assess the stability of rectangular tunnels by adjusting the dimensionless overburden factor, cover-depth ratio, and width-depth ratio in clay with various anisotropic strength ratios. The stability analysis of these tunnels involves employing finite element limit analysis and the AUS model to identify the planes of soil collapse in response to the aforementioned variations. In addition, this study presents the development of soft-computing models utilizing artificial neural networks (ANNs) to forecast the stability of rectangular tunnels across various combinations of input parameters. The findings of this study are presented in the form of design charts, tables, and soft-computing models to facilitate practical applications.