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Keywords = symmetrical tunneling

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28 pages, 8805 KB  
Article
Simulation Analysis of Factors Affecting the Distribution of Internal Blast Reflection Overpressure on Tunnel Linings with Grey Relational Theory
by Zhengpeng Li, Liang Li, Fengzeng Li, Jun Wu and Xiuli Du
Buildings 2026, 16(16), 3243; https://doi.org/10.3390/buildings16163243 - 15 Aug 2026
Viewed by 114
Abstract
Investigating the influence level and law of various factors on the distribution of reflected overpressure resulting from explosions in vehicles carrying hazardous chemicals or explosives is of great significance for accounting for the impact of load distribution in the blast-resistant design of structures. [...] Read more.
Investigating the influence level and law of various factors on the distribution of reflected overpressure resulting from explosions in vehicles carrying hazardous chemicals or explosives is of great significance for accounting for the impact of load distribution in the blast-resistant design of structures. This paper uses LS-DYNA software to simulate and investigate the effects of five factors (charge mass (M), charge eccentricity (X), the aspect ratio of cuboid charge (δL/H), charge inclination (θ), and tunnel diameter (D)) on the distribution of reflected overpressure on the lining. The grey relational degree reveals the relative influence of each factor on the reflected overpressure parameters of the lining cross-section (RPPCS) at the blast center. The results show that M, X, and D have the greatest influence on the RPPCS of the blast center. An independent analysis of each factor revealed that the distribution of reflected overpressure from the central charge changes from two-dimensional symmetry to one-dimensional symmetry. Non-central charge disrupts its symmetric distribution. Inclined charge results in an asymmetric distribution. The intensity and incident angle of the shock wave have a significant effect on the location of the maximum reflected overpressure on the lining cross-section (RPCS-max) at the blast center. In the RPCS-max at the blast center, X and θ change their location. θ can alter its distribution shape. When δL/H is too large, increasing M or δL/H will both reduce the reflected overpressure. The influence of various factors on RPPCS is different. Increases in M and D reduce the non-uniform distribution of RPCS, but other factors have the opposite effect. The research findings provide a basis for considering the effects of load distribution in the design of structures resistant to internal explosions. Full article
(This article belongs to the Section Building Structures)
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19 pages, 2292 KB  
Article
Analytical Model for Tunnel Face Stability in Equivalent Homogeneous Rock Masses with Persistent Joint Sets
by Jianhong Man, Qingwen Li, Lan Qiao and Mingliang Zhou
Symmetry 2026, 18(8), 1336; https://doi.org/10.3390/sym18081336 - 7 Aug 2026
Viewed by 246
Abstract
Reliable assessment of tunnel face stability in rock masses containing persistent joints remains challenging because existing analytical methods generally neglect the influence of joint orientation. This study develops an equivalent analytical model that incorporates joint orientation into the limit analysis framework by modifying [...] Read more.
Reliable assessment of tunnel face stability in rock masses containing persistent joints remains challenging because existing analytical methods generally neglect the influence of joint orientation. This study develops an equivalent analytical model that incorporates joint orientation into the limit analysis framework by modifying rock mass parameters. The proposed model explicitly considers joint orientations from 0° to 90°, enabling anisotropic joint effects to be efficiently represented within the analytical solution. Validation against numerical simulations demonstrates high prediction accuracy with substantially improved computational efficiency. Parametric analyses reveal that joint orientation is the primary factor controlling tunnel face stability, producing a symmetric M-shaped variation in stability and identifying the most unfavorable joint orientations. Rock mass quality, tunnel buried depth, and excavation-induced disturbance also significantly influence stability. The proposed model provides a rapid and practical approach for tunnel face stability evaluation in jointed rock masses, offering valuable support for tunnel design and construction. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Civil Engineering)
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28 pages, 10609 KB  
Article
Robust Design of Tuned Viscous Mass Dampers for Wind-Induced Vibration Control of High-Rise Buildings: An Info-Gap Decision Theory Approach to Manufacturing Uncertainty
by Jinyu Li, Peng Huang and Hongyin Geng
Buildings 2026, 16(15), 2931; https://doi.org/10.3390/buildings16152931 - 23 Jul 2026
Viewed by 345
Abstract
Tuned viscous mass dampers (TVMDs) are effective devices for wind-induced vibration control in supertall buildings, but their performance depends on a precise resonance condition that can be disturbed by manufacturing tolerances. This study identifies an insufficiently examined asymmetric sensitivity mechanism, termed the “dangerous [...] Read more.
Tuned viscous mass dampers (TVMDs) are effective devices for wind-induced vibration control in supertall buildings, but their performance depends on a precise resonance condition that can be disturbed by manufacturing tolerances. This study identifies an insufficiently examined asymmetric sensitivity mechanism, termed the “dangerous diagonal effect”, in which opposite-sign errors in TVMD inertance and stiffness amplify tuning-frequency drift and create a worst-case sensitivity space that conventional symmetric uncertainty models may underestimate. To tackle this challenge without requiring prior statistical distributions unavailable at the design stage, an Info-Gap Decision Theory (IGDT) robust optimization framework tailored to TVMDs under stochastic wind excitation is developed. A Kriging-metamodel-assisted Efficient Global Optimization bi-level strategy reduces the computational burden of the nested worst-case search. Applied to a 76-story, 306 m benchmark building under a dual-criterion constraint combining the ISO 10137 comfort limit and a 30% relative degradation bound, the framework certifies comfort compliance for manufacturing errors up to 23.44% along the dangerous-diagonal direction. Under the most severe coupled degradation scenario, which integrates opposite-sign manufacturing detuning, 50-year power-law aging, and Arrhenius thermal drift, the nominal H2-optimal design collapses to 36.7% vibration reduction efficiency while the IGDT robust design sustains 51.7%, reducing the Monte Carlo failure probability from 3.8% to 1.2% across 500 random realizations. An aeroelastic wind tunnel campaign spanning 620 detuning configurations on a 1:350 scaled model provides physical validation of IGDT design reliability for a TVMD system. The experiments corroborate the dangerous-diagonal sensitivity asymmetry, support the predicted robustness plateau under severe parameter detuning, and show that the IGDT framework maintains comfort compliance where the H2-optimal design fails. Full article
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24 pages, 34241 KB  
Article
Deformation and Control of Bridge Pile Adjacent to Excavation Under Superimposed Disturbances of Shield Tunneling and the Top-Down Method
by Jiarui Wang, Liya Zhang, Hongmei Zhang, Xianghong Ding and Biao Luo
Buildings 2026, 16(14), 2879; https://doi.org/10.3390/buildings16142879 - 19 Jul 2026
Viewed by 403
Abstract
The construction of deep foundation pits for urban metro systems, particularly when in close proximity to existing sensitive structures, can easily induce unacceptable settlement and deformation. When shield tunneling and the top-down method are superimposed in both space and time, the resulting disturbance [...] Read more.
The construction of deep foundation pits for urban metro systems, particularly when in close proximity to existing sensitive structures, can easily induce unacceptable settlement and deformation. When shield tunneling and the top-down method are superimposed in both space and time, the resulting disturbance to the surrounding environment is more complex. A metro station project in Shenzhen was selected as the case study. Field monitoring and numerical simulation were combined to analyze the deformation of nearby bridge piers during different construction stages. The settlement-control effects of different reinforcement measures were also compared. The results indicate that the maximum settlement of the bridge piers throughout the monitored construction period reaches 31.81 mm. In the third stage, the cumulative settlement exceeded 10 mm. After the left-line shield passed through the station, the differential settlement between adjacent piers exceeded 5 mm. In the fourth stage, upon completion of the south section of the negative third floor, the differential settlement within the same pair of piers exceeded 4 mm. The maximum differential settlement between adjacent piers on the side closer to the foundation pit is 8.92 mm, whereas that on the side farther from the pit is 12.53 mm. The maximum values of both the differential settlement between adjacent piers and that within the same pair of piers occur during stages where multiple construction processes overlap. The connections between successive construction procedures are thus identified as weak links in deformation control. The discrepancy in cumulative settlement between symmetrically located piers arises primarily from the different reinforcement methods adopted. Supplementary pile reinforcement provides better performance than sleeve-valve-pipe grouting reinforcement. Because its reinforcement depth is insufficient to extend below the foundation pit excavation surface, the latter method fails to effectively restrain deformation in deep soils. The results describe the spatio-temporal development of pier deformation under combined construction disturbances. They also help identify critical construction stages and compare the settlement-control effects of different reinforcement measures. In addition, the numerical results provide a possible interpretation of pile load-transfer behavior under the combined effects of shield tunneling and top-down excavation. These findings serve as a practical reference for the design, construction sequencing, and risk management of similar metro station projects adjacent to bridges. Full article
(This article belongs to the Section Construction Management, and Computers & Digitization)
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24 pages, 3211 KB  
Article
Investigation into the Influence of Overlapping Shield Tunnel Crossing on the Circumferential Internal Forces of an Existing Tunnel
by Gang Wei, Haoran Cai, Yangyang Liu and Yongjie Qi
Buildings 2026, 16(13), 2675; https://doi.org/10.3390/buildings16132675 - 6 Jul 2026
Viewed by 245
Abstract
To study the changes in circumferential internal forces of an existing shield tunnel when an overlapping tunnel passes through, a surrounding pressure redistribution model for overlapping tunnels was established to calculate the circumferential surrounding pressure of the existing tunnel. Combined with an engineering [...] Read more.
To study the changes in circumferential internal forces of an existing shield tunnel when an overlapping tunnel passes through, a surrounding pressure redistribution model for overlapping tunnels was established to calculate the circumferential surrounding pressure of the existing tunnel. Combined with an engineering case, a detailed three-segment tunnel model was created using Abaqus 2023 finite element software. The circumferential forces of the tunnel were applied to the model, and the circumferential internal forces of the segments were extracted to study the variation law of segment circumferential internal forces. The research results indicate the following: (1) During the excavation of overlapping tunnels, the circumferential surrounding pressure of the existing tunnel decreases, and the circumferential surrounding pressure at any position exhibits a symmetric “8”-shaped distribution. (2) During the excavation of the new tunnel, the circumferential internal forces of the existing shield tunnel increase. In front of the excavation face, the additional internal forces of the tunnel decrease with distance, while within approximately 6 m behind the excavation face, the additional internal forces of the tunnel increase sharply. (3) As the angle between the line connecting the axes of the two tunnels and the z-axis increases, the additional internal forces of the existing tunnel decrease; as the clear distance between tunnels increases, the circumferential internal forces of the existing tunnel decrease, and the additional bending moments and additional shear forces approximately show linear variation. Full article
(This article belongs to the Section Building Structures)
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15 pages, 2240 KB  
Article
Settlement Response of Existing Metro Tunnels Induced by Parallel Symmetric Shield Tunneling: A Model Test Study
by Weitao Chen, Kaihang Han and Jun Zhou
Buildings 2026, 16(13), 2555; https://doi.org/10.3390/buildings16132555 - 26 Jun 2026
Viewed by 287
Abstract
Parallel shield tunneling in close proximity to existing metro tunnels induces additional settlement deformation of existing structures, which poses a challenge to operational safety. In this paper, a self-developed Φ200 mm model shield machine test system is adopted to carry out model test [...] Read more.
Parallel shield tunneling in close proximity to existing metro tunnels induces additional settlement deformation of existing structures, which poses a challenge to operational safety. In this paper, a self-developed Φ200 mm model shield machine test system is adopted to carry out model test research on the settlement response of existing tunnels induced by parallel symmetric shield tunneling. A 1:30-scaled 3D-printed refined assembled segment model is fabricated based on similarity theory, and high-precision distributed optical fiber sensing technology is used for deformation monitoring. The influences of vertical spacing of tunnels, center spacing of new tunnels, axis angle and stratum loss rate on the settlement of existing tunnels are analyzed. The results show that the settlement curve of the existing tunnel arch presents a normal distribution shape, and the maximum settlement occurs near the new tunnel side. The settlement of existing tunnels decreases with the increase in vertical spacing between new and existing tunnels, and increases with the increase in stratum loss rate and center spacing of new tunnels. The research results can provide experimental support for safety control of parallel shield tunnel construction. Full article
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23 pages, 2040 KB  
Article
A Construction-Phase Reliability Framework for Hard Rock TBM Penetration Rate Prediction Under Delayed UCS Information
by Nantapol Monthanopparat and Tawatchai Tanchaisawat
Geotechnics 2026, 6(3), 61; https://doi.org/10.3390/geotechnics6030061 - 26 Jun 2026
Viewed by 334
Abstract
Reliable construction-phase prediction of hard rock tunnel boring machine (TBM) rate of penetration (ROP) remains difficult because ground–machine interaction changes along the alignment and uniaxial compressive strength (UCS) is often incomplete or delayed at ring scale. This study proposes a construction-phase reliability framework [...] Read more.
Reliable construction-phase prediction of hard rock tunnel boring machine (TBM) rate of penetration (ROP) remains difficult because ground–machine interaction changes along the alignment and uniaxial compressive strength (UCS) is often incomplete or delayed at ring scale. This study proposes a construction-phase reliability framework that integrates sequence deep learning, inverse-distance-weighted UCS completion, chronological rolling evaluation, PassRate monitoring, and performance-triggered updating. The framework was developed from a granite-dominated TBM drive in northern Thailand and evaluated under a delayed-UCS information policy. In the Phase-2 forward deployment-style evaluation, the selected gated recurrent unit (GRU) model achieved a root mean square error (RMSE) of 0.1639 m/h, a mean absolute error (MAE) of 0.1186 m/h, and 62.63% within a symmetric ±10% accuracy band over 990 evaluated rings. Direct static application of representative theoretical and empirical models produced substantially lower within-band performance of 11.92–20.71%. One early reliability trigger occurred at Ring 3409, after which UCS updating, retraining, and redeployment restored the monitoring process without further intervention triggers. The results show that construction-phase TBM prediction should be managed as an auditable reliability workflow with explicit information boundaries, rather than as a single static accuracy score. Full article
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21 pages, 6648 KB  
Article
Deformation Rules and Failure Mechanisms of Shield Tunnel Lining with Constant Buried Depth Ratio Under Overload Condition
by Weitao Chen, Kaihang Han and Jun Zhou
Buildings 2026, 16(13), 2546; https://doi.org/10.3390/buildings16132546 - 26 Jun 2026
Viewed by 317
Abstract
The maintenance of shield tunnel linings is critical for the successful operation of super-large-diameter shield tunnels. In this study, the finite element analysis method is used to systematically investigate the deformation behavior of shield tunnel linings with varying diameters based on ABAQUS. Key [...] Read more.
The maintenance of shield tunnel linings is critical for the successful operation of super-large-diameter shield tunnels. In this study, the finite element analysis method is used to systematically investigate the deformation behavior of shield tunnel linings with varying diameters based on ABAQUS. Key parameters such as crown displacement, tensile and compressive strain zones, bolt stress and strain, as well as the deformation and internal force distribution around the lining, are comprehensively analyzed. Additionally, the development of cracks in the tensile zones is examined for comparative analysis. The findings reveal that large-diameter linings exhibit a more rapid increase in convergence deformation, while fewer plastic hinges form before reaching maximum strength. Furthermore, these larger linings are more susceptible to brittle failure and geometric instability compared to smaller-diameter counterparts. The results of this study provide significant theoretical insights for the design, construction, and operation of large-diameter shield tunnel linings, offering valuable references for similar engineering applications. Full article
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20 pages, 6758 KB  
Article
Wheel-AINS: A Vehicle Autonomous Positioning System Based on a Wheel-Mounted MIMU Array
by Guangmin Yuan, Guoyuan He, Xiangyang Guo, Ruijie Li, Chenyang Jiao and Xiaoying Li
Micromachines 2026, 17(7), 767; https://doi.org/10.3390/mi17070767 - 24 Jun 2026
Viewed by 1335
Abstract
In satellite-denied environments such as urban canyons, tunnels, and underground parking facilities, achieving high-precision autonomous positioning for vehicles remains a critical challenge. Although high-precision inertial measurement units (IMUs) can provide accurate dead reckoning, their deployment is limited by cost, size, and power consumption, [...] Read more.
In satellite-denied environments such as urban canyons, tunnels, and underground parking facilities, achieving high-precision autonomous positioning for vehicles remains a critical challenge. Although high-precision inertial measurement units (IMUs) can provide accurate dead reckoning, their deployment is limited by cost, size, and power consumption, making low-cost, microelectromechanical systems IMUs (MIMUs) an attractive alternative solution. However, the single MIMU suffers from substantial measurement noise and bias instability, leading to rapid error divergence that cannot sustain long-term autonomous navigation. To address the above issues, this paper proposes an autonomous positioning system based on a wheel-mounted MIMU array (Wheel-AINS). The system adopts a differential layout in which multiple low-cost MIMU chips are installed at the center of each of the left and right rear wheels, forming redundant sensor arrays. By differentially fusing symmetrically mounted chips, common-mode noise and zero bias are effectively canceled while the wheel rotation provides natural rotational modulation. The fused gyroscope outputs and known wheel radius are then used to estimate the vehicle forward speed, replacing traditional odometers. The estimated wheel speed and vehicle kinematic constraints are then integrated within a Kalman filter framework to suppress the error divergence of the inertial navigation system. A dedicated embedded hardware prototype with multi-chip synchronous acquisition and wireless transmission was developed. Three groups of urban road tests with total distances of 0.85 km, 2.14 km, and 2.49 km were conducted. The results indicate that the average position drift rate of the Wheel-AINS is 0.50%, and the average heading RMSE is 12.2°. The closure error of the 2.49 km trajectory is 10.43 m, reduced by approximately 80% compared with a single MIMU. The ablation experiment reveals that the MIMU array fusion module is the primary source of accuracy improvement, reducing the position RMSE from 155.0 m to 10.1 m, while the dual-wheel distance constraint further optimizes the position RMSE to 8.2 m, but increases the heading RMSE from 13.3° to 13.6°. This demonstrates that the proposed method can substantially improve autonomous positioning accuracy while maintaining a notably low system cost, providing a viable technical pathway for long-endurance vehicle navigation in satellite-denied environments. Full article
(This article belongs to the Special Issue MEMS/NEMS Devices and Applications, 4th Edition)
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33 pages, 5582 KB  
Article
Symmetric and Asymmetric Stress Redistribution in Corrugated Steel–Concrete Composite Tunnel Linings Under Non-Uniform External Pressure
by Beibei Dong
Symmetry 2026, 18(6), 1036; https://doi.org/10.3390/sym18061036 - 16 Jun 2026
Viewed by 320
Abstract
Circular tunnel linings are geometrically symmetric structures, whereas non-uniform external pressure and different steel–concrete layer arrangements may induce asymmetric stress redistribution. To distinguish the axisymmetric response from the asymmetric harmonic response, this study develops an analytical solution for a two-layer corrugated steel–concrete composite [...] Read more.
Circular tunnel linings are geometrically symmetric structures, whereas non-uniform external pressure and different steel–concrete layer arrangements may induce asymmetric stress redistribution. To distinguish the axisymmetric response from the asymmetric harmonic response, this study develops an analytical solution for a two-layer corrugated steel–concrete composite tunnel lining subjected to equivalent external pressure. The concrete layer is modeled as an isotropic elastic material, while the corrugated steel layer is represented as an equivalent cylindrically orthotropic material. The governing equations are formulated in polar coordinates under plane-strain conditions, and the solution is obtained by superposing the axisymmetric component and the harmonic component. Perfect bonding is assumed at the steel–concrete interface, where displacement, radial stress, and shear stress are continuous. The proposed analytical solution is verified using finite element models for three cases: a single-layer homogeneous lining under uniform pressure, a two-layer composite lining under uniform pressure, and a two-layer composite lining under non-uniform pressure. The analytical and finite element results show good agreement, confirming the mathematical consistency and implementation accuracy of the proposed formulation. Based on the verified solution, the effects of layer arrangement, corrugated steel stiffness ratio, and burial depth are investigated. The results show that the corrugated steel layer carries the dominant hoop stress in both layer arrangements. The inner corrugated steel arrangement may be more relevant to internal strengthening of existing tunnels, whereas the outer corrugated steel arrangement provides a useful reference for new composite linings dominated by external ground pressure. Increasing the stiffness ratio transfers more hoop stress to the steel layer and reduces the elastic stress and displacement responses of the concrete layer, although improvement becomes less significant at large stiffness ratios. Increasing burial depth mainly amplifies the response magnitude without changing the overall symmetry pattern. The proposed solution provides a closed-form benchmark for evaluating symmetry-related stress redistribution in corrugated steel–concrete composite tunnel linings within the linear-elastic range. Full article
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21 pages, 5767 KB  
Article
Effect of Cable Failure on the Wind-Induced Vibration of a Single-Pylon Cable-Stayed Bridge
by Jingtao Xing, Haojun Tang, Jia Kang and Yongle Li
J. Mar. Sci. Eng. 2026, 14(12), 1089; https://doi.org/10.3390/jmse14121089 - 12 Jun 2026
Viewed by 319
Abstract
The dynamic characteristics and buffeting response of long-span single-pylon cable-stayed bridges are not fully understood after cable failure occurs in coastal wind environments. This study investigates how the location, number, and pattern of cable failures affect structural performance. A three-dimensional finite element model [...] Read more.
The dynamic characteristics and buffeting response of long-span single-pylon cable-stayed bridges are not fully understood after cable failure occurs in coastal wind environments. This study investigates how the location, number, and pattern of cable failures affect structural performance. A three-dimensional finite element model of a 280 m main-span bridge was established using the aerodynamic coefficients extracted from wind tunnel tests. Modal analyses and nonlinear time-domain simulations were conducted. The results show that frequency reduction concentrates in lower-order vertical bending modes, with the first and second modes being the most sensitive. Variations in frequency are closely related to the failure location of stay cables, with the largest reduction at the mode antinode. Unilateral multiple failures induce bending–torsion coupling, whereas symmetric bilateral failures only lower frequencies. Under wind loads, the failure of stay cables results in the redistribution of static internal forces, primarily to the adjacent stay cables on the same side. This phenomenon is enhanced as the number of failed cables increases. The change in buffeting internal forces results in a non-monotonic trend, and the shorter cables near the pylon are more sensitive. Cable failure, which occurs at different phases of the buffeting process, significantly influences the structure's transient response. The scenario in which the structure is subjected to wind loads after cable failure results in the largest variation amplitude. Full article
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17 pages, 3769 KB  
Article
Analytical and Numerical Analysis of Mechanical Response of Ultra-Large-Diameter Shield Tunnel with the Nonuniform Convergence of Axial Symmetry
by Weitao Chen, Kaihang Han and Jun Zhou
Symmetry 2026, 18(6), 991; https://doi.org/10.3390/sym18060991 - 9 Jun 2026
Viewed by 255
Abstract
In this paper, analytical and numerical analyses of the mechanical response of an ultra-large-diameter shield tunnel with a nonuniform convergence of axial symmetry are conducted. A nonuniform convergence of axial symmetry around the tunnel boundary is adopted. The bending moment and axial force [...] Read more.
In this paper, analytical and numerical analyses of the mechanical response of an ultra-large-diameter shield tunnel with a nonuniform convergence of axial symmetry are conducted. A nonuniform convergence of axial symmetry around the tunnel boundary is adopted. The bending moment and axial force of the tunnel liner with different diameters from 6 to 18 m are obtained and compared in detail. The theoretical analysis results show that at the same buried depth of the tunnel crown, both the maximum absolute bending moment and axial force of the shield tunnel liner grow as the diameter of the tunnel increases. Moreover, the distributions of the bending moments of the tunnel liner along the tunnel boundary present a “8” shape and are axially symmetric along the vertical axis, where the upper and lower parts are positive and the left and right sides are negative. The maximum absolute bending moment of the tunnel liner is at the axis of 280°. Furthermore, the axial force of the shield tunnel liner is always negative, and the maximum absolute axial forces of the tunnel liner are at the axis of 0° and 180°. Finally, it is worth pointing out that the maximum bending moment and axial force increase 26.99 times and 8.99 times, respectively, when the diameter increases only three times from 6 m to 18 m, which is of great guiding significance for the rational design of ultra-large-diameter shield tunnels. The results of the analytical solution are verified by a numerical analysis, which shows that the analytical solution has a higher computational efficiency than the numerical simulation while ensuring accuracy. Full article
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29 pages, 18077 KB  
Article
Deformation Response and Influencing Factors of Piled-Raft Foundation Buildings Induced by Undercrossing Shield Tunnels
by Wen Feng, Jian Xu, Rui Zhang, Lei Fu, Yingjie Zhu, Ziyu Yan, Guohua Zhang and Zongwu Chen
Buildings 2026, 16(11), 2283; https://doi.org/10.3390/buildings16112283 - 5 Jun 2026
Viewed by 361
Abstract
Shield tunnel construction inevitably disturbs existing upper buildings. This paper takes the section from Zhongyi Road Station to Housihu Fourth Road Station of Wuhan Metro Line 12 as the engineering background, where twin shield tunnels pass beneath Zizhu Kindergarten. Based on field monitoring [...] Read more.
Shield tunnel construction inevitably disturbs existing upper buildings. This paper takes the section from Zhongyi Road Station to Housihu Fourth Road Station of Wuhan Metro Line 12 as the engineering background, where twin shield tunnels pass beneath Zizhu Kindergarten. Based on field monitoring data, this paper systematically analyzes the development laws of surface settlement and building settlement. Numerical simulation is adopted and compared with measured data to verify the reliability of the model. With the validated numerical model, this paper investigates the influencing factors of building settlement. The results show that the maximum ground surface settlement during shield construction is approximately 6.84 mm, and the maximum building settlement is about 4.63 mm. The horizontal relative position between piles and tunnels changes the superposition mode of ground settlement troughs. Building settlement reaches the minimum when twin tunnels pass beneath symmetrically. Eccentric crossing aggravates building settlement to a certain extent. The maximum building settlement increases with the rise of tunnel buried depth. The research results can provide a reference for deformation control and construction optimization of similar twin shield tunnels crossing beneath buildings with piled-raft foundations. Full article
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21 pages, 16412 KB  
Article
The Vibration Response of Multi-Story Buildings Under a Symmetric Disturbance Field Induced by Shield Tunneling in Hard Rock
by You Wang, Meiqi Hu, Yue Ma, Bosong Ding and Yang Xiang
Symmetry 2026, 18(6), 914; https://doi.org/10.3390/sym18060914 - 27 May 2026
Viewed by 313
Abstract
Shield tunneling in urban areas can generate ground vibrations that may threaten adjacent buildings, especially in hard rock strata. However, the effect of foundation type on the vibration response of multi-story buildings is not yet fully understood. This study investigates this issue through [...] Read more.
Shield tunneling in urban areas can generate ground vibrations that may threaten adjacent buildings, especially in hard rock strata. However, the effect of foundation type on the vibration response of multi-story buildings is not yet fully understood. This study investigates this issue through a combined approach of field monitoring and three-dimensional numerical simulation based on the Jinan Metro Line 4 project. Five-story frame buildings with pile, raft, and isolated footing foundations were analyzed, and the numerical model was validated against measured data to ensure reliability. The results show that vibration waves attenuate in an approximately symmetric elliptical pattern and are amplified by the presence of buildings. A significant vertical amplification effect is observed, with peak particle velocity at the top floor reaching up to 2.11 times that at the ground surface. Foundation type exerts a significant influence on vibration transmission. Raft foundations exhibit a more uniform vibration distribution, whereas isolated footings demonstrate a weaker attenuation capacity, with only 23.6% attenuation and a first-floor response approximately 3.3 times greater than that of pile foundations. Although the structural safety requirements are satisfied, the vibration levels at upper floors may still exceed the human comfort limit of 75 dB, with the pile-founded building reaching 85.38 dB. These findings improve the understanding of vibration transmission mechanisms under symmetric disturbance conditions and provide a scientific basis for foundation selection and vibration mitigation in urban tunneling projects. Full article
(This article belongs to the Special Issue Symmetry and Finite Element Method in Civil Engineering)
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13 pages, 578 KB  
Article
Hawking Atmosphere of Anti-de Sitter Black Holes
by A. F. Cardona and C. Molina
Universe 2026, 12(5), 141; https://doi.org/10.3390/universe12050141 - 9 May 2026
Viewed by 522
Abstract
This work investigates the semiclassical evolution of the Hawking atmosphere surrounding evaporating, spherically symmetric anti-de Sitter (adS) black holes. We model the evaporation process within a dynamical framework, treating the emission of Hawking radiation as a quantum tunneling process through the black-hole horizon. [...] Read more.
This work investigates the semiclassical evolution of the Hawking atmosphere surrounding evaporating, spherically symmetric anti-de Sitter (adS) black holes. We model the evaporation process within a dynamical framework, treating the emission of Hawking radiation as a quantum tunneling process through the black-hole horizon. Using the Parikh–Wilczek tunneling method, we incorporate backreaction effects, with the emission probability being linked to the resulting change in the Bekenstein–Hawking entropy of the black hole. This probability is then used to compute the time-dependent luminosity of the system, revealing significant deviations from ideal blackbody behavior, particularly for small adS black holes. For these objects, the luminosity does not increase with temperature due to strong mass variations during evaporation. To complement this microscopic approach, we compute the renormalized energy–momentum tensor for a quantum field propagating in the Vaidya-adS geometry modelling the evaporation process. Together, these approaches clarify the interplay between geometry, quantum fields, and thermodynamics in shaping the Hawking atmosphere and the evaporation dynamics of black holes in asymptotically adS spacetimes. Full article
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