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24 pages, 14193 KB

Open AccessArticle

Deformation Estimation and Failure Probability Analysis of Non-Circular Tunnels

by Yong Xia, Dingping Xu, Quan Jiang, Dongqi Hou, Xiangshen Chen, Yang Yu and Qiang Liu

Buildings 2026, 16(9), 1716; https://doi.org/10.3390/buildings16091716 (registering DOI) - 27 Apr 2026

Inherent defects in engineering rock masses inevitably lead to randomness in mechanical parameters and uncertainty in tunnel deformation and failure. To address these challenges, this study proposes a novel coupled analysis method that integrates complex function theory, physical model testing, and Monte Carlo [...] Read more.

Inherent defects in engineering rock masses inevitably lead to randomness in mechanical parameters and uncertainty in tunnel deformation and failure. To address these challenges, this study proposes a novel coupled analysis method that integrates complex function theory, physical model testing, and Monte Carlo simulation (MCS) for the deformation estimation and failure probability analysis of non-circular tunnels. Theoretically, this method provides a high-speed, high-accuracy analytical framework that overcomes the limitations of purely numerical approaches, particularly in handling continuous–discontinuous failure processes. Practically, it enables a more reliable and efficient stability assessment of tunnel systems under uncertain geological conditions. The proposed method is applied to a traffic tunnel at the Baihetan Hydropower Station. A series of uniaxial compression tests on 40 rock specimens are conducted to obtain statistical distributions of rock deformation parameters. An analytical solution for tunnel displacement is derived using plane elastic complex function theory, and the random displacement field is estimated via MCS. Physical model tests reveal that the elastic stage accounts for 83% of the overload failure process, based on which an elastic limit displacement function is established for tunnel arch settlement and surrounding rock convergence. The failure probability of the tunnel is then calculated, and the effects of the mean, coefficient of variation, and cross-correlation coefficient of rock deformation parameters on failure probability are discussed. The entire computational process is characterized by high speed and precision, offering a new and practical tool for tunnel stability evaluation and reliability-based design. Full article

(This article belongs to the Special Issue Solid Mechanics as Applied to Civil Engineering)

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24 pages, 7551 KB

Open AccessArticle

Dynamic Response of Integrated Maglev Station–Bridge Structures Under Varying Support Constraints

by Ruibo Cui, Xiaodong Shi, Yanghua Cui, Jianghao Liu and Xiangrong Guo

Buildings 2026, 16(7), 1296; https://doi.org/10.3390/buildings16071296 - 25 Mar 2026

Viewed by 374

Abstract

Spatial efficiency drives the adoption of integrated station–bridge structures in maglev transit, yet the rigid coupling between track and station poses inherent challenges to vibration serviceability. This study isolates the impact of support constraints, specifically contrasting rigid connections with pinned supports, on the [...] Read more.

Spatial efficiency drives the adoption of integrated station–bridge structures in maglev transit, yet the rigid coupling between track and station poses inherent challenges to vibration serviceability. This study isolates the impact of support constraints, specifically contrasting rigid connections with pinned supports, on the dynamic performance of a five-story maglev station. Using a unified, high-fidelity 3D coupled model that incorporates electromagnetic suspension nonlinearity, we evaluated structural responses under train speeds of 60–120 km/h. Simulations identify a critical operational threshold: while the waiting hall remains compliant with standard comfort criteria (DIN 4150-3), the platform floor exceeds the 1.5% g acceleration limit during dual-track operations at speeds ≥ 100 km/h. Beyond standard safety checks, the main scientific innovation of this study is revealing the mechanical transmission paths of structure-borne vibrations at the track-frame interface. The results demonstrate that rigid connections create full mechanical coupling, directly passing train-induced bending moments into the station frame. Conversely, pinned supports release the rotational degrees of freedom, which physically cuts off the primary energy transmission route. By explaining this structural decoupling mechanism, this work moves beyond a specific engineering case study to provide a fundamental theoretical framework for vibration control in complex maglev hubs. Full article

(This article belongs to the Special Issue Solid Mechanics as Applied to Civil Engineering)

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19 pages, 3344 KB

Open AccessArticle

2D and 3D Stability Analysis of Rectangular Tunnel Roof Based on Tensile Cut-Off Criterion

by Wenqian Cai, De Zhou, Chaoqun Hou, Yongxin Li, Long Xia and Guihua Long

Buildings 2026, 16(6), 1132; https://doi.org/10.3390/buildings16061132 - 12 Mar 2026

Viewed by 239

Abstract

Tunnel roof is subjected to a complex tension-shear stress state after excavation. A tensile cut-off strength criterion is introduced in this study and combined with the upper bound limit analysis method to investigate the stability of a rectangular tunnel roof. First, the expression [...] Read more.

Tunnel roof is subjected to a complex tension-shear stress state after excavation. A tensile cut-off strength criterion is introduced in this study and combined with the upper bound limit analysis method to investigate the stability of a rectangular tunnel roof. First, the expression for the internal energy dissipation rate is derived for the circular cut-off segment of the failure criterion. Power functionals Φ are established for both two-dimensional and three-dimensional rotational collapse mechanisms. The analytical equations for the failure surface are obtained using the variational method. The strength reduction method that incorporates the cut-off criterion is proposed to quantify roof stability. The investigation into the morphology of the collapsing block indicates that the supporting pressure and the reduction coefficient ξ have a significant influence on the collapse shape of the tunnel, suggesting that attention should be paid to the suspension effect of the tunnel roof on stability. The range of the collapsing block under three-dimensional conditions is found to be larger than that under two-dimensional conditions. Parametric influences on the safety factor are examined. Finally, dimensionless design charts for the critical reinforcement pressure are provided for practical tunnel support design. Full article

(This article belongs to the Special Issue Solid Mechanics as Applied to Civil Engineering)

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23 pages, 7374 KB

Open AccessArticle

Analysis of Pressure Transfer and Failure Mechanisms of Tunnel Faces Subject to Excess Slurry Pressure

by Peihua Xia, Jianbo Zhang, Ming Gao, Chuantan Hou and Yue Qin

Buildings 2025, 15(23), 4375; https://doi.org/10.3390/buildings15234375 - 2 Dec 2025

Viewed by 528

Abstract

Conventional tunnel face stability models are constrained by idealized steady-state seepage assumptions, one-dimensional formulations for inherently three-dimensional flow, and the neglect of transient filter-cake effects. To address these limitations, this study focuses on blowout failure triggered by excess slurry pressure in slurry pressure [...] Read more.

Conventional tunnel face stability models are constrained by idealized steady-state seepage assumptions, one-dimensional formulations for inherently three-dimensional flow, and the neglect of transient filter-cake effects. To address these limitations, this study focuses on blowout failure triggered by excess slurry pressure in slurry pressure balance shield tunneling. We establish a limit-analysis framework that couples slurry infiltration with transient seepage, developing a work rate-balance formulation and a three-dimensional rotational failure mechanism. This framework incorporates heterogeneous, time-dependent filter-cake pressure transfer and the spatiotemporal evolution of pore pressure—key factors overlooked in traditional models. Transient seepage simulations demonstrate that the spatiotemporal heterogeneity of the dynamic filter cake provides the fundamental pressure basis for blowout failure. A prominent hydraulic gradient within the potential core failure zone (Z/R ≤ 2.0, Y/R ≤ 2.0) drives failure initiation and propagation, with the vertical hydraulic gradient in the high-risk subregion (Z/R < 0.5) reaching values as high as 12. Results indicate that passive failure risk increases markedly when excess slurry pressure exceeds 200 kPa, accompanied by a sharp decline in the safety factor. Validation against the Heinenoord No. 2 Tunnel case confirms that the proposed three-dimensional model more accurately captures 3D seepage characteristics and critical failure pressures compared to traditional wedge–prism approaches. By overcoming steady-state and one-dimensional simplifications, this framework deepens the understanding of blowout evolution and provides theoretical guidance for the rational control of slurry pressure and improved tunnel-face stability assessment under complex transient conditions. Full article

(This article belongs to the Special Issue Solid Mechanics as Applied to Civil Engineering)

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16 pages, 3115 KB

Open AccessArticle

Influence of Bolt Arrangement on the Shear Performance of Circumferential Joints of Segments in Super-Large Cross-Section Shield Tunnels

by Haijun Wang, Wei Qiu, Linjian Su, Shaoyi Yang, Yi Xie, Bohan Wu and Luxiang Wu

Buildings 2025, 15(23), 4322; https://doi.org/10.3390/buildings15234322 - 28 Nov 2025

Viewed by 427

Abstract

To evaluate the shear performance of circumferential joints in super-large cross-section shield tunnels featuring inclined bolts and distributed mortises and tenons, refined numerical models were developed for three distinct configurations: single-bolt aligned mortise and tenon (SAB), single-bolt offset (SOB), and double-bolt offset (DOB). [...] Read more.

To evaluate the shear performance of circumferential joints in super-large cross-section shield tunnels featuring inclined bolts and distributed mortises and tenons, refined numerical models were developed for three distinct configurations: single-bolt aligned mortise and tenon (SAB), single-bolt offset (SOB), and double-bolt offset (DOB). This study focuses on assessing how variations in bolt arrangement influence the shear behavior of these joints. The results are as follows: Under the effect of the ordinal shearing loading scenario (OSLS), bolts can significantly bear the load, resulting in the superior shear performance of DOB over SAB and SOB. Under the reverse shearing loading scenario (RSLS), bolts exhibit noticeable pullout phenomena, leading to minimal differences in the shear-dislocation curves of the three bolt arrangement pattern joints. The shear mechanical performance of SOB is notably better than that of SAB and SOB under OSLS, but this difference is less evident under RSLS. The mechanical behavior of bolts remains consistent across different bolt arrangement pattern joints during shear deformation. The bolt holes in SAB passing through the mortise and tenon weaken them, and contact failure between bolts and bolt holes further damages the mortise and tenon. Full article

(This article belongs to the Special Issue Solid Mechanics as Applied to Civil Engineering)

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22 pages, 3292 KB

Open AccessArticle

A Two-Stage Support Load Convergence Method for Rock–Support Interaction in Tunnels

by Zundang Xie, Yiwei Gao, Xiuchang Song, Xiaonian Chen, Zhengxiong Bai and Zhen Li

Buildings 2025, 15(22), 4136; https://doi.org/10.3390/buildings15224136 - 17 Nov 2025

Viewed by 676

Abstract

Understanding the dynamic interaction between surrounding rock and support systems is crucial for tunnel design and safety assessment. This study introduces the Support Load Convergence Method (SLCM), which is an innovative analytical approach that efficiently and accurately captures load distribution and deformation in [...] Read more.

Understanding the dynamic interaction between surrounding rock and support systems is crucial for tunnel design and safety assessment. This study introduces the Support Load Convergence Method (SLCM), which is an innovative analytical approach that efficiently and accurately captures load distribution and deformation in various rock types, including the consideration of elastic, elastoplastic, and post-peak softening conditions. Validation against FLAC3D simulations demonstrates that the SLCM significantly improves computational efficiency while maintaining high accuracy. The method provides a reliable tool for evaluating rock–support interaction, optimizing support schemes, and ensuring the stability and safety of underground structures. Full article

(This article belongs to the Special Issue Solid Mechanics as Applied to Civil Engineering)

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20 pages, 16720 KB

Open AccessArticle

Study of Factors Influencing the Longitudinal Mechanical Performance of Shield Tunnels Traversing Soft–Hard Heterogeneous Soils

by Xiaojie Xue, Qingcheng Zeng, Xushu Peng, Qihang Ran, Yi Xie, Bohan Wu and Luxiang Wu

Buildings 2025, 15(18), 3417; https://doi.org/10.3390/buildings15183417 - 22 Sep 2025

Cited by 1 | Viewed by 775

Abstract

To investigate the longitudinal mechanical behavior of shield tunnels traversing soft and hard heterogeneous strata, a refined three-dimensional numerical model was developed using ABAQUS. The model includes tunnel segments, longitudinal bolts, reinforcement, longitudinal thrust, and additional loading conditions to simulate realistic mechanical responses [...] Read more.

To investigate the longitudinal mechanical behavior of shield tunnels traversing soft and hard heterogeneous strata, a refined three-dimensional numerical model was developed using ABAQUS. The model includes tunnel segments, longitudinal bolts, reinforcement, longitudinal thrust, and additional loading conditions to simulate realistic mechanical responses during construction and operation. The results show that significant differential settlement occurs at the interface between soft and hard soils. Greater joint dislocation is observed on the soft soil side, while joint opening is more pronounced on the hard soil side. Compressive damage concentrates at the soil interface, whereas tensile damage is more severe in soft soil zones. The dislocation at the vault is distributed over a wider area but has a smaller magnitude than that at the arch bottom. Parametric analysis indicates that increasing longitudinal thrust enhances tunnel stiffness and reduces joint dislocation. However, it also leads to increased compressive and tensile damage due to greater trans-verse deformation. Optimizing bolt configuration, including diameter, inclination, and quantity, improves longitudinal stiffness and joint integrity, helping to reduce tensile damage and control deformation. These findings provide theoretical support for the structural design and performance optimization of shield tunnels in complex geological environments. Full article

(This article belongs to the Special Issue Solid Mechanics as Applied to Civil Engineering)

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23 pages, 3685 KB

Open AccessArticle

Seismic Stability Analysis of Water-Saturated Composite Foundations near Slopes

by Tao Zhan, Yongxiang Yang, Daobing Zhang, Fei Zhou, Yunjun Wei and Yulong Wang

Buildings 2025, 15(17), 3090; https://doi.org/10.3390/buildings15173090 - 28 Aug 2025

Cited by 1 | Viewed by 700

Abstract

The seismic bearing capacity of water-saturated composite foundations adjacent to slopes is critical for engineering safety, yet it is significantly influenced by complex factors such as earthquakes and heavy rainfall. This paper establishes a failure mechanism model that involves both reinforced and non-reinforced [...] Read more.

The seismic bearing capacity of water-saturated composite foundations adjacent to slopes is critical for engineering safety, yet it is significantly influenced by complex factors such as earthquakes and heavy rainfall. This paper establishes a failure mechanism model that involves both reinforced and non-reinforced zones, comprehensively considering the synergistic effects of seismic force, pore water pressure and group pile replacement rate, and thus addressing the issue that existing models struggle to account for the coupling effects of multiple factors. Based on the principle of virtual work, a general solution for ultimate bearing capacity is derived, and the optimal solution is obtained using the MATLAB R2023a exhaustive method. Findings reveal that pile group support substantially enhances bearing capacity: the improvement becomes more pronounced with higher soil strength parameters (φ, c) and replacement ratios. When the seismic acceleration coefficient increases from 0 to 0.3, the bearing capacity of the unreinforced foundation decreases by approximately 61.6% (from 134.71 kPa to 51.83 kPa), while group pile support can increase the bearing capacity by 433.2%. Notably, when soil strength is inherently high, the marginal benefit of pile group reinforcement diminishes. A case study in Fuzhou validates through numerical simulation that pile groups improve foundation stability by altering energy dissipation distribution, with the discrepancy between theoretical calculations and simulation results within 10%. The research results can directly guide the design of saturated composite foundations near slopes in earthquake-prone areas (such as Fujian and Guangdong) and enhance the seismic safety reserve by optimizing the replacement rate of group piles (recommended to be 0.2~0.3). Full article

(This article belongs to the Special Issue Solid Mechanics as Applied to Civil Engineering)

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18 pages, 2919 KB

Open AccessArticle

Stability of Non-Uniform Soils Slope with Tension Cracks Under Unsaturated Flow Conditions

by Jing Zhang, Jinyu Dong, Ying Zhao, Yukai Wang and Yang Cheng

Buildings 2025, 15(12), 2123; https://doi.org/10.3390/buildings15122123 - 18 Jun 2025

Cited by 2 | Viewed by 1302

Abstract

The soil slopes in nature are normally unsaturated, heterogeneous, and even carry cracks. In order to assess the stability of slope with crack under steady unsaturated flow and non-uniform conditions, this work proposes a novel discretization-based method to generate the rotational failure mechanism [...] Read more.

The soil slopes in nature are normally unsaturated, heterogeneous, and even carry cracks. In order to assess the stability of slope with crack under steady unsaturated flow and non-uniform conditions, this work proposes a novel discretization-based method to generate the rotational failure mechanism in the context of the kinematic limit analysis. A point-to-point strategy is used to generate the potential failure surface of the failure mechanism. The failure surface consists of a series of log-spiral segments instead of linear segments employed in previous studies. Two kinds of cracks—open cracks and formation cracks—are considered in the stability analysis. The maximum depth of the vertical crack is modified by considering the effect of the unsaturated properties of soils. According to the work–energy balance equation, the explicit expression about the slope factor safety for different crack types is obtained, which is formulated as a multivariate nonlinear optimization problem optimized by an intelligent optimization algorithm. Numerical results for different unsaturated parameters and non-uniform distribution of soil strength are calculated and presented in the form of graphs for potential use in practical engineering. Then, a sensitivity analysis is conducted to find more insights into the effect of unsaturation and heterogeneity on the crack slopes. Full article

(This article belongs to the Special Issue Solid Mechanics as Applied to Civil Engineering)

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20 pages, 5512 KB

Open AccessArticle

Design and Analysis of a Novel Prefabricated Foundation for Substation Buildings

by Weicong Tian, Zhan Li and Hongxia Wan

Buildings 2024, 14(12), 4073; https://doi.org/10.3390/buildings14124073 - 21 Dec 2024

Cited by 5 | Viewed by 2463

Abstract

In recent years, prefabricated components have been widely used in the construction of substation superstructures, while cast-in-place foundations remain the primary method for substation foundations. This paper presents and evaluates a novel prefabricated foundation design aimed at enhancing construction efficiency and load-bearing performance. [...] Read more.

In recent years, prefabricated components have been widely used in the construction of substation superstructures, while cast-in-place foundations remain the primary method for substation foundations. This paper presents and evaluates a novel prefabricated foundation design aimed at enhancing construction efficiency and load-bearing performance. The foundation features a modular design, with each module weighing only half that of a cast-in-place foundation of the same size, significantly improving construction convenience and transportation efficiency. The load-bearing performance of the foundation was validated through static load tests and finite element modeling. The results indicate that the foundation demonstrates excellent ductility, with flexural failure as the primary mode, characterized by multiple cracks across the mid-span and complete yielding of longitudinal reinforcing steels. Further parametric analysis shows that increasing the plate thickness ratio (λ) improves the ultimate bearing capacity of the foundation significantly. Additionally, enlarging the cross-sectional size of the shear key or increasing the strength of the wet joint material enhances overall structural synergy, reduces local deformation, and improves load distribution efficiency. Overall, the sensitivity order of factors influencing the bearing capacity of the new prefabricated foundation is plate thickness ratio (λ) > wet joint strength > shear key cross-sectional size. Full article

(This article belongs to the Special Issue Solid Mechanics as Applied to Civil Engineering)

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19 pages, 9052 KB

Open AccessArticle

Study of the Mechanical Behavior of High-Strength Lightweight Concrete and Its Application to Bridge Pavements

by Qi Song, Yue Qin, Chuantan Hou, Hongwu Gao and Mengzhao Li

Buildings 2024, 14(9), 2783; https://doi.org/10.3390/buildings14092783 - 4 Sep 2024

Cited by 3 | Viewed by 1749

Abstract

High-strength lightweight concrete (HSLC) is increasingly in demand for reducing the self-weight of concrete structures, achieved in this study using shale ceramsite aggregate. Despite its potential, HSLC has been underutilized in field projects due to concerns about its strength and long-term stability. This [...] Read more.

High-strength lightweight concrete (HSLC) is increasingly in demand for reducing the self-weight of concrete structures, achieved in this study using shale ceramsite aggregate. Despite its potential, HSLC has been underutilized in field projects due to concerns about its strength and long-term stability. This study investigates the impact of shale ceramsite content on the mechanical properties of HSLC through uniaxial compression, flexural, and bending tests. The results reveal that ceramsite content significantly influences the concrete’s mechanical properties and failure mechanisms. An optimal design of HSLC was proposed in this study and further used in a real field highway project, demonstrating its applicability to bridge pavements. Newly developed fiber Bragg grating sensors were installed in the material to monitor the performance of the HSLC. Concrete performance monitoring was conducted using a new type of fiber Bragg grating sensor independently developed by the research team. The results showed that the higher the ceramsite content, the greater the shrinkage deformation. And similarly, the higher the strength, the greater the shrinkage deformation. The outcome of this study would provide an alternative approach for the application of HSLC in civil infrastructures. Full article

(This article belongs to the Special Issue Solid Mechanics as Applied to Civil Engineering)

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