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The great magnitude differences between the integral tunnel and its structure details make it impossible to numerically model and analyze the global and local seismic behavior of large-scale shield tunnels using a unified spatial scale, even with the help of supercomputers. The paper aims to present a combined equivalent & multi-scale simulation method, by which the tunnel's major mechanical properties under seismic loads can be represented by the equivalent model, and the seismic responses of the interested details can be studied efficiently by the coupled multi-scale model.

The nominal orthotropic material constants of the equivalent tunnel model are inversely determined by fitting the modal characteristics of the equivalent model with the corresponding segmental lining model. The critical sections are selected by comprehensive analyzing of the integral compression/extension and bending loads in the equivalent lining under the seismic shaking and the coupled multi-scale model containing the details of interest is solved by the mixed time explicit integration algorithm.

The combined equivalent & multi-scale simulation method is an effective and efficient way for seismic analyses of large-scale tunnels. The response of each flexible joint is related to its polar location on the lining ring, and the mixed time integration method can speed-up the calculation process for hybrid FE model with great differences in element sizes.

The orthotropic equivalent assumption is, to the best of the authors’ knowledge, for the first time, used in the 3D simulation of the shield tunnel lining, representing the rigidity discrepancies caused by the structural property.

Evaluation of the quality and performance of a tunnel lining during the installation of segments are the main objects of tunneling projects. Because the quality is affected by several attributes, the purpose of this paper is an appropriate multivariate data analysis that is helpful in extracting applicable knowledge of the data collected regarding the related attributes of the initial installed rings.

Principal component analysis (PCA) is used to analyze the data obtained by the quality control team. The authors use canonical correlation analysis (CCA) to extract some linear combinations of the original attributes of the two groups that produce the largest correlations with the second set of variables.

The authors reduce the dimensionality of the original data set for further analyses, and use a small number of uncorrelated variables rather than a larger set of correlated variables to take effective and efficient action to control the quality of the tunnel lining. The authors also explore the correlation structure and relationship between two main groups of characteristics used for assessing the quality of the installed rings. Then, instead of a large number of the original characteristics in the two groups, the authors can easily control these few to attain a reasonable quality for the tunnel lining.

This is a case study, and for each ring selected for inspection, 16 different characteristics are measured and the observations are recorded. The authors use PCA and CCA to analyse the data and interpret the results. Although the methods are not new, applying them to this data results in useful and informative outcomes and interpretation.

The behavior of joints has a significant effect on the stability of water conveyance tunnel. The purpose of this paper is to study the contact and friction at the joint of the tunneling segment lining and establish its contact friction model. At the same time, the stress and deformation characteristics at the joint of the segment under hydrostatic load are analyzed.

In this study, the contact and friction in a bolted joint are examined using shear testing. The feasibility of the proposed model is verified by a numerical simulation of tests and a theoretical analysis. Accordingly, the effect of joints on the lining is explored under internal hydrostatic loading.

The results show that the openings of tunnel segments in joints gradually expand from the positions of the inner and outer edges to the location of the bolt. Moreover, the stress concentration zone is formed at the bolt. Under hydraulic loading, the opening displacement at the joint increases as the water pressure increases; nevertheless, it does not exceed engineering requirements. When the water pressure of the tunnel lining joint reaches 0.5 MPa, the opening of the joint slowly increases. When the water pressure exceeds 0.7 MPa, the opening of the joint rapidly and significantly increases.

Contact and friction in a bolted joint were examined using shear testing. A cohesive zone model of bolted joints was proposed based on test results. The influence of joint behavior on the stability of water conveyance tunnel was studied.

Transfer relations represent analytical solutions of the linear theory of circular arches, relating each one of the kinematic and static variables at an arbitrary cross-section to the kinematic and static variables at the initial cross-section. The purpose of this paper is to demonstrate the significance of the transfer relations for structural analysis by means of three examples taken from civil engineering.

The first example refers to an arch bridge, the second one to the vault of a metro station and the third one to a real-scale test of a segmental tunnel ring.

The main conclusions drawn from these three examples are as follows: increasing the number of hangers/columns of the investigated arch bridge entails a reduction of the maximum bending moment of the arch, allowing it to approach, as much as possible, the desired thrust-line behavior; compared to the conventional in situ cast method, a combined precast and in situ cast method results in a decrease of the maximum bending moment of an element of the vault of the studied underground station by 46%; and the local behavior of the joints governs both the structural convergences and the bearing capacity of the tested segmental tunnel ring.

The three examples underline that the transfer relations significantly facilitate computer-aided engineering of circular arch structures, including arch bridges, vaults of metro stations and segmental tunnel rings.

Multilayer composite liner structures are the primary structural form of hydraulic tunnels. However, the bearing mechanism of multilayer composite liners has not been investigated thoroughly. Many existing design schemes do not properly achieve a balance between structural safety, anti-seepage capacity, and cost effectiveness. Thus, a new composite liner structure type and its theoretical model was proposed.

A novel hydraulic tunnel composite liner structure with a polyurea spray coating interlayer was proposed in this study. A theoretical model based on the state-space method was developed and verified using FEM models and existing theoretical models. Parametric analysis was conducted based on the theoretical model to investigate the influence of various variables, including interfacial shear stiffness, inner liner thickness, and outer liner elastic modulus.

It was concluded that the proposed theoretical model can be used successfully to calculate multilayer composite liner structures with high calculation efficiency. The overall deformation stiffness of the composite liner system increased with the interfacial shear stiffness. The sprayed coating interlayer significantly affects the residual force distribution between the outer and inner liners, which can also be affected by the adjustment of the thickness of the outer and inner liners. Thus, attention should be paid to these factors in the rational design of the proposed composite liner system.

With the development of China’s water conservancy projects, complex geological conditions, high surrounding rock stress, high internal and external water pressures, and other unique application scenarios have gradually increased. This places higher requirements on the bearing performance and impermeability of hydraulic tunnel lining structures. On the other hand, conventional hydraulic tunnel lining structures can hardly achieve a satisfactory balance between economy, structural safety, and impermeability. Thus, the proposed structure has the potential to be used in a wide range of applications.

This study aims to propose a series of numerical and surrogate models to investigate the aerodynamic pressure inside cracks in high-speed railway tunnel linings and to predict the stress intensity factors (SIFs) at the crack tip.

A computational fluid dynamics (CFD) model is used to calculate the aerodynamic pressure exerted on two cracked surfaces. The simulation uses the viscous unsteady κ-ε turbulence model. Using this CFD model, the spatial and temporal distribution of aerodynamic pressure inside longitudinal, oblique and circumferential cracks are analyzed. The mechanism behind the pressure variation in tunnel lining cracks is revealed by the air density field. Furthermore, a response surface model (RSM) is proposed to predict the maximum SIF at the crack tip of circumferential cracks and analyze its influential parameters.

The initial compression wave amplifies and oscillates in cracks in tunnel linings, resulting from an increase in air density at the crack front. The maximum pressure in the circumferential crack is 2.27 and 1.76 times higher than that in the longitudinal and oblique cracks, respectively. The RSM accurately predicts the SIF at the crack tip of circumferential cracks. The SIF at the crack tip is most affected by variations in train velocities, followed by the depth and length of the cracks.

The mechanism behind the variation of aerodynamic pressure in tunnel lining cracks is revealed. In addition, a reliable surrogate model is proposed to predict the mechanical response of the crack tip under aerodynamic pressures.

Under the repeated action of the construction load, opening deformation and disturbed deformation occurred at the precast box culvert joints of the shield tunnel. The objective of this paper is to investigate the effect of construction vehicle loading on the mechanical deformation characteristics of the internal structure of a large-diameter shield tunnel during the entire construction period.

The structural response of the prefabricated internal structure under heavy construction vehicle loads at four different construction stages (prefabricated box culvert installation, curved lining cast-in-place, lane slab installation and pavement structure casting) was analyzed through field tests and ABAQUS (finite element analysis software) numerical simulation.

Heavy construction vehicles can cause significant mechanical impacts on the internal structure, as the construction phase progresses, the integrity of the internal structure with the tunnel section increases. The vertical and horizontal deformation of the internal structure is significantly reduced, and the overall stress level of the internal structure is reduced. The bolts connecting the precast box culvert have the maximum stress at the initial stage of construction, as the construction proceeds the stress distribution among the bolts gradually becomes uniform.

This study can provide a reference for the design model, theoretical analysis and construction technology of the internal structure during the construction of large-diameter tunnel projects.

In order to improve the comprehensive evaluation level of shield tunnel structure health, taking a subway tunnel section as an example, and combined with the onsite measured data, such as regular inspection, health monitoring and disease remediation, this paper introduces the variable weight theory to improve the traditional fixed-weight evaluation method from structural deformation, current durability and disease status.

Considering the influence of the fluctuation of each index value on the index weight, a comprehensive structural health evaluation model of shield tunnel based on an improved variable weight matter-element extension model is proposed.

Compared with the traditional fixed-weight evaluation method, this model can correct the evaluation distortion caused by the fluctuation of index value and has optimal effect.

The sensitive analysis shows that several key indicators of the main threats to tunnel structure are obtained to improve the efficiency of operation, maintenance and management of shield tunnel structure.

The paper aims to predict longitudinal deformation of a tunnel caused by grouting under the tunnel bottom in advance according to the grouting parameters, which can ensure the safety of the tunnel structure during the grouting process and also help to design the grouting parameters.

The paper adopted the analytical approach for calculating the longitudinal deformation of a shield tunnel caused by grouting under a tunnel, including usage of the Mindlin’s solution, the minimum potential energy principle and case validation.

The paper provides a variational method for calculating the longitudinal deformation of a shield tunnel in soft soil caused by grouting under the tunnel, which has high computational efficiency and accuracy.

This paper fulfils an identified need to study how the longitudinal deformation of a shield tunnel in soft soil caused by grouting under the tunnel can be calculated.

Fire analysis of precast segmental tunnels involves several problems, mainly related to the soil-structure interaction during fire exposure, coupled with material degradation. Temperature increase in the tunnel is the cause of thermal expansion of the lining, which is resisted by the soil pressure. Furthermore, the increase of temperature in the lining leads to severe damage to the reinforced concrete precast elements, which can jeopardise structural safety.

This problem has been analysed using an ideal case of a precast segmental tunnel excavated in a stratified soil. The analysis has been conducted with a commercial nonlinear FE element code. Initially, excavation of the tunnel was modelled in order to predict stresses in the lining due to the soil pressure and eventually fire exposure was considered. The reinforced concrete lining was modelled with a crack model in order to simulate the actual behaviour.

Results show the importance of considering the interaction with the soil and the degradation of the concrete lining.