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Recently, subsea tunnel construction has developed rapidly in China. The traffic volume of subsea metro tunnels is large. Once a safety accident occurs, economic losses and social impacts will be extremely serious. To eliminate accidents in operational subsea metro tunnel structures, a health risk prediction method is proposed based on a discrete Bayesian network. Detecting and monitoring data of the tunnel structures in operation were used to evaluate the health risk by employing the proposed method. This method establishes a Bayesian network model for the health risk prediction of the shield tunnel structure through the dependency relationship between the health risk of the operational tunnel structure and 13 risk factors in five aspects: the mechanical condition, material performance, integrity state, environmental state, and deformation state. By utilizing actual detection and monitoring data of various risk factors for the health risk of the operational subsea metro shield tunnel structure, this method reflects the actual state of the tunnel structure and improves the accuracy of health risk predictions. The validity of the proposed method is verified through expert knowledge and the subsea shield tunnel structure of the Dalian Subway Line 5. The results demonstrate that the health risk prediction outcomes effectively reflect the actual service state of the shield tunnel structure, thus providing decision support for the control of health risks in the subsea metro shield tunnel. [ABSTRACT FROM AUTHOR]

Active faults pose significant threats to the structural integrity of mountain tunnels in seismic active zones. Post-earthquake reconnaissance revealed that numerous tunnels were damaged during past earthquakes, specifically those crossing active fault zones. In this study, the structural response and damage mechanism of a water conveyance tunnel subjected to reverse faulting was investigated. A three-dimensional finite element model incorporating the cohesive interface elements was developed to simulate the nonlinear process of the reverse fault rupture. The ground deformation and tunnel damage characteristics predicted by the numerical analysis were in good agreement with the field observations and experimental results, which proved the feasibility of the proposed simulation scheme. Moreover, a parametric study was conducted to estimate the effects of dip angle, surrounding rock property, tunnel rigidity, and friction coefficient between linings on tunnel performance. The results showed that the damage zone with softer rock masses of grade IV to V, based on the Chinese Guidelines for Design of Highway Tunnel, generally led to moderate structural damage to the tunnel. The tunnel's performance in the damage zone can be further enhanced by increasing tunnel rigidity and smoothness of the external surface of the secondary lining. [ABSTRACT FROM AUTHOR]

Seismic waves propagation with an oblique angle to the tunnel axis will cause asynchronous tunnel motions and have a significant effect on the axial response. A high-precision 2.5D finite element method is established in the frequency domain to simulate the 3D seismic response of the tunnel. This method avoids the disturbance caused by the truncation of the tunnel in the longitudinal direction. Meanwhile, a 2.5D zigzag-paraxial boundary is derived to further improve the calculation efficiency of the 2.5D finite element model. Moreover, by combining the 2.5D finite element method, 2.5D zigzag boundary condition and seismic motion input methods, an obliquely incident substructure method for plane seismic waves is built by converting the plane seismic wave into equivalent nodal forces. The proposed 2.5D finite element method is verified by comparing with a reference solution. Finally, the 2.5D finite element method is applied to study the seismic response of the long lined tunnel. Parameter analyses illustrate that the wave propagation effect to the tunnel axis has a non-negligible influence on the axil deformation of long tunnels. [ABSTRACT FROM AUTHOR]

When the numerical analysis of a long lined tunnel is carried out, the calculation amount of the finite element model becomes restricted large-scale parameter analysis. In this paper, an efficient and high-precision 2.5-dimensional (2.5D) frequency-domain finite element method is used to simulate the three-dimensional response of tunnels under the action of oblique incident plane seismic waves. This method can save calculations and avoid the boundary effect caused by the longitudinal truncation of the tunnel. The 2.5D zigzag-paraxial boundary is developed. The artificial boundary is attached to the structure's surface. The substructure method for oblique plane seismic waves is established. Comparing the substructure method with the analytical solution, the correctness of the site response is verified first. The accuracy of the 2.5D finite element substructure method is further verified. The parameter analysis of different incident angles and conversion angles shows that the underground tunnel does not reach the maximum of structural seismic response when the seismic wave is vertically incident. The location of the soil–rock interface on the tunnel is further discussed. The results show that when the underground tunnel crosses the location of the soil–rock interface, the seismic response of the tunnel will be amplified. [ABSTRACT FROM AUTHOR]

In addition to seismic waves, coseismic displacement is also generated during earthquake events, which decreases gradually away from the seismogenic fault and may bring damages to tunnels in the area. This study aims to investigate the nonlinear response of tunnels under coseismic displacement induced by strike-slip fault. First, a method for applying coseismic displacement on the finite-element model (FEM) is developed by converting the displacement into equivalent nodal forces applied on the element nodes. Then, the nonlinear response of the tunnel under coseismic displacement is numerically investigated, considering the influence of the angle of the tunnel axis with respect to the fault trace, the epicentral distance, and the earthquake magnitude. The numerical results show that the tunnel might suffers tensile damages under coseismic displacement induced by the strike-slip fault, which indicates the coseismic displacement, as one kind of earthquake loads, should also be considered in seismic analysis for tunnels. Moreover, some other conclusions can be drawn: (1) The tensile deformation of the tunnel increases first and then decreases, as the tunnel axis changes from being perpendicular to the fault trace to being parallel to the fault trace, which is converse for the shear deformation; (2) the damage degree on the tunnel lining increases first and then decreases while the epicentral distance increases; (3) with an increasing earthquake magnitude, the tunnel damage increases dramatically. This study offers an insight into further research on tunnel response under coseismic displacement. [ABSTRACT FROM AUTHOR]

An analytical solution for the seismic-induced thrust and moment of the circular tunnel in half-space under obliquely incident P waves is developed in this study, which is the superposition of the solution for deep tunnels under incident and reflected P waves and the reflected SV waves. To consider tangential contact stiffness at the ground-tunnel interface, a spring-type stiffness coefficient is introduced into the force-displacement relationship. Moreover, the tunnel lining is treated as the thick-wall cylinder, providing more precise forecasts than beam or shell models used in previous analytical solution, especially for tunnels with thick lining. The reliability of the proposed analytical solution is assessed by comparing with the dynamic numerical results. Based on the proposed analytical solution, parametrical studies are conducted to investigate the effect of some critical factors on the tunnel's seismic response, including the incident angles, the tangential contact stiffness at the ground-tunnel interface, and the relative stiffness between the ground and the tunnel. The results demonstrate that the proposed analytical solution performs well and can be adopted to predict the internal forces of circular tunnels under obliquely incident P waves in seismic design. [ABSTRACT FROM AUTHOR]

The failure mechanism of tunnels crossing faults is a critical issue for tunnels located in seismically active regions. This study aims to investigate the nonlinear response of rock tunnels crossing inactive faults under obliquely incident seismic P waves. Based on the equivalent nodal force method together with the viscous-spring boundary, an incident method for the site, which contains fault and is subjected to obliquely incident seismic P waves, is developed first. Then, based on the proposed incident method, the nonlinear response and the failure process of the tunnel crossing inactive fault are numerically studied. The numerical results show that the failure mechanism of the tunnel crossing inactive fault can be attributed to the combined action of the seismic waves and its associated fault slippage. Finally, parameter studies are conducted to investigate the effects of the wave impedance ratio of the fault to the surrounding rock and the incident angle of P waves. By the parameter analysis, it can be concluded that: (1) with decreasing the wave impedance ratio of the fault to the surrounding rock, the seismic response of the tunnel increases significantly; (2) the seismic response of the tunnel increases first and then decreases with the increasing of the incident angle of P waves. This study offers the insight for further research on the seismic stability of tunnels crossing inactive faults. [ABSTRACT FROM AUTHOR]

Analytical solutions are widely adopted in the preliminary seismic design of tunnels, which gives credit to their quick response and convenience to provide the internal forces and displacements of tunnels. In the first part of this paper, five analytical solutions are extensively verified by comparing them with the reference solution which obtained by the dynamic finite element method. Some suggestions are given for their application in design according to the prediction results. The analytical solutions contain some assumptions, which may not be applicable to all possible scenarios. Therefore, the application scope of analytical solution in practical engineering is limited, and this application scope has not been discussed at present. In the second part of this paper, the applicability evaluation index is established for the first time to evaluate the critical condition for the application of analytical solution. Then, the applicability function is obtained by fitting the relationships between the critical condition and the flexibility ratios, which can be convenient to calculate the critical condition for the application of analytical solutions in engineering. Finally, the applicability of analytical solution in some engineering projects is correctly evaluated based on the proposed applicability evaluation index and applicability function. • The results of dynamic finite element analysis are used as reference solutions to verify the five analytical solution. • Applicability evaluation index is proposed to evaluate the critical condition for the application of analytical solution. • Applicability function is obtained by fitting the relationships between the critical condition and the flexibility ratios. • The applicability of analytical solution in some engineering projects is correctly evaluated. [ABSTRACT FROM AUTHOR]

Analytical solutions can quickly and simply evaluate stresses and displacements in tunnels and are widely adopted in the preliminary design phase of tunnels. Tunnels must be able to withstand static loading and seismic loading. This paper proposes new analytical solutions for the stresses and displacements of tunnels under static and seismic loading. The tunnel lining is treated as a thick-walled cylinder. Moreover, the contact stiffness coefficient k 0 and the stress release coefficient η 0 are introduced to consider the arbitrary contact conditions at the ground–lining interface and the amount of excavation unloading. The new analytical solutions are verified by comparison with finite element analysis results. The results demonstrate the accuracy and applicability of the proposed analytical solutions. In addition, parametric analyses are conducted to explore the effects of the stress release coefficient η 0 and stiffness coefficient k 0 at the ground–lining interface, as well as the incident angle α of shear waves. The analysis results indicate that the proposed analytical solutions offer satisfactory performance and can be applied as an effective tool for preliminary tunnel design. [ABSTRACT FROM AUTHOR]

The faults play an important role in inducing tremendous potential threat to the stability capability of embedded tunnels in strong earthquake events. Based on the finite element method with the viscous-spring artificial boundary, the earthquake motions of oblique incidence can be transformed into the equivalent nodal forces acting on the truncated boundary of finite element model. In the present work, the formulas of equivalent nodal forces for the 2-D plane P waves with arbitrary incident angles are deduced and implemented into the commercial software ABAQUS. The accuracy of the formulas and the implementation are demonstrated by the numerical examples of a 2-D semi-infinite space and an circular lined tunnel in half-space subjected to obliquely incident P waves. The proposed numerical method is employed to investigate the non-linear responses of the tunnels within surface normal fault ground under obliquely incident P waves. The numerical results indicate that the tunnels buried in the hanging wall, in the foot wall and across the fault, suffer different failure patterns. The tunnels across the fault suffer the most serious plastic damage, followed by that within the hanging wall. Moreover, the seismic responses of the tunnels across the fault and within the hanging wall increase with the inclination degree of the incident P waves, as well as opposite relationship for tunnels within the foot wall. [ABSTRACT FROM AUTHOR]

A simplified analytical solution is developed for estimating the thrusts and bending moments of the circular tunnel in half space under the obliquely incident SV wave. The seismic waves impinging on the tunnel is obtained according to the elastic wave motion theory in half space firstly, which is the superposition of the incident and reflected SV waves and reflected P wave. Then, by considering the tunnel lining as a thick-wall cylinder, analytical solutions for internal forces of circular tunnel due to the incident and reflected SV waves and the reflected P wave are deduced, which enables more precise forecasts than previous analytical solutions by the thin shell model. The total tunnel internal forces are obtained finally through the superposition of the above solutions under three kinds of waves. The accuracy of the proposed analytical solution is verified by comparing with the dynamic numerical results. Moreover, the discussion about the effect of critical factors on the accuracy of the proposed analytical solutions is conducted, including the tunnel structure inertia, the seismic wavelength, the lining thickness and the tunnel depth. These results demonstrate that the proposed analytical solution performs well and can be adopted to predict the internal forces of circular tunnel under obliquely incident SV wave in seismic design. • Analytical solutions for circular tunnel in full space under SV and P waves are developed. • Analytical solution for circular tunnel in half space under obliquely incident SV wave is developed. • The present solutions are verified by comparing with dynamic numerical results. • Discussion about the effect of critical factors on the accuracy of the proposed analytical solutions is conducted. [ABSTRACT FROM AUTHOR]

• A 3-D obliquely incident method for P waves was developed. • Nonlinear seismic response of a tunnel under 40 artificial accelerograms with different incident angles is analyzed. • PGV has incremental effect on the seismic response of tunnels under earthquake P waves with large incident angles. • PGA intends to increase the response of tunnels subjected to earthquake P waves with small incident angles. • PGD has little effect on the seismic response of tunnels. The response mechanism of tunnels under earthquake loads is a critical issue in tunnels located in seismically active regions. This study aims to investigate the seismic response and damage sensitivity of tunnels under earthquake motions with different peak ground acceleration, velocity and displacement (PGA, PGV and PGD). Based on the design acceleration response spectrum (ARS), four groups of total 40 artificial accelerograms are synthesized with specified PGA, PGV and PGD. In addition, for considering the wave travelling effect on the tunnel axial response, an obliquely incident method for P waves is developed by using the equivalent nodal force method. Then, the nonlinear response of tunnels subjected to artificial accelerograms with different incident angles are simulated, respectively. The numerical results indicate that the PGV and PGA have accretion effect on the seismic response of the tunnel. However, the impact of PGD on the tunnel earthquake response is less evident. The PGV has obvious incremental effect on the dynamic response of tunnels subjected to earthquake P waves with large incident angles. Compared with PGV, the PGA intends to increase the response of tunnels significantly under P waves with small incident angles. Thus, it is important to take the PGA and PGV into account during seismic analysis and design for tunnels. [ABSTRACT FROM AUTHOR]

Evaluating the impact of the isolation layer on the tunnel's response is crucial in the practical engineering. An analytical solution for the longitudinal seismic response of a tunnel covered by an isolation layer is first proposed in this study based on an improved elastic foundation beam model. Wherein, an equivalent beam model for the tunnel-isolation layer system is built. The tangential interaction effect at the ground-isolation layer-tunnel interfaces is taken into account by solving the ground-isolation layer-tunnel model under out-of-plane shearing stress. The proposed solution is verified by comparison with dynamic numerical results. Finally, the proposed analytical solutions are employed to investigate the seismic mitigation effects of the isolation layer on the longitudinal response of the tunnel, as well as the influence of the elastic modulus, thickness and Poisson's ratio of the isolation layer. The results indicate that the isolation layer can significantly reduce the longitudinal shearing force of the tunnel but always amplifies the longitudinal bending moment in most cases. Moreover, the mitigating effect of the isolation layer on the longitudinal response of the tunnel is sensitive to the elastic modulus and thickness, except for Poisson's ratio of the isolation layer. • An equivalent beam model for the tunnel-isolation layer system is built. • Tangential interactions at the ground-isolation-tunnel interfaces are considered. • Analytical solution of response for tunnel with isolation layer is proposed. • Seismic mitigation effects of the isolation layer are investigated. [ABSTRACT FROM AUTHOR]

The fault zone plays a vital role in the internal force responses of the tunnel. An analytical solution of the tunnel under the fault zone creeping is developed by taking account of normal and tangential interaction between the ground and tunnel. First, the elastic foundation beam model is used. Wherein, the normal interaction is considered by applying the displacements of the free field on the distal end of normal foundation springs. And the tangential interaction is transformed into bending moment applied on the beam. The analytical solution of the tunnel's response is gotten based on the model. Secondly, the numerical solutions from finite element model of 3D are provided to verify the validity of the proposed analytical solutions. Finally, the effect of the fault zone width, the elastic modulus of the fault and the concrete's grade of the lining are investigated. The results show that with the width of the fault zone increasing, the internal force decrease. The concrete's grade of the lining has opposite effects on the internal force of the tunnel. And with the growth of the elasticity modulus of the fault zone, the shear force and bending moment increase and decrease, respectively. • An analytical solution considering the tangential interaction at the ground-tunnel interface is developed. • The proposed analytical solution is verified by the numerical result obtained from the finite element model of 3D. • Effects of fault zone width, elasticity modulus of fault zone and concrete's grade of the lining are discussed. [ABSTRACT FROM AUTHOR]

The incident direction plays an important role in the seismic response of long lined tunnels. A simplified analytical solution is developed for estimating the seismic response of the circular tunnel under obliquely incident shear waves, including the principle stress and the internal forces and deformations on the cross section and longitudinal of the tunnel. Based on the elastic wave theory, the oblique incident shear wave can be decomposed into an axially propagating shear wave and a shear wave propagating transversely to the tunnel axis. A modified elastic foundation beam model is used to calculate the tunnel longitudinal response, which is based on Timoshenko beams resting on Winkler foundations with considering different tangential contact conditions. Furthermore, by adopting wave theory and Fourier transform, longitudinal response of tunnels under arbitrary seismic load can be obtained. Moreover, the flattening effect and out-plane response of tunnel cross-section caused by longitudinal bending are considered. The proposed analytical solution is verified by comparing with the dynamic numerical results. The effect of the incident angle, ground condition and contact condition on the seismic response of long lined tunnel is investigated by the simplified analytical solution. It is demonstrated that the proposed solution can be adopted to predict internal forces and deformations of circular tunnels under obliquely incident shear wave in preliminary design. • A simplified analytical solution is developed for estimating the seismic response of the circular tunnel under obliquely incident shear waves. • A modified foundation beam model is used for the tunnel longitudinal response, with considering different tangential contact conditions. • By adopting wave theory and Fourier transform, longitudinal response of tunnels under arbitrary seismic load can be obtained. • Moreover, the flattening effect and out-plane response of tunnel cross-section caused by longitudinal bending are considered. • Parameter studies are conducted to investigate the effects of incident angle, ground condition and contact condition. [ABSTRACT FROM AUTHOR]

This study aims to analysis the longitudinal seismic responses of circular tunnels across soil-rock stratum longitudinally ("soil-rock" means two different stratums, not just the soil and rock ground). Based on an improved elastic foundation beam model, an analytical solution is derived to investigate the seismic response of long tunnels across soil-rock stratum, subjected to sinusoidal shear motions. The improved elastic foundation beam model adopts the Timoshenko beam and Winkler foundation, with considering tangential contact conditions at the ground-tunnel interface. The free field reaction considers the reflection and transmission by the soil-rock interface and the wave passage effect. Explicit formulations are obtained for tunnel displacement, rotation angles, bending moments and shearing forces. The proposed solution is verified by comparing with the dynamic numerical results, as well as traditional analytical solutions. Finally, a parametric study is conducted to investigate the influence of traveling wave effect, earthquake frequency, shear wave velocity ratio of two stratums, lining stiffness and contact condition on tunnel seismic responses. The proposed analytical solutions can be used to predict the longitudinal seismic response of deep circular tunnels crossing soil-rock stratum in engineering design. [ABSTRACT FROM AUTHOR]

[Display omitted] • Machine learning is used to predict geological condition in super-large SPBM tunnel. • Performance of RF, SVM and AdaBoost in rock mass classification is evaluated. • Performance of seven formation prediction models is compared. • Slurry system parameters and cutter type are important for geological prediction. Real-time and precise prediction of geological conditions is extremely beneficial to the safe and efficient construction of slurry pressure balanced shield machines (SPBMs), especially for super-large diameter tunnels. Machine learning algorithms provide an effective way to predict geological conditions and have been successful in hard-rock tunnel boring machine (hard-rock TBM) tunnels or earth pressure balance shield machine (EPBM) tunnels. However, the effectiveness of machine learning in predicting geological conditions for super-large diameter SPBM tunnels is still unknown. This study systematically demonstrated the application of machine learning algorithms to the prediction of geological conditions in super-large diameter SPBM tunnels based on field data from the Heyan Road crossing river tunnel. The relationship between SPBM parameters and geological conditions was first evaluated, and subsequently, an adaptive model was proposed to determine the number of input variables. The performance of three algorithms, random forest (RF), AdaBoost, and support vector machine (SVM), in rock mass classification, and seven algorithms, multi-objective random forest (MORF), single-target-RF, regressor chain-RF, single-target-AdaBoost, regressor chain-AdaBoost, single-target-SVM, and regressor chain-SVM, in formation percentage prediction, were compared. The results showed that machine learning algorithms can effectively predict the geological conditions in super-large diameter SPBM tunnels. Specifically, RF had the best performance in rock classification compared with AdaBoost and SVM. MORF outperforms the other six algorithms in terms of formation percentage prediction. Additionally, sensitivity analysis indicates that the newly proposed parameters, including slurry system parameters and cutter type, have a clear positive effect on the performance of geological condition prediction. [ABSTRACT FROM AUTHOR]

An analytical solution can easily and quickly give the internal forces in tunnels due to seismic waves, by which, the relationship between the key parameters could also be clarified. These methods are widely used in preliminary seismic design of tunnels. This paper presents new analytical solutions for thrust and moment of circular composite-lined tunnels with arbitrary layer linings under obliquely incident SV waves and P waves. Wherein, the lining is regarded as a thick-wall cylinder. Moreover, the proposed analytical solutions can consider different contact conditions of the ground-tunnel and lining-lining interface. The new analytical solutions are verified by comparing with the dynamic finite element analysis results. The results show the accuracy and applicability of the proposed analytical solutions. Parametric analyses are performed to explore the effects of the flexibility coefficient δ , incident angle and steel lining on the seismic response of tunnels. [ABSTRACT FROM AUTHOR]

Tunnels, as critical underground infrastructures, often intersect with faults. Field investigations have underscored the susceptibility of fault-crossing tunnels to extensive damages during earthquakes. Hence, large-scale shaking table tests are conducted to investigate the deformation pattern and failure mechanism of fault-crossing tunnels under transverse excitation, particularly in non-rupture scenarios. The dynamic behavior of the tunnel, as expected, is dominated by the surrounding strata. Acceleration responses vary notably across different regions of the fault site. The disparity increases with the increments of seismic intensity and input frequency. The tunnel section at the interface between the fault and the hanging wall manifest the strongest acceleration, where the largest strains of the tunnel and most of the lining cracks also occur, highlighting its vulnerability to seismic vibrations. The damage-induced non-linearity of the tunnel is then identified by the decreasing dominant frequency thereof. The fault-crossing tunnel exhibits unique three-dimensional shearing-torsional deformations, elucidated through the test data and an analytical model. This deformation pattern provides a better understanding of the seismic responses of fault-crossing tunnels under seismic vibrations. • Dynamic responses of fault-crossing tunnels under seismic vibrations are studied by large-scale shaking table tests. • Faults have significant influence on tunnels under seismic vibrations even without rupture. • Vulnerable region of the tunnel, which is most intensely affected by the fault, is identified. • Deformation pattern and failure mechanism of fault-crossing tunnels under seismic vibrations are revealed. [ABSTRACT FROM AUTHOR]

A circular tunnel in a homogeneous infinite ground subjected to a vertically incident shear wave with an arbitrary vibration direction in the horizontal plane is considered in this study. A simplified analytical solution with explicit formulations for the deformation and stress of the tunnel lining is presented here. The superposition of two solutions under SH and SV waves are derived first. In the analytical solutions, the tunnel lining is taken as a thick-walled cylinder, which enables more precise forecasts and is much closer to practical engineering than the thin shell model adopted in other previous solutions. Moreover, the analytical solutions consider the slippage effect at the ground-lining interface by introducing a spring-type flexibility coefficient into the interaction force-displacement relationship. The results of the analytical solutions are verified by a comparison with the results of the dynamic numerical solutions via a 3-D ground-lining interaction model under earthquakes; the results show good agreement. By using the analytical solutions, the effects of the vibration direction, ground condition, lining thickness and flexibility coefficient on the seismic response of the tunnel are investigated. Additionally, the appropriate range of seismic wavelengths for the analytical solutions is discussed. The proposed solutions can be applied to the seismic analysis and design of tunnel structures. • Analytical solution is presented for circular tunnel under vertically incident shear wave with arbitrary vibration direction. • The tunnel lining is treated as a thick-wall cylinder, which enable precise forecasts. • Different slippage effects at the ground-lining interface are considered. • Effects of vibration direction, ground condition, lining thickness and flexibility coefficient are investigated. [ABSTRACT FROM AUTHOR]

Analytical solutions based on the elastic foundation beam model for the bending response of circular tunnels under longitudinally propagating shear waves are studied considering the tangential contact conditions at the ground-tunnel interface. First, two kinds of new analytical solutions based on Timoshenko beams resting on Winkler or Pasternak foundations are developed considering different contact conditions at the ground-tunnel interface. The contact conditions are considered by introducing a spring-type flexibility coefficient in the force–displacement relationship. Then, the new analytical solutions, as well as the traditional solutions using Euler or Timoshenko beams on Winkler or Pasternak foundations, are compared with the dynamic numerical results. The new analytical solutions exhibit good agreement with the dynamic numerical results for different contact conditions. However, due to the neglect of the tangential interaction between the tunnel and surrounding ground, traditional solutions are only suitable for predicting the seismic response of tunnels in the full-slip condition. Finally, a parametric study is conducted to investigate the effects of the earthquake frequency, ground condition, lining thickness and contact condition. The proposed analytical solutions can be used to predict the seismic response of circular tunnels under longitudinally propagating shear waves in engineering design. [ABSTRACT FROM AUTHOR]