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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]

Simplified analytical solutions are very useful tools for the seismic preliminary design of tunnels and can quickly and easily give seismic responses to structures. This study presents simplified analytical solutions for the stress and deformation of circular composite-lined tunnels subjected to in-plane S-waves. Unlike previous solutions for single-lined tunnels, the proposed analytical solutions are suitable for tunnels with arbitrary numbers of linings. Moreover, tunnel linings are treated as multilayer thick-walled cylinders in the new solutions. Compared with thin shell or beam models used in previous analytical solutions, thick-walled cylinders provide more precise forecasts. In addition, the slippage effect at the lining-lining and ground-lining interface is considered by introducing a spring-type flexibility coefficient into the interaction force–displacement relationship. To verify the proposed analytical solutions, dynamic numerical examples are studied. The proposed solutions have good agreement with the dynamic numerical results and outperform previous analytical solutions. Finally, parameter studies are conducted to investigate the effect of the flexibility coefficient, degraded zone around the outermost lining and steel plate supporting the innermost lining on the seismically induced stresses and deformations. The proposed analytical solutions are applicable for approximately evaluating the seismic responses of circular tunnels with composite linings. [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]

As a common type of foundation in ocean engineering, steel foundation encounters great corrosion risk and serious safety hazards throughout its lifecycle. Besides reducing the thickness of steel members, corrosion also has a significant impact on the soil-structure interfacial shearing property by changing the roughness characteristics of steel surface, and eventually affects the bearing capacity of steel foundation in submarine soil environment. In this study, electrolytic accelerated corrosion experiments are conducted first to prepare corroded steel samples suffered different degrees of corrosion. Then, the effect of corrosion on the soil-steel foundation interfacial shearing property is investigated by interfacial shearing experiment and discrete element numerical simulation. The analysis results show that the interface shearing strength under different corrosion degrees can be regarded as following Mohr-Coulomb strength theory. The shearing strength parameters, i.e. the interfacial cohesion and interfacial friction coefficient, increase with the corrosion degree. Finally, the influences of corrosion on the bearing capacity of a steel pipe pile foundation are studied by finite element simulation, with considering the steel thickness reduction and the variation of soil-steel interfacial shearing strength. The numerical results demonstrate the necessity of considering the variation of the interfacial shearing property induced by corrosion. [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]

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]