Elastic-slip interface effect on dynamic response of underwater convey tunnel in saturated poroelastic soil subjected to plane waves

doi:10.1016/j.tust.2020.103468

Tunnelling and Underground Space Technology

Volume 103, September 2020, 103468

https://doi.org/10.1016/j.tust.2020.103468 Get rights and content

Abstract

In engineering construction, the elastic-slip interface often exists around the tunnel. An elastic-slip interface model is proposed to analyze the dynamic response of underwater convey tunnel, and the surrounding soil is assumed to be saturated poroelastic medium. The reflected, refracted and scattered waves in the free surface water, the surrounding soil medium and the tunnel are expressed by wave function expansion method. Based on Biot’s dynamic theory, an elastic-slip interface is developed to analyze the scattering of P and SV waves around the tunnel. The interface coefficients (normal and tangential spring coefficients and slip coefficient) are introduced to analyze the elastic-slip interface effect on the dynamic stresses under different wave frequencies. It can be concluded that the effect of normal spring coefficient is greater than that of tangential spring coefficients. The interface effect in the region of low frequency is greater than that of high frequency. The interface effect under different surface water depths and embedded depths of tunnel is also examined. Comparison with existing numerical results validates this dynamic model.

Introduction

With the increasing demand of traffic vehicles, more and more underwater convey tunnels are built to shorten the distance and time. The advantages of underwater convey tunnels, such as all-weather operation and expressing no effect on navigation and the surrounding environment lead to considerable progress in the construction technology of underwater tunnels (Zhang, 2014, Miao et al., 2018).

To make sure of the safe operation of underwater convey tunnels, the investigation on the strength is very important in the design and maintenance of tunnels. Helmberger constructed a plane layered oceanic crustal model, and De Hoop's modification of Cagniard's method was used to obtain the exact transient response when a point source was located in the fluid layer (Helmberger, 1968). Lee and Nam studied the effect of excavation advance rate on the seepage forces acting on the tunnel face, and it was found that the effect of effective overburden pressure was reduced slightly by the arching effect induced by tunnel excavation (Lee and Nam, 2004). By using the conformal mapping methods, the analytical solutions were derived for two-dimensional, steady ground water flow into a horizontal tunnel in a fully saturated, homogeneous, isotropic, and semi-infinite aquifer. The distribution of the hydraulic head and the pore pressure in the rock mass surrounding the tunnel was calculated, and the constant hydraulic head and constant water pressure boundary conditions at the tunnel perimeter were taken into consideration (Ming et al., 2010). Feng et al. conducted a large-scale model test of segment lining structure for underwater shield tunnel with large cross section, and the impact effect of surrounding rock deterioration was discussed. It was found that the seepage forces acting on the tunnel face due to groundwater flow may seriously affect the stability of the tunnel face (Feng et al., 2012). By using Finite Element Method, Akgun et al. studied the distributions of induced stress and deformations in the rock mass and the interaction of the support systems with the rock mass on the stress was analyzed (Akgun et al., 2014). Shan and Ling investigated the wave propagation in an elastic solid with a fluid layer, and the Scholte equation was used to derive the wave velocity. The analytical solutions were obtained by power series expansion method (Shan and Ling, 2018). By using the nonlinear finite element analysis software ABAQUS, Yan et al. investigated the dynamic cracking and failure of the segmental lining structure of an underwater shield tunnel subjected to a derailed high-speed train impact, and it was found that impacting the structure can lead to V-shaped continuous and penetrating cracks in the segment and to continuous long strip or polygonal shaped cracks in the joint surfaces around the impacting area of the segments as well as their outer surfaces near the joint surface (Yan et al., 2018).

When a seismic source occurs in the water at a height less than a wavelength from the water-solid interface, a prominent S-wave arrival can be observed. It travels kinematically as if it is excited at the projection point on the interface. The nongeometric S-wave can also be excited at a fluid-solid configuration if the S-wave speed in the solid medium is less than the sound speed in the water. Allouche and Drijkoningen found the existence of non-geometric wave at the water bottom interface, and the effect of the ratio of the S-wave velocity and the sound speed of water was discussed (Allouche and Drijkoningen, 2016). The non-geometric wave can show significant effect on the strength of underwater tunnels. Most recently, Huang et al. (2019) investigated the scattering of plane P, SV waves around twin lining tunnels embedded in an elastic half-space, and the effect of slipping-stiffness coefficient and viscosity coefficient at the lining-surrounding rock interface on the dynamic stress distribution was explored.

For the underwater tunnels, the surrounding soil medium is often poroelastic and saturated. In construction engineering, the interface properties can be optimized to decrease the local stress around the embedded tunnels. In the earthquake prone area, the interface around the tunnel can also have great influence on the dynamic strength of the tunnel (Liu et al., 2019). Due to existence of bi-materials, some elastic materials often exist in the practical interface between the tunnel and surrounding medium, and the slip at the interface under loadings is also an important character. The reflection and refraction of non geometric waves at the surface of the fluid layer and the interface around the tunnel are so complicated. However, this problem has not been addressed in the past.

The main objective of this paper is to investigate the dynamic response of an underwater convey tunnel subjected to plane waves. The surrounding medium around the tunnel is assumed to be the saturated and poroelastic. To simulate the practical interface condition, the elastic-slip interface model around the tunnel is introduced. The wave fields in the four regions (the saturated poroelastic medium, the free surface water, the tunnel lining and the convey water) are described by wave function expansion method. In numerical examples, the dynamic stress under different interface properties and embedded depths is analyzed in detail.

Section snippets

Problem formulation

A semi-infinite soil medium is covered by free surface water with depth of h₁. To simulate the practical soil medium covered with water, the saturated poroelastic medium is introduced. A circular tunnel filled with inviscid and ideal compressible water is embedded in the soil medium. The inner and outer radii of the tunnel are denoted by a₁ and a₂. The embedded depth of tunnel in the soil medium is h₂. A plane SV wave with frequency $ω$ propagates in the saturated poroelastic medium, and the

Wave fields in the saturated poroelastic medium

In poroelastic material, the isotropic, permeable porous rock, and the pore-filling fluid are in mechanical equilibrium. The stress is positive when it is tensile. The state of rock and the fluid is described by the total stress ( $σ_{ij}$ ) on the bulk material, and the fluid pressure field p. Based on Biot's theory for saturated poroelastic medium, the dynamic equilibrium equation with dissipation taken into account are written as (Biot, 1956) $N \nabla^{2} u + \nabla [(A + N) e + Q ε] = (ρ_{11} \frac{\partial^{2} u}{\partial t^{2}} + ρ_{12} \frac{\partial^{2} U}{\partial t^{2}}) + b (\frac{\partial u}{\partial t} - \frac{\partial U}{\partial t})$ $\nabla (Q e + R ε) = (ρ_{12} \frac{\partial^{2} u}{\partial})$

Boundary conditions and solving procedure

The boundary conditions at the interface between the saturated poroelastic soil and the free water are expressed as $σ_{x x (s)} = σ_{(w 1)}, σ_{x y (s)} = 0, u_{x (s)} = u_{x (w 1)}, (y = 0)$

The free surface of water can be written as $σ_{(w 1)} = 0, (y = h_{1})$

In the practical interface between the tunnel and surrounding medium, some elastic materials often exist, and the slip at the interface under loadings is also an important character. In ideal interface model, the elastic and slip characters cannot be considered. To simulate the practical interface

Numerical results and parameter analysis

To analyze the dynamic response of convey tunnel under different parameters, the following numerical examples are given. By solving Eqs. (70), (71), (72), (73), (74), (75), (76), (77), the expanded coefficients can be obtained. The displacement and stress fields in the regions can be further obtained, so that the problem can be solved.

For convenience, a dimensionless wave number $\bar{k}$ is defined. $\bar{k}$ is the ratio of the inner diameter of the tunnel lining to the wavelength of the incident wave,

Conclusions

The elastic-slip interface model is proposed to analyze the dynamic stress around an underwater convey tunnel embedded in saturated poroelastic medium. The wave fields in the regions are expressed by wave function expansion method. To satisfy the boundary conditions at the straight boundaries, two circular arcs with large radii are used. The dynamic stress under different interface properties is analyzed, and some important conclusions are drawn.

a)
The effect of normal spring constant on the

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work is supported by the National Natural Science Foundations of China (Nos. 11790282, U1534204) and the National Natural Science Foundations of Hebei, China (A2019210037).

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Elastic-slip interface effect on dynamic response of underwater convey tunnel in saturated poroelastic soil subjected to plane waves

Abstract

Introduction

Section snippets

Problem formulation

Wave fields in the saturated poroelastic medium

Boundary conditions and solving procedure

Numerical results and parameter analysis

Conclusions

Declaration of Competing Interest

Acknowledgements

Tunn. Undergr. Sp. Tech.

Int. J. Pres. Ves. Pip.

Tunn. Undergr. Sp. Tech.

Tunn. Undergr. Sp. Tech.

Tunn. Undergr. Sp. Tech.

J. Sound. Vib.

Tunn. Undergr. Sp. Tech.

Geotechnical investigations and preliminary support design for the Gecilmez tunnel: A case study along the Black Sea coastal highway, Giresun, northern Turkey

Tunn. Undergr. Sp. Tech.