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Tide-induced hydraulic response in a semi-infinite seabed with a subaqueous drained tunnel

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Abstract

In this study, analytical solutions for tide-induced pore pressure, seepage force and water inflow into a subaqueous drained tunnel are developed. The results are compared with numerical solutions from a commercial software. The effects of the soil permeability, shear modulus, lining thickness and buried depth of the tunnel on tide-induced pore pressure, seepage force and water inflow are discussed. Larger tide-induced pore pressure and seepage force are obtained for smaller tunnel depth and higher soil permeability. The phase lags of the maximal tide-induced pore pressure at different depths are determined and investigated.

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Abbreviations

a I0, a Im, a II0, a IIm :

Coefficients (see Eqs. (20)–(23))

A n :

Coefficient

Arg:

The argument of a complex number

B n :

Coefficient

β f :

Compressibility of the pore fluid

c lk , c sk :

Coefficients, \(c_{\text{lk}} = \sqrt {i\omega C_{\text{ls}} }\); \(c_{\text{sk}} = \sqrt {i\omega C_{\text{ss}} }\)

C s :

Coefficient of composite compressibility

C ls, C ss :

Coefficients of composite compressibility for the lining and seabed

E :

Young’s modulus

E n :

Coefficient

G :

Shear modulus of the soil

G n :

Coefficient

Γ 0, Γ m :

Coefficients

γ f :

Unit weight of the fluid

H (1) n ,H (2) n :

Hankel functions of the first kind and the second kind, respectively

h :

Burial depth of the tunnel

i:

Imaginary unit

Im:

Imaginary part of a complex number

k l , k s :

Permeability coefficients of the lining and seabed, respectively

n :

Soil porosity

n l , n s :

Porosities of the lining and seabed, respectively

p :

Tide-induced pore pressure

p I , p II :

Tide-induced pore pressures in the seabed and lining, respectively

p max :

Maximal tide-induced pore pressure

p 0 :

Amplitude of the hydrodynamic pressure acting on the mud line

ρ, θ :

Polar coordinates

ρ 2 , θ 2 :

Expressions of ρ and θ

Q :

Water inflow into the tunnel

R, r :

External and internal radii of the lining, respectively

Re:

The real part of a complex number

S r :

Degree of saturation

S rl, S rs :

Degrees of saturation of the lining and seabed, respectively

t :

Time in seconds

T :

Period of the tide

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {u}\) :

Soil displacement vector

ν :

Poisson’s ratio

ν l , ν s :

Poisson’s ratios of the lining and seabed, respectively

V ′0 , V ′ n :

Coefficients

ω :

Tide angular frequency (=2π/T)

W ′ n :

Coefficient

x, y :

Cartesian coordinates

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Acknowledgements

The preparation of this paper was supported by the National Natural Science Fund of China under Research Project Nos. 51338009, 51678523 and 51278462. The authors greatly appreciate the support provided.

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Authors and Affiliations

  1. Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, 388 Yuhangtang Rd., Hangzhou, 310058, China

    Hongwei Ying, Chengwei Zhu & Xiaonan Gong

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  1. Hongwei Ying
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  2. Chengwei Zhu
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  3. Xiaonan Gong
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Correspondence to Hongwei Ying.

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Ying, H., Zhu, C. & Gong, X. Tide-induced hydraulic response in a semi-infinite seabed with a subaqueous drained tunnel. Acta Geotech. 13, 149–157 (2018). https://doi.org/10.1007/s11440-017-0525-5

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