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Dynamic Response of Curved Wall LTSLS Under the Interaction of Rainwater Seepage and Earthquake

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Abstract

When water permeates the loess, the strength of the loess will be greatly reduced; thus, it is necessary to study the effect of seepage on the seismic response of a loess tunnel. Fields of structure and fluid are simulated using ADINA, and the calculation model of a curved wall loess tunnel with a super-large section (LTSLS) is established. Rainwater is simulated using an incompressible constant parameter model. Considering the action of near- and far-field earthquake and pulse effects, the Galerkin method is used to solve the interaction of stress and seepage fields. By contrasting and analyzing the maximum principal stress, the minimum principal stress, the maximum displacement of lining and the internal force of the tunnel structure, the influence of rainwater seepage on the mechanical properties of LTSLS is studied, and meanwhile, dynamic responses of LTSLS under the interaction of rainwater seepage and earthquakes are studied. The results show that if rainwater seepage is only considered for shallow buried LTSLS, the pore water pressure of a tunnel is so small that it may be neglected. The damage degree of LTSLS under the interaction of rainwater seepage and earthquakes is more than that under a single field. When considering the interaction effect of rainwater and earthquakes, the pore water pressure, principal stress and displacement under a near-field earthquake with pulse effect are greater than those under a near-field earthquake without pulse effect and a far-field earthquake under the same condition.

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Abbreviations

K :

Stiffness matrix

ΔS :

Displacement increment

L :

Nodal forces corresponding to the pore water pressure among nodes

ΔP :

Increment of pore water pressure

F :

External node load

I :

Unbalanced force of the previous incremental step in the iterative process

\({\hat{\varvec{B}}}\) :

Volume change rate corresponding to the node deformation rate

\(\varvec{\nu}\) :

Derivative of S with respect to time

\({\hat{\varvec{H}}}\) :

Volume change rate corresponding to pore pressure change

P :

Pore water pressure

Q :

Flow quantity by node

B :

Volume change corresponding to node deformation

t :

Time

H :

Fluid volume change corresponding to pore water pressure change

R :

Correction of fluid volume change

M :

Mass matrix

C :

Damping matrix

\({\ddot{\varvec{u}}}\left( {\varvec{t}} \right)\) :

Acceleration vector of a node

\({\dot{\varvec{u}}}\left( {\varvec{t}} \right)\) :

Velocity vector of a node

\({\varvec{u}}\left( {\varvec{t}} \right)\) :

Displacement vector of a node

\({\ddot{\varvec{u}}}_{{\varvec{g}}}\) :

Earthquake acceleration

\({\varvec{P}}_{{\varvec{f}}}\) :

Surface load vector

\(\gamma\) :

One of the basic constant parameters of Newmark-β

δ :

The other of the basic constant parameters of Newmark-β

T max :

Biggest vibration period of an isolated body

\(\alpha_{T}\) :

Tangential correction coefficient

\(\alpha_{N}\) :

Normal correction coefficient

K BN :

Normal spring stiffness

K BT :

Tangential spring stiffness

C BN :

Damping of the normal damper

C BT :

Damping of the tangential damper

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Acknowledgements

This paper is a part of the education ministry doctoral tutor foundation of China (Grant No.: 20136201110003) and a part of the national natural science foundation of China (Grant No.: 51478212).

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Authors and Affiliations

  1. School of Civil Engineering, Lanzhou University of Technology, Lanzhou, China

    Xuansheng Cheng, Huan Feng, Shangrong Qi, Xiaoyan Zhang & Bo Liu

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  1. Xuansheng Cheng
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  2. Huan Feng
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  3. Shangrong Qi
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  4. Xiaoyan Zhang
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Correspondence to Xuansheng Cheng.

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Cheng, X., Feng, H., Qi, S. et al. Dynamic Response of Curved Wall LTSLS Under the Interaction of Rainwater Seepage and Earthquake. Geotech Geol Eng 35, 903–914 (2017). https://doi.org/10.1007/s10706-016-0148-x

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  • DOI: https://doi.org/10.1007/s10706-016-0148-x

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