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Similarity Solution for the Synchronous Grouting of Shield Tunnel Under the Vertical Non-Axisymmetric Displacement Boundary Condition

Part of: Generalities, axiomatics, foundations of continuum mechanics of solids Equilibrium (steady-state) problems

Published online by Cambridge University Press:  11 October 2016

Jinfeng Zou  and
Songqing Zuo
Jinfeng Zou*
Affiliation:
School of Civil Engineering, Central South University, Changsha, Hunan 410083, China
Songqing Zuo*
Affiliation:
School of Civil Engineering, Central South University Railway Campus, Changsha, Hunan 410075, China
*
*Corresponding author. Email:zoujinfeng_csu@163.com (J. F. Zou), zsq2011510409@163.com (S. Q. Zuo)
*Corresponding author. Email:zoujinfeng_csu@163.com (J. F. Zou), zsq2011510409@163.com (S. Q. Zuo)
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Abstract

Similarity solution is investigated for the synchronous grouting of shield tunnel under the vertical non-axisymmetric displacement boundary condition in the paper. The synchronous grouting process of shield tunnel was simplified as the cylindrical expansion problem, which was based on the mechanism between the slurry and stratum of the synchronous grouting. The stress harmonic function on the horizontal and vertical ground surfaces is improved. Based on the virtual image technique, stress function solutions and Boussinesq's solution, elastic solution under the vertical non-axisymmetric displacement boundary condition on the vertical surface was proposed for synchronous grouting problems of shield tunnel. In addition, the maximum grouting pressure was also obtained to control the vertical displacement of horizontal ground surface. The validity of the proposed approach was proved by the numerical method. It can be known from the parameter analysis that larger vertical displacement of the horizontal ground surface was induced by smaller tunnel depth, smaller tunnel excavation radius, shorter limb distance, larger expansion pressure and smaller elastic modulus of soils.

Keywords

Vertical non-axisymmetric displacement boundarystresses and displacementsvirtual image techniquecylindrical cavity expansion sourceimage sourcestress harmonic functionshield tunnelsynchronous groutingmaximum grouting pressure

MSC classification

Secondary: 74G15: Numerical approximation of solutions 74A10: Stress
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 1 , February 2017 , pp. 205 - 232
Copyright
Copyright © Global-Science Press 2017 

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