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Geomechanics and Engineering
  Volume 19, Number 3, October30 2019 , pages 201-215
DOI: https://doi.org/10.12989/gae.2019.19.3.201
 


Elastic solutions for shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface
Ling Wang, Jin-Feng Zou, Tao Yang and Feng Wang

 
Abstract
    A new approach of analyzing the displacements and stress of the surrounding rock for shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface is investigated in this study. In the proposed approach, by using a virtual image technique, the shear stress of the vertical ground surface is revised to be zero, and elastic solutions of the surrounding rock are obtained before stress revision. To revise the vertical normal stress and shear stress of horizontal ground surface generated by the combined action of the actual and image sinks, the harmonic functions and corresponding stress function solutions were adopted. Based on the Boussinesq\'s solutions and integral method, the horizontal normal stress of the vertical ground surface is revised to be zero. Based on the linear superposition principle, the final solution of the displacements and stress were proposed by superimposing the solutions obtained by the virtual image technique and the stress revision on the horizontal and vertical ground surfaces. Furthermore, the ground settlements and lateral displacements of the horizontal and vertical ground surfaces are derived by the proposed approach. The proposed approach was well verified by comparing with the numerical method. The discussion based on the proposed approach in the manuscript shows that smaller horizontal ground settlements will be induced by lower tunnel buried depths and smaller limb distances. The proposed approach for the displacement and stress of the surrounding rocks can provide some practical information about the surrounding rock stability analysis of shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface.
 
Key Words
    shallow tunnel; non-axisymmetric displacement boundary; virtual image technique; linear superposition principle; ground settlement
 
Address
Ling Wang: 1.) School of Civil Engineering, Central South University, No.22, Shaoshan South Road,
Central South University Railway Campus, Changsha, Hunan Province, People\'s Republic of China
2.)Department of Environmental Design, Hunan University of Technology and business, No. 8 569, Yuelu Road,
Hunan University of Technology and Business, Changsha, Hunan Province, People\'s Republic of China

Jin-Feng Zou, Tao Yang and Feng Wang: School of Civil Engineering, Central South University, No.22, Shaoshan South Road,Central South University Railway Campus, Changsha, Hunan Province, People\'s Republic of China
 

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