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Analytical solutions of stresses and displacements for deeply buried twin tunnels in viscoelastic rock

Lookup NU author(s): Professor Stefano Utili



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


A set of analytical solutions is presented to calculate the stresses and displacements generated when two closelylocated circular tunnels are sequentially excavated in viscoelastic rock. The solutions are provided for circulartunnels excavated in time dependent rock for any type of linear viscoelastic model, e.g. Burgers and Poyting-Thomson model. In the presented solutions the sequential excavation of the tunnels is also accounted for. Theradii of the twin tunnels are time-dependent functions reflecting the excavation process adopted.The solutions are provided as analytical expressions in integral form. These were obtained by extending theprinciple of correspondence to solid media with time varying boundaries. A comparison of the stresses anddisplacements predicted by the analytical solutions and FEM analyses for an example case of twin tunnelsexcavated in a generalized Kelvin medium shows a good agreement between the two methods. Then, aparametric analysis was performed to investigate the influence of the tunnel spacing on displacements andstresses for various excavation processes. Several dimensionless charts summarizing the result of the parametricanalysis are provided for the benefit of practitioners.

Publication metadata

Author(s): Wang HN, Zheng GS, Utili S, Jiang MJ, Wu L

Publication type: Article

Publication status: Published

Journal: International Journal of Rock Mechanics and Mining Sciences

Year: 2017

Volume: 93

Pages: 13-29

Print publication date: 01/03/2017

Online publication date: 16/01/2017

Acceptance date: 03/01/2017

Date deposited: 22/02/2017

ISSN (print): 1365-1609

ISSN (electronic): 1873-4545

Publisher: Pergamon Press


DOI: 10.1016/j.ijrmms.2017.01.002


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