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Analytical solutions for tunnels of elliptical cross-section in rheological rock accounting for sequential excavation

Lookup NU author(s): Professor Stefano Utili


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Time dependency in tunnel excavation is mainlydue to the rheological properties of rock and sequentialexcavation. In this paper, analytical solutions for deeplyburied tunnels with elliptical cross-section excavated inlinear viscoelastic media are derived accounting for theprocess of sequential excavation. For this purpose, anextension of the principle of correspondence to solid mediawith time varying boundaries is formulated for the first time.An initial anisotropic stress field is assumed. To simulaterealistically the process of tunnel excavation, solutions aredeveloped for a time-dependent excavation process with themajor and minor axes of the elliptical tunnel changing fromzero until a final value according to time-dependent functionsspecified by the designers. In the paper, analyticalexpressions in integral form are obtained assuming theincompressible generalized Kelvin viscoelastic model forthe rheology of the rock mass, with Maxwell and Kelvinmodels solved as particular cases. An extensive parametricanalysis is then performed to investigate the effects of variousexcavation methods and excavation rates. Also thedistribution of displacements and stresses in space at differenttimes is illustrated. Several dimensionless charts forease of use of practitioners are provided.

Publication metadata

Author(s): Wang HN, Utili S, Jiang MJ, He P

Publication type: Article

Publication status: Published

Journal: Rock Mechanics and Rock Engineering

Year: 2015

Volume: 48

Issue: 5

Pages: 1997–2029

Print publication date: 01/09/2015

Online publication date: 20/12/2014

Acceptance date: 09/11/2014

ISSN (print): 0723-2632

ISSN (electronic): 1434-453X

Publisher: Springer


DOI: 10.1007/s00603-014-0685-7


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