A closed-form elastic solution for stresses and displacements around tunnels

A closed-form plane strain solution is presented for stresses and displacements around tunnels based on the complex potential functions and conformal mapping representation. The tunnel is assumed to be driven in a homogeneous, isotropic, linear elastic and pre-stressed geomaterial. Further, the tunn...

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Bibliographic Details
Published in:International journal of rock mechanics and mining sciences (Oxford, England : 1997) England : 1997), 2002-10, Vol.39 (7), p.905-916
Main Authors: Exadaktylos, G.E., Stavropoulou, M.C.
Format: Article
Language:English
Subjects:
Applied sciences
Buildings. Public works
Computation methods. Tables. Charts
Earth sciences
Earth, ocean, space
Engineering and environment geology. Geothermics
Engineering geology
Exact sciences and technology
Geotechnics
Soil mechanics. Rocks mechanics
Structural analysis. Stresses
Tunnels, galleries
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Summary:A closed-form plane strain solution is presented for stresses and displacements around tunnels based on the complex potential functions and conformal mapping representation. The tunnel is assumed to be driven in a homogeneous, isotropic, linear elastic and pre-stressed geomaterial. Further, the tunnel is considered to be deep enough such that the stress distribution before the excavation is homogeneous. Needless to say that tunnels of semi-circular or “D” cross-section, double-arch cross-section, or tunnels with arched roof and parabolic floor, have a great number of applications in soil/rock underground engineering practice. For the specific type of semi-circular tunnel the distribution of stresses and displacements around the tunnel periphery predicted by the analytical model are compared with those of the FLAC 2D numerical model, as well as, with Kirsch's “circular” solution. Finally, a methodology is proposed for the estimation of conformal mapping coefficients for a given cross-sectional shape of the tunnel.
ISSN:1365-1609
1873-4545
DOI:10.1016/S1365-1609(02)00079-5