Analytical solutions for rheological processes around bores and tunnels

Author:

Fülöp TamásORCID,Szücs Mátyás

Abstract

AbstractFive analytical solutions are presented for processes of linear viscoelastic, homogeneous, and isotropic solids around freshly opened bores / tunnels in various initial stress fields. The solutions are obtained via a simple and direct realization of Volterra’s principle. This realization is based on an appropriate decomposition of the known solution of the corresponding elastic problem and leads to ordinary differential equations in the time variable in the viscoelastic case. Fairly rich temporal behaviors are revealed.

Funder

NRDI

NKFIH

Publisher

Springer Science and Business Media LLC

Subject

General Engineering,General Mathematics

Reference34 articles.

1. Mindlin RD (1939) Stress distribution around a tunnel. Proc Am Soc Civ Eng 65(4):619–642

2. Papkovich PF (1939) Elasticity theory. Oborongiz Press, Moscow

3. Savin GN (1970) Stress distribution around holes. National Aeronautics and Space Administration, Washington, DC

4. Davis RO, Selvadurai APS (1996) Elasticity and geomechanics. Cambridge University Press, Cambridge

5. Hefny AM, Lo KY (1999) Analytical solutions for stresses and displacements around tunnels driven in cross-anisotropic rocks. Int J Numer Anal Methods Geomech 23:161–177

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