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Using Muskhelishvili and Kolosov complex potential functions, an elastic solution is presented in this study in order to investigate stress components around circular tunnels reinforced by concrete lining with constant thickness. It was assumed that rock mass and concrete behave as isotropic linearly elastic materials. The rock mass undergoes an in situ stress field. It was also supposed that rock and concrete interface is in no-slip condition so that they have common displacement. Due to complexity of the problem for concrete reinforced layer, conformal mapping functions were utilized in order to find a solution. Supposing plane strain condition, the problem was solved, and a closed-form solution was obtained. The solution was compared to Kirsch solution, in which the lining thickness was reduced to zero, and also ABAQUS finite element software results, which showed a good agreement, except for ABAQUS software predictions around crown of tunnel lining periphery where some discrepancies were found; also it was demonstrated that this solution predicts stress components at inner lining periphery much more accurately than ABAQUS software. Finally, a sensitivity analysis based on rigidity and thickness of liner was conducted and some propositions were made on design of concrete liner. The advantage of this solution lays in the fact that it has quicker and more accurate calculation process compared to numerical methods.

Keywords: Plane theory of elasticity, Circular tunnels, Complex potential functions

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