The stress state around lined non-circular hydraulic tunnels below the water table using complex variable method

• An elastic solution is proposed to investigate stress components around non-circular hydraulic tunnels.
• The solution considers the effect of groundwater and internal water pressure.
• The solution is based on complex variable method.
• A good agreement was found between stress components predicted by the solution and ABAQUS finite element software.
• The solution was also reduced for practical uses in pressure tunnels, under high internal and external water pressure.

An elastic plane-strain solution for lined non-circular hydraulic tunnels, below the water table, is presented. Tunnels are assumed to be subjected to uniform ground load, and excavated in a semi-finite aquifer with fully saturated and drained geomaterial. Rock mass and concrete shows a homogenous, isotropic linear elastic behavior, and the non-seepage condition dominates the model. Muskhelishvili complex potential functions combined with conformal mapping method were used to investigate stress field around the tunnels. The solution was compared with ABAQUS finite element software through an example that showed a good agreement. Moreover, the proposed solution predicted the boundary values of the problem along the internal lining periphery much more accurately than did the ABAQUS solution. In the next part, an attempt was made to reduce the solution to be more practical and simply applicable for pressure tunnels when a large water pressure is exerted on the linings. The significance of the work is in the fact that it incorporates non-uniform distribution of water pressure for groundwater and water inside tunnels, and predicts stress components in a highly accurate and fast process. The method could also be used for the openings in half-plane medium under non-uniform ground load.