Comparison of analytical and numerical solutions for stresses and displacements around unlined tunnels with arbitrary cross section inside anisotropic rock masses

The implementation of closed-form solutions for stress and displacement fields around tunnels with arbitrary geometry, often based on the complex variable theory and the method of conformal mapping, can be quite challenging from a mathematical point of view. In this paper a solution strategy for the implementation of a chosen closed-form solution from literature is presented, including the possibility to account for rock mass anisotropy and arbitrary tunnel geometries. The evaluation of the involved elastic potential functions is described, respectively derivatives thereof, in terms of solving non-linear constrained optimization problems. To validate our approach, the analytical results for stresses and displacements around a tunnel with semicircular geometry are compared to numerical results from finite element computations. The outcome of the study should be regarded as a basis for the development of refined analytical solutions within anisotropic rock masses considering more realistic boundary conditions and effects such as material non-linearity.