Complex Predictions for Stress and Displacement of Deep Buried Tunnels with Concrete Lining in Parallel Inclined Multi-Layered Surrounding Rocks

A plane strain analytical model was developed for the interaction between inclined multilayered rock strata and concrete tunnel lining in deep buried tunnels, with both structures treated as homogeneous isotropic elastic bodies and two contact modes, no-slip and full-slip, considered. A non-iterative complex variable function method was employed, by which analytical challenges in multiply connected domains were overcome and explicit stress and displacement solutions were obtained. Validation was performed through boundary-condition checks and comparative numerical simulations. The results show that under different tangential contact modes, layer inclinations, and lateral pressure coefficients, the stress error on the inner surface of the lining remains in the order of 10−2 Pa. The stress and displacement components on both sides of each interface satisfy the associated continuity conditions with excellent agreement. The proposed analytical method nearly perfectly satisfies all boundary and continuity conditions. Under non-hydrostatic loading conditions, the numerical and analytical results for different tangential contact modes also show excellent agreement. The von Mises stress errors are generally controlled within 0.03 MPa, and the maximum relative error—located near the inner surface of the lining—remains below 4%, while displacement errors stay below 0.2 mm. Interface stress jumps are accurately captured and oscillations in zones with high stiffness contrast are effectively avoided. The method is presented as a fast and reliable analytical tool for tunnel design under complex multilayered rock conditions.