Analyzing time-dependent rock-concrete interaction: A solution for non-circular tunnels

Many researchers have explored the complex time-dependent behavior of rock-concrete interaction in lined tunnels. However, for non-circular tunnel configurations, no analytical solution has been proposed yet. The presence of varying curvature along tunnel boundaries in non-circular tunnels leads to diverse effects on stress and strain components in both the lining and surrounding mass over time. As time progresses, the accuracy of stress and strain assessment significantly decreases, especially at boundaries with high curvature, even when fine grid mesh sizes are used in numerical models. To address these challenges, a novel time-dependent analytical solution in plane strain is introduced for evaluating induced stress and strain fields around a lined non-circular tunnel subjected to non-hydrostatic in situ stress. The solution, developed using the complex variable method by Muskhelishvili and conformal mapping functions, results in a system of first-order linear differential equations. This approach was validated using COMSOL finite element software, demonstrating a substantial reduction in stress evaluation errors and time consumed compared to the software. Finally, a sensitivity analysis on Burgers model parameters performed, which revealed different effects on stress induced around tunnels in short and long-term. Notably, this solution is applicable to tunnels of any shape and compatible with various linear viscoelastic constitutive models for rock masses.