Viscoelastic solution for reinforcing tunnels with rock bolts under the coupling effect of strata rheology and stress release

During tunnel construction in weak strata, the coupled effects of ground rheological behavior and stress release significantly influence both construction progress and safety. As a critical support measure in tunneling engineering, the time-dependent mechanical interaction between rock bolts and the surrounding rock under such complex conditions remains insufficiently understood. To elucidate the time-dependent interaction mechanism between rock bolts and surrounding rock under these challenging engineering conditions, this study develops an analytical solution for bolted tunnels that explicitly couples tunnel excavation-induced stress release and ground rheology. The rheological behavior of the ground is characterized using classical Maxwell and Kelvin-Voigt creep models, while the stress release effect is represented through the virtual support pressure method. A closed-form analytical solution is ultimately derived via integral transforms. The solution accounts for two types of rock bolts: end-anchored rock bolts and fully grouted rock bolts, which are distinguished by modifying the contact conditions at the boltrock interface. Numerical simulations verify the validity and engineering applicability of the proposed analytical method. Furthermore, parametric studies are conducted to examine the influence of bolt parameters and stress release parameters on surrounding rock deformation. The proposed analytical approach provides researchers and engineers with an improved theoretical understanding of the interaction between rock bolts and tunnel surrounding rock in weak strata.