Mechanical response of surrounding rock supported by NPR long and short anchor cables under seismic action

Conventional anchor cable support systems exhibit limited adaptability in deep soft rock tunnels. To address this issue, an NPR long and short anchor cable coordinated support method is proposed. Based on the proposed support system, analytical solutions for surrounding rock stress and deformation are derived. Elastoplastic theory and a zonal method that accounts for strain softening behavior are adopted. An improved quasi-static method is established for surrounding rock stress analysis under seismic loading. The analytical solutions are validated through numerical simulations, and the influence of key parameters on support performance is evaluated. The results indicate that in the plastic flow zone, the peak tangential stress occurs at the elastoplastic interface, while the radial stress gradually increases with depth and ultimately approaches the in-situ stress level. This clarifies that the elastoplastic interface is a key support reinforcement region of the surrounding rock, providing a basis for support location selection. The analytical solution is in good agreement with the numerical results in terms of stress distribution and evolution trend. Compared with the unsupported condition, the NPR long and short anchor cable system reduces the maximum surrounding rock displacement by more than 20% and leads to a more uniform axial force distribution. Overall, the proposed method significantly improves support effectiveness and enhances surrounding rock stability under seismic loading.