Analytical solution for the longitudinal seismic response of a shield tunnel with isolation layers under incident shear waves

The analysis of tunnel isolation has primarily focused on cross-sectional analysis, with little attention devoted to longitudinal analysis. The objective of this study was to develop a simplified analysis method for longitudinal isolation that can be efficiently applied in practical engineering. Therefore, a mechanical model of an isolated tunnel was established based on the Kelvin model, and an analytical solution for an isolated tunnel subjected to shear waves was derived. The numerical verification demonstrated the applicability and accuracy of our analytical solution, and an analysis was conducted to assess the effects of seismic motion amplitude and frequency, isolation layer, and soil on the isolation performance. The results indicate that the proposed mechanical model has good applicability and accuracy for analyzing the seismic and isolation performances of tunnels. The isolation effect is found to be insensitive to seismic motion amplitude, whereas the internal force response and joint opening of a tunnel increase at low frequencies and decrease at high frequencies. Additionally, the isolation effect is more prominent at low frequencies. Furthermore, the isolation effect increases with an augmented thickness of the isolation layer and a decreased elastic modulus of the isolation layer. As the foundation coefficient increases, the isolation effect of the isolation layer becomes more pronounced.