Analysis of tunnel lining internal forces under the influence of S and P-waves: An analytical solution and quasi-static numerical method

This paper employs analytical and pseudo-static approaches to analyze the tunnel response under the compression (P) and shear (S) waves. In the first step, Einstein and Schwartz’s method is revised for calculating Tunnel Lining Internal Forces (TLIFs) under P-wave. Next, a comprehensive comparison is performed between TLIFs under S and P-waves in two extreme contact interfaces of no-slip (NS) and full-slip (FS) conditions. Lastly, the effect of the intermediate layer was investigated by quasi-static finite element numerical modeling. The results showed that the maximum value of the axial force under the P-wave exceeds that of the S-wave in both the NS and FS conditions. Also, the amount of bending moment and shear force in both the NS and FS conditions under the S-wave is almost twice the P-wave. In general, the weak interlayer causes a decrease in the maximum axial force and the axial force values in the range of placement of the weak interlayer with the tunnel. Besides, it increases the maximum bending moment and shear force compared to the homogeneous medium. It was also observed that the weak interlayer with low thickness causes unpredictable behavior under S and P-waves. Overall, the presence of a layer with different stiffness led to a significant effect on the TLIFs under S and P-waves and increased the complexity of the dynamic analysis of tunnel lining. Therefore, it should be simulated separately under NS and FS conditions. • An analytical method is presented for calculating tunnel lining internal forces (TLIFs) under P-wave. • A comprehensive comparison is performed between TLIFs under S and P-waves. • The effect of the intermediate layer was investigated by quasi-static FEM. • The axial force difference caused by the S-wave under NS and FS conditions is much higher than that caused by the P-wave by assuming the a h = a v = a s as well as V S = V P . • The presence of a layer with different stiffness led to a significant effect on the TLIFs under S and P-waves.