Internal force of a tunnel lining induced by seismic Rayleigh wave

In preliminary seismic analysis and design of a tunnel lining, compared to the frequently-assumed incident S-wave, analytical solutions to internal forces (axial force or thrust, bending moment and shear force) induced by incident R- (Rayleigh) wave are relatively few. Furthermore, in existing solutions the ground-structure interactions, temporal and spatial seismic response variations are not considered simultaneously. In this paper new closed-form solutions to internal forces induced by R-wave were derived for a tunnel lining. Comparison between the proposed solutions and the ones given in literature were made through a typical problem. It shows that: if R-wave propagates along the axis of a tunnel, the longitudinal axial force, bending moment and shear force on a cross section can reach their respective maxima. The maximum resultant normal stress given by literature may be over-predicted; if R-wave propagates perpendicularly to the tunnel's axis, the circumferential thrust, bending moment and shear force on a longitudinal section can also reach their respective maxima with the maximum thrust being much higher than that due to S-wave; the P-wave component of R-wave is predominant.