Theoretical insights into tunnel portal dynamics: effects of SV waves on seismic partitioning and structural strain

Abstract

The tunnel portal, influenced by the slope geometry and the fractured surrounding rock, constitutes a vulnerable point in terms of seismic resistance. To investigate its dynamic response under SV waves, we derive the displacement wave field for a single-sided slope subjected to SV wave incidence, based on the principles of wave dynamics and Ray theory. An elastic foundation beam model for the tunnel portal is developed, accounting for the interaction between the tunnel and the surrounding rock. Analytical expressions for the hoop and longitudinal strains are derived, and the effects of the slope angle, seismic wavelength, frequency, and elastic foundation modulus are examined. By analyzing the distribution of strain extrema under vertically incident SV waves, we identify the seismic weak points of the tunnel portal. Key findings include the following: under SV wave incidence, the hoop strain response at the crown and inverted arch is significantly higher than at the spandrel, foot, and waist, with the crown and inverted arch identified as the seismic weak points. In contrast to SH waves, SV waves cause a shift in the strain peak due to wave transformation, leading to variations in the damage locations along the tunnel's longitudinal axis. The strain distribution at the tunnel portal exhibits a bimodal characteristic, and the seismic reinforcement zoning for the portal section under vertically incident SH waves remains valid.