Damage evolution of tunnel portal during the longitudinal propagation of Rayleigh waves

Rayleigh waves significantly compromise the safety of tunnel portals. This paper establishes a three-dimensional numerical model, with a plastic-damage model for the concrete lining structure, to analyze the damage evolution of the tunnel portal during the longitudinal propagation of Rayleigh waves. To generate the wave field, a Rayleigh wave input method based on viscous-spring artificial boundary is developed. The submodeling technique is employed to overcome difficulties introduced by contradictions between element size, model scale and affordable computational cost. The simulation results, including the deformation of pavement at the entrance and the crack pattern of the tunnel lining, correspond well with the field observation of the Longxi Tunnel during the Wenchuan Earthquake. This paper proposes that the opening width of predominant circumferential cracks and a dimensionless damage index based on the internal damage variable can be used to quantitatively estimate the damage extent of the lining structure. The result of damage assessment shows that all damage is limited within a certain scope of the tunnel portal and that the extent of each crack decreases with its increasing distance from the entrance. The extent of damage may also be induced through earthquake loading with a relatively lower amplitude. Therefore, the cyclic and accumulative effect of successive earthquake loading over time, rather than simply, the effect of loading with a maximum amplitude, can determine the final damage state of lining structure. Although incapable of preventing the appearance of hairline cracks, the strengthening effect of reinforcement remarkably reduces the maximum width of crack openings and the overall damage extent of the lining structure. Moreover, the presence of reinforcing steels prevents micro-cracks from expanding to wider crack, which is essential to keep the tunnel lining waterproof and mechanically stabilized. The simulation methodology introduced in this paper could also potentially reliably predict the damage process of the tunnel lining and the extent of damage under the effect of complicated earthquake loading, aside from the Rayleigh wave.