Rockfall seriously threatens the construction and operation safety of karst tunnel. Obtaining the damage characteristics of tunnels under rockfall impacts is of great significance to optimize the design of protective structures, but is still unclear. In this study, a bond-based peridynamic (BBPD) method taking the strain rate influence of failure criterion into account is proposed. The accuracy and effectiveness of the proposed BBPD method was verified by comparing it with two experimental tests. Further numerical analyses using the proposed BBPD method were conducted to identify the influence of factors, including the impact velocity and impact position, on the damage characteristics of protection measures of a karst tunnel under rockfall impact. Protection measures include the composite lining, the composite lining with reinforced arch, and the composite lining with reinforced arch and buffer layer. The results show that the structural damage index follows a three-stage growth rule, including rapid growth period, slow growth period, and gradual stability period. The impact velocity and position have a significant effect on the structural damage index. The higher the impact velocity and the closer the impact position to the structural vault area, the greater the structural damage index. Under the three protection conditions, the tunnel damage index basically meets the requirements from large to small: the composite lining > the composite lining with reinforced arch > the composite lining with reinforced arch and buffer layer. The advantage for damage index reduction is not obvious for polyurethane thicknesses over 2.5 m. Finally, a composite lining with reinforced arch and buffer layer is proposed, which can resist the impact of the rockfall with a mass of 7.5 t falling freely from 105 m.
Cai et al. (2026) studied this question.