Abstract: According to the basic mechanics and kinematics laws of rockfall impacting backfilling shed tunnel, the theoretical calculation formula of rockfall impact load is derived from three aspects using Laplace transform: rockfall impacting semi-infinite backfill, rockfall impacting finite thick backfill, and considering the interaction between backfill and substructure. The theoretical formula is verified by numerical simulation and relevant test data, and is compared with the other calculation formulae. The research shows that the theoretical value obtained from the proposed formula and the results of numerical simulation and laboratory tests all have a relatively stable law. The theoretical values are 6%−41% larger than the numerical values, and the difference between the theoretical value and the 95th percentile value of Pichler test is within 6%. Although the theoretical value in this paper is larger than that of all the other formulae, it is more consistent with numerical data and test data, thus it can better represent the real rockfall impact load. The formula can reflect the influences of thickness and properties of backfill, i.e. the smaller the thickness of backfill, the greater the impact load, and the thickness amplification factor can be determined according to the h/r table. The dynamic interaction between the backfill and the structure leads to the increase of the impact load on structure, which can be defined as dynamic amplification factor; the larger the thickness of backfill, the smaller the dynamic amplification factor. The proposed theoretical formula can consider the influence of many factors such as rockfall size, rockfall shape, rockfall energy, and thickness and properties of backfill. Therefore, the theoretical value can be used to design structure of shed tunnel directly.

Key words: rockfall impact load, Laplace transform, shed tunnel, semi-infinite backfill, thickness amplification factor, dynamic amplification factor