## 1 Introduction  
Under complex geological conditions such as mud-rock flow and landslides, long-distance oil and gas pipelines are inevitably impacted by rockfalls, seriously resulting in pipeline corrosion, cracking, deformation, and other damages [1; 2; 3; 4]. The serious structural damages of buried pipelines caused by rockfalls attracted much attention from engineers and researchers in recent years. In addition, with the recent rapid development of damage detection and structural health monitoring technology [5; 6; 7], the monitoring technology of buried pipelines was also developed and it plays an important role in the safe operation of pipeline network systems. In order to further analyze the damage mechanism of buried pipelines, it is necessary to conduct experimental and numerical studies on the strain behavior of buried pipelines subjected to impact loads for the safe operation of pipelines, as well as for loss prevention and environmental protection. In recent years, many researches on buried pipelines under impact loads mainly focused on finite element analysis (FEA) and the theoretical derivation. Among them, three main calculation modes in FEA were applied to investigate the buried pipelines, including the beam mode [8; 9], the shell mode [10; 11], and the beam-shell mode [12]. Compared to the beam mode, the shell mode is widely used in FEA due to the more accurate results in calculating the distribution of the large deformation of pipelines. [PERSON] et al. [13] applied the shell mode to simulate the large deformation section of a pipeline under fault movement and concluded that the shell mode could clearly analyze the local buckling and the large deformation of pipeline, but this model had no consideration of the effect of soil property when calculating the sliding friction of pipeline-soil. For further research, [PERSON] et al. [14] and [PERSON] et al. [15] established the soil-pipeline model in FEA, and completely studied the effects of different parameters (the initial defects, the impact energy, the pipeline wall thickness, the buried depth of pipeline, and the soil properties) on the strain behavior of buried pipelines under impact loads. Furthermore, thorough research on the cross-section deformation and the soil pressure on the pipeline during the impact process was carried out by [PERSON] et al. [16] through the three-dimensional distinct element code software. The results indicated that the main factors affecting the cross-section deformation of the pipeline were the impact velocity and the mass of rockfall. Alongside finite element research, theoretical researches on buried pipelines under impact loads were more comprehensive. Among them, the theoretical researches mainly focused on the theoretical calculation of the impact force on soil and the earth pressure on pipelines. The impact of rockfall can be simplified to a low-speed collision problem in engineering practice. There are three main theoretical methods for calculating the impact force on soil: the Hertz collision theory [17; 18; 19], the energy theory, and the inelastic collision method [20]. In the former two methods, rockfall and soil are regarded as elastic bodies, unlike the impact force on soil in actual working conditions. The latter method is more reasonable for the consideration of the energy loss, while the calculation process is more complicated. Subsequently, [PERSON] et al. [21] developed a new mathematical model of the impact force from rockfalls to obtain the wallop amplification coefficient, but some differences still existed between the actual situation and the theoretical conditions. Moreover, [PERSON] et al. [22] also studied a new method for calculating the impact force of the rockfall with the consideration of the rockfall weight and the rebound effect, and they validated the feasibility of the proposed calculation method of impact force using examples.