## 1 Introduction  
The drilling and blasting method is efficient, economical and reliable in many engineering construction projects, such as in tunnel excavation [1], mining [2] and damming [3]. The study of rock dynamics under an impact load is an important problem [4]. The dynamic mechanical properties of rock materials are quite different from the static properties, so the response of rock materials under impact loading is a hot issue in rock dynamics [5]. Stimulated by engineering practice, the testers have become increasingly modern and intelligent, which provides scientific and effective research methods for the study of the mechanical properties of the rock dynamics [6, 7]. The split Hopkinson pressure bar (SHPB), invented in 1949, has been extensively used to determine a material's dynamic performance [7, 8, 9, 10]. The application of the SHPB on rocks was first reported by [PERSON] [11], in which a rock stress-strain curve was derived. Subsequently, scholars have conducted many valuable studies using the SHPB, such as compressive strength and tensile strength studies [12; 13]. It is worth noting that only some of the energy from explosives is used to break rocks during blasting engineering construction, and the rest acts on the surrounding rock. The surrounding rock may experience deformation, instability, collapse and other accidents. The main reason is that although the stress wave generated by a single blast may not damage the surrounding rock in the middle and far areas, the primary joints of the rock mass will expand and gradually penetrate under the effect of multiple low amplitude stress waves and finally failure will occur [14]. This is a process of cumulative damage of the rock mass, which is characterized by the deterioration of the mechanical properties and reductions in bearing capacity and stability. Therefore, it is of great practical significance to study the damage characteristics of rocks under impact loading, especially the cumulative damage evolution law under multiple stress waves [15]. Although scholars have conducted many studies on the dynamic mechanical properties of rocks, there are only few studies on the damage behavior of rocks under repeated impact loading. [PERSON] et al. [16] found that the damage of sandstone occurred near the dynamic peak stress, and subsequently the internal cracks of the rock entered the development stage. [PERSON] et al. [17] and [PERSON] et al. [18] performed dynamic damage studies on granite and leptynite using a modified SHPB. They found that the P-wave velocity and axial strain gradually deteriorated with repeated impacts. [PERSON] et al. [19] conducted repeated impact tests on granite and found that the cumulative damage depended on the peak stress of the dynamic load with a fixed duration. [PERSON] et al. [20; 21] carried out repeated impact tests by using an SHPB system with axial and confining pressures and established a damage evolution model of sandstone. [PERSON] et al. [22; 23] studied the dynamic characteristics of green sandstone subjected to repeated impacts and reported that the initiation of new cracks and the elongation of existing cracks were the main mechanisms for the degradation of the sandstone under repeated impacts. However, the dynamic damage evolution law, damage threshold and failure pattern of rocks have rarely been studied. Therefore, it is urgent to improve the understanding of the dynamic damage behaviors of rocks subjected to repeated impacts. Meanwhile, the study of the dynamic constitutive model of rock materials is helpful to further analyze the dynamic mechanical and damage behaviors under different stress conditions. Currently, the common constitutive models for rock dynamics include the Holmquist-Johnson-Cook (HJC) model [24], the Riedel-Hiermaier-Thoma (RHT) model [25] and the Johnson-Holmquist (JH) model series [26]. All three of these models consider the high strain rate, large strain and nonlinear high pressure and softening due to material damage under impact loading.