## 1 Introduction  
To cope with the threat of increasingly powerful earth-penetrating weapons, in modern wars ammunition depots, command posts and other fortifications are mostly located inside mountains. Mountains contain soil, crushed stones, large rocks and other media, resulting in complex penetration conditions. Red sandstone, limestone and granite are common rocks in mountains and can be used as natural defense barriers. Therefore, it is of certain practical significance to study the damage characteristics of projectiles to different rocks and provide some reference for the research of earth-penetrating projectiles [1; 2; 3; 4]. Researchers have conducted extensive penetration tests on concrete and granite. [PERSON] et al. [5] carried out penetration tests on concrete with 51 MPa strength in the speed range of 500-1500 m/s and proposed a theoretical model for determining the upper limit of rigid penetration velocity. [PERSON] et al. [6] studied the relationship between the shape coefficient of the abraded projectile head and the target velocity after the test and proposed a modified model for calculating the penetration depth. [PERSON] et al. [7] studied the penetration regularity of projectiles into granite in a large velocity range. [PERSON] et al. [8] obtained the destruction effects of crater diameter, crater depth and crack distribution on the surface of the target at three impact speeds. [PERSON] et al. [9] carried out tests on the penetration of high-strength steel projectiles with oval-head long rods into granite at impact speeds of 1200-2400 m/s with a light-gas gun and proposed a penetration calculation model considering the mass loss of projectiles. [PERSON] et al. [10] obtained the relationship between the penetration depth and penetration speed of granite and established an empirical formula for predicting the penetration depth of high strength rock. Besides, the synthesis and characterization of some new brittle materials were also very important topics for several applications [11; 12; 13; 14; 15; 16]. However, limestone and red sandstone, as common mountain materials, lack relevant penetration experimental research. In recent years, research on the static and dynamic mechanical properties of granite, limestone and red sandstone has been very rich, and the mechanical properties of limestone and red sandstone have been well revealed [17; 18]. [PERSON] et al. [19] found that the fracture/damage mode of granite is mainly brittle and that the damage starts at the weak rock-crystal interface. [PERSON] et al. [20] analyzed the propagation process of stress waves in sandstone under high dynamic loading. [PERSON] et al. [21] found that the peak strength, maximum strain and elastic modulus of prefractured red sandstone increased with increasing crack inclination. [PERSON] [22] carried out an experimental study on the mechanical properties of frozen-thawed red sandstone. During the freeze-thaw process, there are three deterioration modes: cracking, particle shedding and sheet shedding. According to [PERSON]'s viewpoint on energy fracture, the influence of the target surface fracture on the energy loss of the projectile can be obtained [23; 24]. The mechanical characteristics of uniaxial reloading of limestone after damage can be divided into three stages: the stable stage, stable growth stage and secondary stable stage [25]. Limestone undergoes a linear elastic stage, plastic hardening stage and failure stage during compression [26; 27]. The damage mode of granite is mainly brittle, whereas limestone and red sandstone have certain elastic-plastic properties. The mechanical properties of concrete and rock have been well studied by scholars, but research on the penetration and failure characteristics of rock is very limited. In limited related studies, the ballistic properties of limestone were revealed to some extent. [PERSON] et al. [28] penetrated a large number of limestone targets with rigid projectiles of similar shape and different sizes.