## 2 Effect of Blast Loading on Protective Structures  
The protective structures must withstand dynamic loads created by explosions from high energy bombs and missiles, as well as loads from blast waves and debris collisions. These dynamic loads vary significantly with the characteristics of the weapon used to perform the hit. Generally, it is reasonable to set the protective performance required for protective facilities considering the mission, enemy, terrain and weather, troops and support available, time available, and civil considerations. Rather than direct hits, the structure should have a degree of protection against indirect weapon effects such as artillery projectiles [13; 14]. In a blast wave, as a significant amount of energy is suddenly released from an explosion, the pressure at the point of explosion rapidly increases and simultaneously spreads in all directions. When the shock front of the blast wave reaches a certain point at time \(t_{a}\), as shown in Figure 1, the pressure at that point instantaneously rises from the ambient pressure to the maximum incident pressure. The pressure then decreases and returns to the ambient pressure at \(t_{a}+t_{0}\) (positive phase), continues to decrease below the ambient pressure for the duration \(t_{0}\)-, and then returns to the ambient pressure at \(t_{a}+t_{0}+t_{0}\)(negative phase), after which it dissipates. The maximum pressure in the negative phase is referred to as the maximum suction pressure and is less than the positive pressure. In the pressure-time curve, the area of the positive and negative phases corresponds to the impulse [15; 16]. In terms of blast wave loading resulting from an explosion at a distance from a reinforced concrete structure, as shown in Figure 2, two cases can be considered: an explosion that occurs in air, or on a surface. When an explosion occurs in air, before the blast wave reaches the protective structure, a Mach front is formed by the interaction with reflected waves from the surface. The height of the Mach front increases with an increasing distance from the point of explosion, which is the same as the path of the triple point at which the incident pressure, reflected wave, and Mach front overlap. If the height of the protective structure is lower than the path of the triple point, then uniform blast wave loading is applied. Conversely, considering a surface explosion, the incident waves from the point of explosion merge with the reflected waves and propagate while forming a hemispherical single wave. In protective structure design, the blast wave front is assumed to have uniform pressure. Surface explosions are known to have a larger blast wave effect than explosions in the air [17; 18]. The protection levels used by the ROK Armed Forces comprises of a total of four stages; the displacement ductility and rotation angle thresholds proposed in the US Unified Facility Criteria (UFC) 3-340-02 are used for the protection levels [15]. The protection level, which is the protection goal of the protective structures including artillery positions, must comprehensively consider the degree of  
Figure 1: Idealized pressure–time curve of blast wave. Figure 2: Propagation of blast wave. protection and enemy threats in terms of operations and information, as well as the facility's purpose of use. Once the protection level is determined, the structure must be operated within a certain range according to the protection level from blast loadings. Table 1 presents the allowable limit of the rotation angle according to each protection level applied to brittle materials such as concrete. The rotation angle refers to the maximum rotation angle at the point of the member when the blast loading is applied as shown in Figure 3 [19]. Thus, it is the ratio of elastic deformation to maximum deformation.