## 2 Literature Review  
[PERSON] et al. [6] summarized the history and key points of impact formulae and described some representative scabbing and perforation limit formulae in detail. The Army Corps of Engineers (ACE) proposed an impact formula based on extensive impact tests [9], conducted using 37, 75, 76.2, and 155 mm steel cylindrical missiles. After obtaining additional experimental data for 0.5 caliber bullets, the scabbing and perforation limit thickness formulae were modified (Equations (4) and (5)). Additional tests were conducted with a panel thickness of 3-18 times the projectile diameter and a concrete strength of 10-50 MPa. The difference between Equations (2), (3) and Equations (4), (5) is within 10%. The data for larger missiles were analyzed using the original formula. Therefore, Equations (2) and (3) are more appropriate for designing the impact resistance of nuclear power plants [11]. \[\frac{x_{pe}}{d_{p}}=\frac{3.5\times 10^{-4}}{\sqrt{f_{c}^{\prime}}}\Bigg{(} \frac{M  
modified as shown in Equations (6) and (7). The scabbing and perforation limit formulae, which are related to penetration depth, were proposed as shown in Equations (8) to (11).  
\[G=3.8\times 10^{-5}\frac{NM_{p}}{d_{p}\sqrt{f_{c}^{2}}}\bigg{(}\frac{V_{imp}}{d _{p}}\bigg{)}^{1.8} \tag{6}\]  
\[G=\bigg{(}\frac{x_{pe}}{2d_{p}}\bigg{)}^{2}\text{ for }\frac{x_{pe}}{d_{p}} \leq 2\text{ or }G=\frac{x_{pe}}{d_{p}}-1\text{ for }\frac{x_{pe}}{d_{p}}>2 \tag{7}\]  
\[\frac{h_{pf}}{d_{p}}=3.19\bigg{(}\frac{x_{pe}}{d_{p}}\bigg{)}-0.718\bigg{(} \frac{x_{pe}}{d_{p}}\bigg{)}^{2}\text{ for }\frac{x}{d}\leq 1.35 \tag{8}\]  
\[\frac{h_{pf}}{d_{p}}=1.32+1.24\bigg{(}\frac{x_{pe}}{d_{p}}\bigg{)}\text{ for }1.35<\frac{x_{pe}}{d_{p}}<13.5 \tag{9}\]  
\[\frac{h_{sc}}{d_{p}}=7.91\bigg{(}\frac{x_{pe}}{d_{p}}\bigg{)}-5.06\bigg{(} \frac{x_{pe}}{d_{p}}\bigg{)}^{2}\text{ for }\frac{x_{pe}}{d_{p}}\leq 0.65 \tag{10}\]  
\[\frac{h_{sc}}{d_{p}}=2.12+1.36\bigg{(}\frac{x_{pe}}{d_{p}}\bigg{)}\text{ for }0.65<\frac{x_{pe}}{d_{p}}\leq 11.75 \tag{11}\]  
where \(x_{pe}\) is the penetration depth (m); \(N_{p}\) is the nose shape factor (0.72, 0.84, 1.0 and 1.14 for flat, hemispherical, blunt and very sharp noses, respectively); \(M_{p}\) is the mass of the projectile (kg); \(d_{p}\) is the diameter of the projectile (m); \(V_{imp}\) is the impact velocity of the projectile (m/s); \(h_{pf}\) is the perforation limit thickness (m); \(h_{sc}\) is the scabbing limit thickness (m); and \(f^{\prime}{}_{c}\) is the compressive strength of concrete (Pa). After World War II, the safety of nuclear power plants became a major issue, and the impact resistance of concrete members was extensively studied. [PERSON] [17] proposed an impact formula with a dynamic increase factor (\(S_{Hughes}\)), considering the strain rate effect of concrete materials (Equations (12) to (19)). [PERSON] suggested that, unlike the other impact formulae, the tensile strength of concrete governs the impact mechanism, and developed a dimensionless impact factor considering this fact. The penetration depth formula was derived from the force-penetration depth model, and the perforation limit thickness and scabbing limit were derived from the upper bounds of the data.