# Development of Energy-Based Impact Formula--Part I: Penetration Depth
## 5 Conclusions  
In this paper, an energy-based impact formula for predicting the penetration depth of a (steel fiber-reinforced) concrete panel under impact loading is derived using various factors and the theoretical background framework. In addition, the new impact formula is verified with impact test results obtained for various test variables. The derivation process and results of comparisons of the newly proposed penetration depth formula are summarized as follows:  
* There are six types of energies involved in the penetration failure of a concrete panel colliding with a high-velocity projectile. These are the kinetic energy of a projectile (\(E_{K}\)), deformed energy of a projectile (\(E_{DP}\)), elastic penetrated energy of the target concrete panel (\(E_{EP}\)), overall deformed  
Figure 11: Ratio of tested to predicted penetration depth by detailed formula and simplified formula.  
energy (\(E_{SD}\)), spalling-resistant energy of a concrete panel (\(E_{SP}\)), and tunneling-resistant energy (\(E_{T}\)), which occurs when the kinetic energy is concentrated by a long projectile and/or high velocity. Using these energies and energy conservation law, a new energy-based penetration depth formula is derived.
* The spalled cone is related to the shear stress controlled by compression, while the scabbed cone is related to that controlled by tension. These shear stresses must account for the strain rate effect, where the _fib_ Model Code 2010 (_fib_, 2010) is used in this study. The strain rate is defined as the force applied on the projectile's nose, as suggested by [PERSON] et al. (1994), and is newly derived in this paper by using the theoretical background.
* The penetration depth formula is derived using the drag force, volume, and area of the spalled cone, which leads to an energy density. The spalling energy can be concentrated by a high velocity and/or a long projectile, and these effects can be applied to the penetration depth formula. The concentrated energy can produce the tunneling depth, which is also derived from the energy density.
* The accuracy of the new penetration depth formula is examined and compared to the existing impact formulae, such as the modified NDRC, ACE, Haldar, UKAEA, UMIST, and Li-Chen formulae. The mean value of the tested penetration depth compared to the predicted penetration depth of the new impact formula is 1, meaning that it is the best of these impact formulae. The standard deviation of the new impact formula for predicting the penetration depth is 0.23, which is also the best.  
Conceptualization, S.K.; Formal analysis, S.K.; Funding acquisition, T.H.-K.K.; Investigation, S.K.; Methodology, S.K.; Project administration, T.H.-K.K.; Supervision, T.H.-K.K.; Validation, S.K.; Writing--original draft, S.K.; Writing--review & editing, T.H.-K.K. Both authors have read and agreed to the published version of the manuscript.  
This work was supported by the Nuclear Safety Research Program through the Korea Foundation Of Nuclear Safety (KoFONS) using the financial resource granted by the Nuclear Safety and Security Commission (NSSC) of the Republic of Korea. (No2003007). This manuscript is based on the PhD dissertation by [PERSON] [60]. The authors declare no conflict of interest.