Development of Energy-Based Impact Formula—Part I: Penetration Depth

Abstract

Predicting the damage to a concrete panel under impact loading is difficult due to the complexity of the impact mechanism of concrete. Based on the experimental results obtained by various researchers, the energies involved in the impact mechanism are classified into seven categories: Kinetic energy, deformed energy of a projectile, elastic penetration resistance energy of the panel, overall deformed energy of the panel, spalling-resistant energy, tunneling-resistant energy, and scabbing-resistant energy. Using these impact mechanisms and the energy conservation law, a new energy-based penetration depth formula is proposed to predict the penetration depth. This is validated using 402 impact test results, which include those with high-strength concrete, ultra-high-performance concrete (UHPC), or steel fiber-reinforced concrete, those under very high-velocity impact, and those with a very low ratio of target panel thickness to projectile diameter. It is found that the new impact formula predicts the penetration depth quite well.

Numerical Assessment and Repair Method of Runway Pavement Damage Due to CBU Penetration and Blast Loading

“…There are several formulas which can be applied to assess penetration depth into a concrete pavement. The US Army recommends assessing the depth of damage on a concrete panel in accordance with UFC 3-340-01 [5,6]. In order to assess the penetration depth into concrete, in order to design protection structures against impact loading, CONWEP, Army Corps, Haldar, Ammann and Whitney, UKAEA, BRL, Modified Petry, and Modified NDRC formulas can be used [7].…”

Development of Energy-Based Impact Formula-Part II: Scabbing Depth, Scabbing Limit, and Perforation Limit

“…In Part I of Kim and Kang's paper [22], the scabbing failure could occur in the case where the target concrete panel's thickness was insufficient to absorb the impact energy (Figure 1). The impact force from the collided point at the front face was transmitted to the opposite face, and reflected and transferred to the tensile force, which could peel the concrete panel.…”

“…Similar to the slab punching failure studied by Choi et al [24], the rear face failure is governed by the tension stress and shear stress. The dynamic shear stress (Equations ( 20)-( 24)) capacity controlled by the dynamic tension was derived by Kim and Kang [22]. Herein, if there was no measured concrete tensile strength (f t,st ), the fib Model Code 2010 [25] provided the equation for obtaining the tensile strength of concrete, based on compressive strength.…”

“…Figure 9 shows the panel thickness (h) divided by the predicted scabbing limit thickness (h sc ), based on the new proposed formula. The modified NDRC, Hughes, and UK Atomic Energy Authority (UKAEA) formulae predict the penetration depth well, as shown in the Paper I [22]. Only the experimental results obtained from the test program conducted by Kim [29] are used for the analysis of scabbing limit thickness, because all other experimental results in other studies presented unclear scabbing depth and failures.…”

“…Hwang et al [12] proposed energy-based penetration depth based on the theoretical background. Kim and Kang [22] defined the impact mechanism and energies involved and proposed the penetration depth formula using the energy conservation law. The impact mechanism involves seven types of energy: kinetic energy (K E ), deformed energy of the projectile (E DP ), elastically deformed energy of the concrete panel (E EP ), overall deformed energy of the concrete panel (E SD ), spalling-resistant energy (E SP ), tunneling-resistant energy (E T ), and scabbing-resistant energy (E SC ).…”