A Modified Energy Method to Assess the Residual Velocity of Non-Deforming Projectiles That Perforate Concrete Barriers

Abstract

In assessing vulnerability of a concrete barrier it is important to know the projectile's residual velocity, in case of perforation. The residual velocity is a measure of the resistance level provided by the barrier in case it is breached. It is also an important parameter in studying the response of barriers, whether experimentally or analytically. This paper proposes a formula to evaluate the residual velocity of a perforating non-deforming projectile. It is based on a semi-empirical approach that consists of theoretical assumptions regarding the damaged barrier under striking velocities that are higher than the perforation velocity and on empirically-calibrated parameters. The main hypothesis is that once a concrete barrier is perforated part of the projectile's striking energy is dissipated through fracture of the ejecting crater into concrete fragments, as well as additional cracking of the barrier. A parameter denoted γd is introduced as a function of the perforation-limit and striking velocities, and thus a common regression formula is deduced. A suitable energy balance and additional pertinent physical assumptions lead to formulation of an expression for the residual velocity, based on the knowledge of the perforation velocity. This approach yields a non-dimensional expression for the residual velocity, which agrees well with published experimental results (different than the ones used for calibration of the model's parameters).

A note on the deep penetration and perforation of hard projectiles into thick targets

“…By further considering the kinetic energy carried by the ejected fragments on the rear face of the concrete slabs, Wu et al [17] proposed the expression to predict the residual velocity of projectile after perforations. Recently, by introducing the energy dissipated through the fracture of ejecting fragment into pieces, Grisaro and Dancygier [20] proposed a modified energy balance model of the projectile perforating on the concrete slab. However, the perforation limit in the model of Grisaro and Dancygier [20] was obtained by curve-fitting the test data and only applied for residual velocity predictions.…”

“…Recently, by introducing the energy dissipated through the fracture of ejecting fragment into pieces, Grisaro and Dancygier [20] proposed a modified energy balance model of the projectile perforating on the concrete slab. However, the perforation limit in the model of Grisaro and Dancygier [20] was obtained by curve-fitting the test data and only applied for residual velocity predictions.…”

Hard projectile perforation on the monolithic and segmented RC panels with a rear steel liner

“…of the projectile perforating the monolithic and segmented RC slab with or without a thin steel liner. Compared with the existing prediction formulae for V r proposed by Cargile et al [8] and Grisaro and Dancygier [18], Eqs.…”

“…5 in Refs. [18], which lies in that the ballistic limit V BL used in the present calculations are obtained by NDRC [30] formula and by data fittings in Refs. [18], respectively.…”

“…Li et al [17] further proposed the critical impact kinetic energy of the projectile for perforating the target, which showed better agreement with the flat nosed projectile perforation test data by comparing with the energy forms of UMIST, NDRC and Chen and Li et al [13e16] formulae. Grisaro and Dancygier [18] newly proposed a modified energy method to assess the residual velocity of non-deforming projectiles perforating the RC barriers, in which the energies dissipated through fracture of the ejecting crater into fragments, as well as the additional cracking of the barrier were considered empirically.…”