A modified energy method to assess the residual velocity of non-deforming projectiles that perforate concrete barriers

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 γ<>d<> 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).