A universal formula for calculating the penetration depth in concrete structures at projectile velocity below 1000 m/s

Abstract

In recent years, with the increasing use of reinforcement and widespread use of ultra-high performance concrete (UHPC) materials in concrete structures, it is difficult to accurately calculate the penetration depth of these concrete structures by existing formulas. To develop a universal formula applicable to all types of concrete structures, this paper investigates and evaluates existing formulas for calculating the penetration depth of concrete structures. Based on these formulas, we derive a new expression considering the volume reinforcement ratio and a preliminary form of the universal formula. Two penetration tests were conducted on a normal concrete structure and an UHPC structure, followed by the establishment and validation of two numerical models based on the test results. According to regression analysis and linear interpolation methods, we determine the reinforcement ratio impact factor (α) in the new expression, yielding the final form of the universal formula. Finally, validation with 26 sets of test data and comparison with existing formulas demonstrate that the proposed formula in this paper offers higher calculation accuracy and better universality. The calculation formula presented in this paper is applicable not only to normal concrete structures but also to UHPC structures. This formula holds significant reference value for the protective design of concrete structures, providing a basis for evaluating the anti-penetration performance of concrete structures.