The Riedel, Hiermaier, and Thoma (RHT) model, a concrete material model, is primarily utilized for impact and explosive analysis involving high strain rates. While the original RHT model yielded sufficiently comparable results for penetration depth, it exhibited limitations in accurately representing the dynamic response of concrete, particularly in underestimating tension damage (spalling). Previous studies aimed at enhancing the RHT model have focused on adjusting the input parameters to better approximate experimental data. In this study, we propose a novel model designed to address the shortcomings related to dynamic tensile failure behavior in the original RHT model. Our approach involves incorporating user-defined functions, allowing for improved representation of the concrete's dynamic response, especially in the context of tensile failure. The model's accuracy was validated through single-element simulations. The viability of the numerical simulation algorithm has also been verified for projectile penetration. After validation, the study examines how projectile penetration influences the damage. Numerical results illustrate that damage resulting from projectile penetration significantly influences the failure mode and stress wave propagation of the target. The results confirmed that the developed constitutive model can well describe the dynamic behavior of the RCC slab under projectile impact. The research findings offer crucial insights for designing protective structures against projectile penetration.