###### Abstract
[PERSON] revised the NDRC hypothesis and suggested a model where I\({}_{\text{h}}\) is a non-dimensional impact factor [1,3] and N\({}_{\text{h}}\) is a nose shape factor [1,3]. [PERSON] proposed that the tensile and compressive strength of the concrete (ft/fc) ratio is constant [1,3,7]. [PERSON] also showed the importance of the strain rate  
Figure 1: Penetration of concrete caused by ogive nose rigid projectile. and the dynamic increase factor (DIF), represented by 'S' [1,3,7]. [PERSON] and [PERSON] introduced a model for penetration depth by revising the NDRC and Kar models [1,3]. The CRIEPI Model, mentioned below in Table 1, assumes the thickness of the concrete barrier Hr = 20 cm (0.2 m) [1,3]. In 1985, the United Kingdom Nuclear Electronics (UKNE) began intrinsic research on the behavior of concrete structures resisting hard projectile penetration by creating the R3 Concrete Impact Working Party [1,3]. The UMIST model for penetration depth (X) improved the form with the reflection of the nose shape [1,3]. [PERSON] and [PERSON] [1,3,8] further advanced [PERSON] et al. 's [1,3,9] model and proposed a semi-empirical or semi-analytical model for penetration depth (X). The model is in a non-dimensional homogenous form, and these models are valid for an extensive scope of penetration depth, where \(I\) is the impact function, and \(N\) is the geometry function. \(S=72f_{c}^{-0.5}\) is an empirical function of \(f_{c}\) (MPa). The [PERSON] and [PERSON] model is applicable for \(X\)/\(d\geq 5.0\)[2,4]. [PERSON] and [PERSON] [1,3,8,10] recommended \(X\)/\(d<5.0\) for small-to-medium penetration depths, where h is the length of the nose of the projectile. In the case of narrow penetrations when \(X\)/\(d<0.5\), the penetration depth is given by [1,3,8,10]. [PERSON] and [PERSON] [1,3,8,10] recommended a simplified model of \(X\)/\(d=0.5\)(\(I\)) to predict the penetration depth for deep penetration. The details of the discussed models are given in Appendix A Table 1.  
Since 2005, researchers turned their attention to developing models in terms of the required critical impact energy [1,2]. Furthermore, research also turned to the advancement of concrete, creating high-performance concrete (HPC), ultra-high-performance concrete (UHPC), and high-performance fiber-reinforced concrete (HPFRC). However, until today, normal concrete and normal reinforced concrete are still the most commonly used materials for the construction of structures. The revised interest of researchers on concrete penetration depth emerged in 2015, when [PERSON] and [PERSON] implemented an evolution of the statistical model developing technique, the neural network, to develop a model for the prediction of the rigid projectile penetration depth in concrete. Furthermore, in 2021, research was conducted using gradient tree boosting machine learning to predict RC panel failure modes under impact loading. These two kinds of research emerged with the need for the redevelopment of the model, using advanced machine learning tools to develop a prediction model based on an extensive collection of experimental data. Therefore, this research is focused on developing a model based on an extensive collection of 257 experimental test data, using machine learning symbolic regression. Furthermore, the proposed prediction model is validated with the prediction of the NDRC and Li and Chen models, because, in the literature, the most prominent model used to predict penetration depth is the Li and Chen dimensionless model [1].