## 1 Introduction
The CDP model also conducted modeling of an RC beam reinforced with other materials such as Fiber Reinforced Polymer (FRP) or ultra-high performance concrete (UHPC). [PERSON] et al. [9] studied reinforcing RC beams with web openings by using CFRP with a maximum deviation in the ultimate load of about 17%. [PERSON] et al. [12] used the CDP model for both RC and UHPFRC material when modeling the pre-damaged RC beams reinforced by UHPCR under the four-point bending test. The simulated and experimental results showed good agreement in the load-displacement curve; the deviation did not exceed 6% but the damage patterns did not fit between those results. Furthermore, [PERSON] et al. [13] simulated the post-tensioned reinforced concrete beams by using the CDP model with a maximum of 9% error in ultimate load between the simulation and experimental results. All studies mentioned above show that the CDP model is a good model to simulate the working behavior of reinforced concrete beams under different loads or in interaction with other structures. However, those studies only researched the behavior of the load-displacement curve between simulated and experimental results and did not mention the crack propagation with detailed characteristics of the crack in width, length, and space. In recent times, some studies have paid attention to using the CDP model to calculate the crack width. [PERSON] et al. [14] used the CDP model to model RC beams' working behavior under four-point bending. The numerical results were then utilized to estimate the crack width by using strain on either side of the element multiplied by the length of the element. The numerical results showed good agreement with the experimental results, with a maximum error of 15% in the crack width of an RC beam. However, there was no comparison in damage patterns in terms of each crack's width, length, and space. [PERSON] al. [15] presented a practical FE method to capture RC beams' cracking and crushing behavior. The method for capturing the crack width was introduced using a smeared crack combined with a crack band method. The results showed good agreement in the load-displacement curve and crack width between FEA and the experiment. However, the method to calculate the crack strain, length, and space of each crack was not introduced. From the lack of studies using the CDP model to estimate crack patterns, this study aims to develop an FE model using the CDP model to model the load-displacement curve and present a method to calculate the width, length, and spacing of crack patterns. The assumption of concrete compression and tension behavior depends on the FE model's mesh size as a starting point as the mesh size significantly influences the crack width calculation in the FE model. After validating the simulation results with the experimental results, the FE model was examined under a parametric study to investigate the influence of different diameters of rebars and the space between rebars on the working behavior of the RC beam. The proposed FE models, utilizing the CDP model, effectively capture load-displacement curves, crack propagation, and patterns. The study emphasizes the significant influence of a reinforcement diameter on crack behavior. The findings hold practical applications for predicting and optimizing the performance of reinforced concrete beams. This study is structured as follows: Section 2 presents an overview of the experiment. Then, Section 3 introduces the FE analysis, including the element types and model for modeling the behavior of concrete and reinforcement, the method to calculate the crack width, and the choice of ABAQUS solver. Section 4 presents the results and discussion related to the accuracy of the model and a parametric study. Finally, Section 5 summarizes the study's key findings and discusses their implications.