## 1 Introduction  
Reinforced concrete (RC) structures are popular in modern construction due to their durability, strength, and versatility. However, RC beams are susceptible to cracking due to diverse factors such as overload, substandard construction practices, and environmental effects like corrosion. These cracks can compromise the stability of the structure and may fail if not addressed. Therefore, the objective of this study is to study the mechanisms and characteristics of crack development in RC beams to ensure their safety and longevity. Numerical techniques such as finite element analysis have become popular tools for investigating crack development in RC beams. These techniques provide detailed insights into beam behavior under varying load conditions and can guide design decisions to reduce the risk of cracking. Numerous numerical methods have been developed to model crack propagation in concrete structures. One notable approach is the Extended Finite Element Method (XFEM), an extension of the Partition of Unity Finite Element Method (PUFEM). Another method involves using the Finite Element Method (FEM) in conjunction with the Concrete Damaged Plasticity (CDP) model. XFEM's applicability has been explored in previous studies [1; 2; 3] for analyzing cracks in concrete structures. For instance, [PERSON] et al. [1] utilized XFEM with one or two crack planes to simulate crack propagation and the load-displacement behavior of concrete beams. While the load-displacement curves exhibited good agreement with experimental data, the crack patterns did not align well with the observed results. When employing XFEM, it is necessary to define the initial crack geometry or location accurately. Therefore, replicating experimental crack patterns in the simulation model requires creating an initial pattern that closely matches the observed cracks. This step poses significant challenges when attempting to predict crack patterns in structures during the design phase without the availability of experimental data. The crack band method, introduced by [PERSON] et al. [4], is widely utilized in addressing nonlinear finite element analysis (FEA) challenges. It is often employed in the smeared crack approach, as discussed in studies [5; 6]. [PERSON] et al. [7] applied the smeared crack method to model crack patterns in RC beams, achieving a maximum deviation in crack width of approximately 48% compared to experimental results. However, it is important to note that the use of the crack band model may pose challenges, particularly when dealing with large finite elements and the presence of reinforcements [5]. These challenges can impact the effectiveness of the model, introducing potential issues during the solution process. Recently, the CDP model, which was developed by [PERSON] et al. [8], has been popular in modeling the working behavior of concrete structures due to its ability to capture the cracking and crushing of concrete accurately. Many studies have applied the CDP model to research the nonlinear behavior of concrete structures under different loading conditions. [PERSON] [9] used the CDP model to model the nonlinear behavior of an RC deep beam under a three-point bending test. The FE results showed a good agreement in the load-displacement curve and damage patterns, with a maximum of 6.92% in error at ultimate displacement. [PERSON] and [PERSON] [10] developed an FE model using the CDP model in combination with a surface-based cohesive model to simulate NSC-UHPFRC specimens under different loading conditions. The maximum deviation of the model was found to be 15.9%. The FEA results also matched well with the experimental (EXP) results in both load-displacement curve and damage patterns, with a maximum of 22% deviation in ultimate displacement. Also, [PERSON] et al. [11] utilized the CDP model to model the working behavior of the UHPFRC beam under a four-point bending test with a deviation of 10% between FEA and EXP.