###### Abstract
Excessively wide fractures will accelerate the corrosion of the steel bar and then reduce the bearing capacity of the component, which often causes serious safety hazards. To address the aforementioned issues, [PERSON] [11] proposed an improved model incorporating internal pressure, crack width, and failure modes, aiming to provide a more precise estimation of the bond strength between deformed bars embedded in concrete under various crack cases. In view of the behavior of fractures in reinforced concrete segments used in shield tunnels, the Code for Design of Segments for Shield Tunnels [12] compiled in Japan has systematically proposed empirical formulas for fracture width calculation based on cake-slip theory, but the values of some variables are not clearly expressed. Due to the complexity of factors affecting the fracture width of segments, it is difficult to establish a universally applicable fracture width calculation formula, which needs to be improved using finite element analysis. The finite element analysis of reinforced concrete structures is performed by combining the finite element analysis method and the mechanical properties of the reinforced concrete. Since the research on reinforced concrete is based on many test results and the complexity and high cost of tests restrict the development of fracture research on reinforced concrete structures, the use of finite element and other numerical methods to analyze the mechanical properties of reinforced concrete structures has become a research focus. The effect of crack width on the corrosion rate of reinforcement was numerically analyzed by [PERSON] [13]. The segment simulations were directed at investigating concentrated loading, representative of the jack thrust force applied while installing the segments during the tunnel boring machine (TBM) installation phase [14]. A numerical investigation is conducted here to study the mechanical behavior of continuous-joint shield tunnels, strengthened by the SPCC strengthening technique [15]. The Mohr-Coulomb failure criterion was used in early finite element analysis, but later studies showed that the polygonal cone could not accurately reflect the failure surface of concrete. In terms of the constitutive relationship of concrete, scholars from various countries have proposed various models, such as those based on linear elastic theory [16], nonlinear elastic theory [17], elastic-plastic theory [18], internal time theory [19], viscoelastic theory [20] and viscoplastic theory [21]. However, due to the complex characteristics of concrete materials, there is no recognized theory that can be widely applied to concrete structures under various conditions. The combination of reinforcement and concrete is an important problem in the finite element analysis of steel and concrete. In the early days of related research, steel bars and concrete were divided into small units for calculation, but this approach is not suitable for large structures and three-dimensional analysis. Later, [PERSON] [22] in the United States proposed an integral steel bar model, which transforms steel bars into equivalent concrete and calculates their properties according to a unified stiffness matrix. This model is more suitable for the analysis of large concrete structures. The simulation of bond slip between steel bars and reinforced concrete is a difficult problem in the finite element analysis of reinforced concrete structures. After long-term research and development, scholars have proposed a variety of bond units, such as double-spring bond units, quadrilateral slip units, and contact units. The bond slip model has also developed from an early linear model to a nonlinear model and continues to improve. The simulation of fracture width is always a difficult problem in the finite element analysis of reinforced concrete structures. Because the occurrence of fractures makes concrete discontinuous and the basic principle of finite elements comes from continuum mechanics, it is difficult to simulate the cracking behavior of concrete accurately.