## 1 Introduction
The use of two-dimensional plane stress finite elements [18; 19] can avoid some of the simplified assumptions inherent in one-dimensional beam elements, such as the effects of shear stress, but they are unsuitable for full-scale three-dimensional structural analysis as they do not capture out-of-plane responses. Three-dimensional analyses based on triaxial stress-strain relationships and embedded reinforcement offer the highest quality approximations, but they still face limitations due to high computational costs and a lack of robustness in some cases [20; 21]. These challenges have led various researchers to use different material models and other elements to conduct analyses of large-scale reinforced concrete structures with sufficient accuracy and numerical stability [15]. Several methods have been proposed to represent the interaction between the concrete and reinforcement. The first approach, which is the simplest, assumes reinforcement is distributed in appropriate directions within concrete elements using a smeared or distributed representation [19]. For reinforced concrete barriers, the authors of [11] used the smeared model but it has limitations in representing cracks in the concrete areas around the reinforcement and the local behavior of the reinforcement. The second approach models the reinforcement and concrete separately and shares the nodes between the reinforcement and the concrete [22]. In [23], regarding reinforced concrete barriers, a similar method was used for modeling. While this modeling approach does not present significant issues in small-scale modeled barriers and simple beam tests, achieving the appropriate element ratio in actual concrete structures can take considerable time, and in some cases, modeling may not be feasible at all. Due to these challenges, sometimes, the rebar arrangement is ignored, and only the concrete of the barrier is modeled as a rigid body [10]. Additionally, reinforced concrete barriers can be modeled by connecting solid elements and rebar as rigid elements [2; 9] or with interface elements to represent rebar-concrete friction [5]. However, this also requires significant time to model complex rebar arrangements. To address these issues, methods have been proposed that involve independently meshing rebar and concrete elements and applying additional constraints between them. However, these methods still require substantial time to connect the two elements. To resolve the issue of the time required for modeling with additional constraints between rebar and concrete, the researchers in [12; 13] used the Constrained_Lagrange_In_Solid model provided by LS-DYNA to represent the interaction between rebar and concrete, conducting crash analyses of reinforced concrete barriers. This method, primarily based on fluid-structure coupling analysis to represent interactions between different elements, improves the convenience of modeling reinforced concrete structures. However, it remains highly dependent on mesh quality and density [24]. When designing reinforced concrete barriers on bridges, they are often assumed to be rigid bodies, which distinguishes them from flexible barriers made of steel, aluminum, or composite materials [25; 26]. Additionally, the bridge deck is often not considered in some cases [26]. Therefore, this study models three cases for comparative analysis: treating the barrier as a rigid body, analyzing the reinforcement with the lower section fixed, and modeling the cantilever bridge deck portion beneath the barrier foundation. Key considerations in barrier design include the strength of the barrier, occupant risk, and vehicle trajectory. This study investigates the interaction between the reinforced concrete barrier and the bridge deck. It compares the results of the three models concerning these design considerations and proposes a rational modeling approach.