# Permanent Deformation Mechanism of Steel Bridge Deck
## 1 Introduction
### Review of Relevant Research Literature
#### 1.2.3. Putting Behavior of SBDP Investigated Through the Discrete Element Method  
The DEM, based on the assumption of a discontinuous medium, applies [PERSON]'s second law to track both the translational and rotational motions of individual particles while simultaneously capturing contact forces and interparticle interactions. This approach enables the characterization of force chain transmission within granular assemblies, thereby providing a meso-mechanical basis for interpreting the macroscopic mechanical behavior of materials [25; 26; 27; 28]. Extensive studies have employed DEM to investigate the permanent deformation behavior of asphalt mixtures. For example, virtual rutting simulations were performed by [PERSON] et al. [29], in which internal displacement fields and contact force distributions were systematically examined. Their findings demonstrated that DEM-based simulations are particularly effective in capturing deformations resulting from the combined effects of material densification and lateral flow. Furthermore, DEM has been adopted by [PERSON] et al. [30] and [PERSON] et al. [31] to evaluate the influence of porosity levels, spatial distribution, and void geometry on the rutting resistance of asphalt concrete. [PERSON] et al. [32] utilized DEM to simulate uniaxial static creep tests, in which aggregate angularity, orientation, surface texture, and distribution were precisely controlled. Their results highlighted the critical role of aggregate morphology in enhancing the deformation resistance of asphalt mixtures. However, most existing DEM studies have been confined to conventional asphalt pavements, and investigations targeting the rutting evolution in SBDP remain limited. In practice, the SACSS, composed of a discontinuous asphalt mixture layer and a continuous isotropic steel plate, exhibits highly heterogeneous behavior that cannot be adequately represented using a single numerical technique. To overcome this limitation, a coupled discrete element-finite element (DEM-FEM) modeling framework can be employed. In this hybrid approach, the FEM is used to simulate the continuum response of the steel plate,while the DEM captures particle-scale interactions within the asphalt mixture. For instance, [PERSON] et al. [33] utilized DEM to represent the granular behavior of debris flows and FEM to simulate the structural response of reinforced concrete bridge piers, thereby investigating impact-induced stress and failure mechanisms. [PERSON] et al. [34] applied a DEM-FEM coupling method to examine the interaction between tires and granular foundations. Similarly, [PERSON] et al. [35] modeled non-uniform load transfer from tires to the pavement structure using FEM and described the contact interactions and meso-mechanical behavior among asphalt mixture particles using DEM. Through this approach, particle displacement, velocity, and force chain evolution under rolling tire loads were effectively evaluated. Nonetheless, prior studies have primarily focused on the influence of material properties within the asphalt mixture, whereas external structural factors--such as the stiffness of the steel deck and the presence of surface cracks--have received insufficient attention. To address this research gap, particularly regarding meso-scale analysis of rutting evolution mechanisms in SBDP, the remainder of this study is structured as follows. Section 2 presents laboratory rutting tests conducted at 30 \({}^{\circ}\)C and 45 \({}^{\circ}\)C, which were used to calibrate the contact model parameters between asphalt mortar and coarse aggregates in the numerical model. In addition, rutting tests were performed on SACSS under three different SAIB conditions at the same temperatures to provide a foundation for validating the numerical simulations. Section 3 details the development of a three-dimensional (3D) SACSS model using the DEM-FEM coupled method. Contact parameters between particles and the steel plate were determined through a combination of laboratory and virtual direct shear tests.