# Permanent Deformation Mechanism of Steel Bridge Deck
## 5 Conclusions  
This study established a 3D discrete-continuous coupling model of SACSS and conducted virtual rutting tests to analyze the meso-mechanism of the permanent deformation of SBDP under the temperature-stress coupling effect. The primary conclusions are as follows:  
(1) The SBDP was simulated using the DEM, while the steel plate was constructed in FLAC3D and coupled to the DEM domain through a defined contact model. The finalized SACSS model was subjected to virtual rutting tests under three SAIB conditions. The simulation results showed that, under 0% and 17% SAIB debonding conditions, the virtual test curves closely matched the laboratory test results. Under the 100% SAIB debonding condition, although the rutting depth at 30 \({}^{\circ}\)C was slightly lower in the simulation compared with the experimental value, this discrepancy was attributed to differences in interface friction settings. At 45 \({}^{\circ}\)C, the simulated and experimental curves demonstrated excellent agreement in both trend and magnitude. Overall, SAIB failure was found to aggravate rutting development, and the simulation results exhibited good agreement with the experimental data. This consistency fully validates the rationality of the proposed 3D SACSS model and its parameter configuration, providing a reliable basis for further elucidation of the rutting evolution mechanism in SBDP. (2) A comparative analysis of rutting depth evolution between models with and without surface cracks at 30 \({}^{\circ}\)C and 45 \({}^{\circ}\)C revealed that the presence of surface cracks significantly accelerated rutting development during the initial loading stage. At 30 \({}^{\circ}\)C, the rutting depth in the cracked model was approximately 35.77% higher than that of the  
Figure 23: Method for extracting the rotational information of aggregates within the specimen. Figure 24: Variation curves of the average rotation angle of coarse aggregates at different temperatures. in intact model within 60 min, whereas at 45 \({}^{\circ}\)C, this difference reduced to 9.4%. These results indicate that the influence of surface cracks on rutting behavior is more pronounced at lower temperatures, while at elevated temperatures, the overall flowability of the asphalt mixture becomes the dominant factor. In addition, the evolution of interparticle contact failures (including tensile and shear failures) in the asphalt mixture at 30 \({}^{\circ}\)C was examined. The development of cracking followed a two-stage pattern: an initial slow-growth phase (0-20 min) and a subsequent rapid-growth phase (20-60 min). During the initial phase, tensile failures at the mesoscale were predominant, while the structural integrity of the material remained largely intact. In the rapid phase, the number of contact failures increased sharply, leading to a notable decline in structural stability, accompanied by periodic 'acceleration-deceleration' fluctuations. Throughout the entire loading process, tensile contact failures consistently outnumbered shear failures, with the disparity becoming more evident in the later stage. This suggests that loading duration exerts a significantly greater influence on tensile failure mechanisms within the asphalt mixture than on shear failure mechanisms. (3) The elastic modulus of the steel plate was found to have a significant impact on the vertical displacement of the asphalt mixture. At 45 \({}^{\circ}\)C, a steel plate with an elastic modulus of 206 MPa effectively suppressed vertical deformation, thereby enhancing the high-temperature stability of the SBDP structure. The probability distribution of contact forces within the asphalt mixture exhibited a negative exponential trend. Strong force chains accounted for 25.4% within the asphalt mortar, 26.3% at the mortar-aggregate interfaces, and 29.2% between aggregates. Weak force chains dominated the internal force network, comprising approximately 70-75% of all contacts.