## 1 Introduction  
Every spring, as temperatures rise, the ice in rivers begins to melt. Under the action of water flow, the ablated river ice cracks and rushes along the river channel, which produces a huge impact on the hydraulic structures, such as bridge piers, that impede the flow of river ice, seriously threatening the safety and stability of the structures [1]. Therefore, an in-depth study of the impact effect of ablating river ice on bridge piers is crucial for ensuring the safe and reliable operation of bridges in regions characterized by low temperatures. For the problem of structure-ice interaction, relevant research has been carried out by scholars [2, 3, 4]. [PERSON] [5] developed an innovative model that enhances the Matlock model, specifically focusing on ice-induced vibrations. The model revealed that the average ice force generated on the structure as well as the rupture frequency of ice mainly depends on the ice's own parameters. Based on the actual form and structural data of a prototype bridge pier, and based on the contact-collision theory and nonlinear finite element analysis theory, [PERSON] [6] thoroughly investigated the effects of ice strength, elastic modulus, and ice thickness on the maximum ice force of streaming ice with the help of LS-DYNA. The simulation results compellingly demonstrate that the impact force shows an increasing trend as the strength, elastic modulus, and thickness increase. [PERSON] [7] conducted a study on the collision process between river ice and a bridge pier using LS-DYNA. The results of the simulation indicate that the maximum value of the ice force over time initially increases as the speed of the river ice rises. However, after reaching a certain point, this value begins to decrease with further increases in river ice speed. [PERSON] [8] performed numerical simulations of ice-structure interactions using the discrete element method (DEM) and verified its unique advantages in characterizing the non-homogeneity of ice materials and dynamic damage processes. In summary, the current studies on the interaction between structures and ice [9; 10] mainly focus on the mechanical characterization of frozen ice [11; 12; 13; 14], while insufficient attention has been paid to the impact effect of porous ice during the ablation period. During spring ablation, changes in the internal porosity of the ice significantly affect its mechanical properties--the dense ice structure formed in winter gradually evolves into a porous medium containing gas bubbles and microcracks [15]. Existing impact studies mostly treat ice as a homogeneous material [16; 17], neglecting the effect of porosity, a key parameter, on impact loading. This simplification may lead to the deviation of ice load prediction at bridge abutments, which in turn affects the reliability of the ice-resistant design of bridges in cold regions. This paper adopts the discrete element method to carry out the simulation of the pore ice impact process, taking the piers of the Heihe-Blagoveshcensk Amur River Bridge as the research object, systematically simulating the impact process under different ice speeds, ice thickness, and porosity conditions, and focusing on revealing the quantitative relationship between the porosity and the peak value of the impact force. The research results will be the first time an ice load dynamic model has been established considering the porosity parameter, which will directly serve bridge engineering practices in cold regions: on the one hand, it can provide refined load inputs for the anti-icing design of bridge piers, avoiding the risk of misestimation of load caused by neglecting the porosity effect in the traditional method; on the other hand, it can provide theoretical support for the safety assessment of existing bridges and effectively improve the safety of bridges operating in high latitude areas during the spring flood season, by revealing the dynamic evolution law of ice load during the melting period.