## 3 Results and Discussion  
### Influence of Ice Velocity on River Ice Impact Forces at Bridge Abutments  
The river ice porosity is set to 0, the ice thickness is set to 0.5 m, and the ice velocities of 0.25 m/s, 0.5 m/s, 0.75 m/s, 1 m/s, 1.25 m/s, 1.5 m/s, 1.75 m/s, 2 m/s, 2.25 m/s, 2.5 m/s, 2.75 m/s, and 3 m/s are used for the discrete elemental simulation of the impact between the river ice and the bridge abutment. The time course of the ice force is illustrated in Figure 4, and the ice row damage at the simulation time of 1 s is shown in Figure 5.  
Figure 4: Time course of ice force at different ice speeds: (**a**) 0.5 m/s; (**b**) 1 m/s; (**c**) 2 m/s; (**d**) 2.5 m/s.  
River ice is the most common source of impact on bridge abutments; river ice in the river under the action of high-speed water flow impacts bridge abutments, provoking a bridge-structure response; the transient effect of the impact is intense, and has the most significant effect on the bridge abutment.  
Ice rows have an impact on bridge abutments and other structures; when the speed is low, the driving force of the ice row on the impact to the bridge abutment is insufficient, and the ice row in the full width of the structure may be completely wedged into the scope of a full stop, shear or immediately rebound back. With the increase in ice speed, the ice row is partially embedded in the abutment but still cannot go further, then with the increase in kinetic energy of the ice row, the reaction force of the abutment to the ice row will gradually increase. At this time, the ice force manifests itself as a single amplitude of force, this stage of the ice row does not reach its destructive strength. When the ice speed continues to increase, reaching a certain critical speed point, the river ice's driving force is sufficient, the ice row incurs partial or overall split damage. The ice row as a whole contains the destructive strength of the ice, and the river ice in contact with the front end region of the ice body incurs large-scale destruction, from the bearer to crushing and cracking after only a moment. At this time, the river ice impact force reaches its peak, and the subsequent impact force is manifested as multiple discrete peaks with lower ice force. As the ice velocity continues to increase, the river ice is not strong enough to support a larger impact force, and the magnitude of the maximum force is no longer determined solely by the ice velocity, but depends more on the ice strength. Eventually, the peak impact force stabilizes with the  
Figure 5: Ice raft destruction patterns at different ice velocities: (**a**) 0.5 m/s; (**b**) 1 m/s; (**c**) 2 m/s; (**d**) 2.5 m/s.  
strength of the ice and does not continue to increase with velocity. Moreover, at high ice velocities, when the river ice reaches its maximum destructive strength, the size of the ice raft does not affect the impact force.  
Figure 6 shows the maximum ice force applied to the bridge abutment at different ice velocities. As shown in the figure, the extreme value of the ice load increases significantly with the increase in velocity, and the ice load reaches the maximum value when the river ice velocity is 1 m/s. As the velocity continues to increase, the ice load's extreme value eventually remains stable.