## 3 RVE of the Calculated Uniaxial Compressive Strength of Yellow River Ice
### Verification of Uniaxial Compressive Strength  
The compression failure mode is one of the typical failure modes of Yellow River ice, and uniaxial compressive strength is also an important strength parameter among the mechanical properties of Yellow River ice. Several scholars have conducted a large number of uniaxial compression tests on lake ice and river ice, finding that the compressive strength of ice not only changes with external conditions such as temperature and loading rate, but also is affected by the microscopic components inside the ice. Differences in ice crystal  
Figure 8: Schematic diagram of mesh size changes of RVE of Yellow River ice. size and content can cause changes in the mechanical properties of river ice. Therefore, there are certain differences in the compressive strength of river ice under different growth conditions. Based on the determined RVE of the calculated strength of the Yellow River ice, a simulation analysis was carried out on the failure process of the river ice under uniaxial compression. To analyze the changes in the physical properties of the Yellow River ice in uniaxial compression, an RVE model for the calculated strength of the Yellow River ice was established. Boundary constraints and loads were applied to the model, and the shape and size of the Yellow River ice crystals were assumed to remain unchanged. The crack propagation process of the Yellow River ice RVE in uniaxial compression was simulated, and the stress-strain changes of the Yellow River ice in displacement loading were analyzed. The failure results of river ice under uniaxial compression are shown in Figure 9. The crack propagation process of the Yellow River ice RVE in uniaxial compression are shown in Figure 10.  
Figure 10: The crack propagation process of the Yellow River ice RVE in uniaxial compression. (**a**) Starting to crack; (**b**) crack development; (**c**) gradual destruction; and (**d**) final destruction. Figure 9: Failure results of the Yellow River ice RVE under uniaxial compression. It can be seen from Figure 9 that the failure of the RVE of the calculated strength of the Yellow River ice under uniaxial compression can be divided into two types: crystal failure and grain boundary failure. The failure direction was parallel to the loading direction, and the main form of failure was fan-shaped failure. By calculating and analyzing the uniaxial compressive strength of RVE models of Yellow River ice in five different random distributions, it can be concluded that the average uniaxial compressive strength of Yellow River ice was 2.35 MPa, which is similar to the average uniaxial compressive strength of 2.44 MPa simulated in reference [31]. The typical stress-strain curve failure process is shown in Figure 11. The effectiveness of the RVE model of the calculated strength of the Yellow River ice was objectively verified. Uniaxial Compressive Strength of the RVE of the Calculated Strength of the Yellow River Ice in Different Particle Sizes  
Due to the differences in the hydraulic conditions of different river channels, the average particle size of the Yellow River ice was variable. Based on previous experimental observations and the results of previous research on the crystal size of Yellow River ice [32], it can be concluded that the average particle size of Yellow River ice varied within 5-20 mm. The RVE size of the calculated strength of the river ice was determined to be 250 mm. Based on the determined RVE of the calculated strength of the Yellow River ice, a fixed size of 250 mm was used to simulate the RVE of the Yellow River ice with different average particle sizes, and the influence of the average particle size on the uniaxial compressive strength of the RVE of the Yellow River ice was analyzed. Figure 12 shows the variation in the uniaxial compressive strength of the RVE of Yellow River ice with the same sample size but with different average particle sizes.