## 3 Results and Discussion
### Ice Modeling in the Bohai Sea  
The simulated flexural strength (\(\sigma_{f}\)) and compressive strength (\(\sigma_{c}\)) were compared to the actual strength of the Bohai Sea ice by the three-point bending test and the uniaxial compressive test [35]. The measured mean and the maximum flexural strengths were 1.08 MPa and 2.42 MPa, respectively. The measured mean and maximum compressive strengths were 2.56 MPa and 5.98 MPa, respectively. The Young's modulus in the Bohai Sea was assumed to be 1.0 GPa. The two particle sizes, 5 mm and 10 mm, were considered. For the relative Young's modulus ratio (\(E_{s}/E_{b}\)) of 1.5 and the assumed Young's modulus of actual ice of 1.0 GPa, the bond Young's modulus was \(1/1.5=0.66\) GPa. The assumed bond Young's modulus could not affect the flexural strength. The bond strength for the mean flexural strength was \(1.08/1.55=0.7\) MPa and the bond strength for the maximum flexural strength was \(2.42/1.55=1.56\) MPa. In the uniaxial compressive tests, the bond Young's modulus was 0.85 GPa from Equation (22). The bond strength for the mean compressive strength was \(2.56/4.04=0.63\) MPa and the bond strength for the maximum compressive strength was \(5.98/4.04=1.48\) MPa. Table 3 shows the ice properties used in  
Figure 10: Effect of relative particle size on (**a**) flexural strength; (**b**) compressive strength.  
Figure 9: Effect of relative particle size on the simulated Young’s modulus: (**a**) three-point bending test; (**b**) uniaxial compressive test.  
and the mechanical properties of the simulated ice was investigated. The effects of the bond Young's modulus (\(E_{b}\)), the bond strength (\(\sigma_{b}\)), and the relative particle size ratio (\(h/d\)) on the mechanical properties of the simulated ice were studied. The simulated Young's modulus (\(E_{s}\)) increased in proportion to the bond Young's modulus (\(E_{b}\)), while the flexural strength was not affected by the bond Young's modulus. This was because that the normal stiffness of the bond was proportional to the bond Young's modulus. The simulated flexural strength (\(\sigma_{f}\)) and the compressive strength (\(\sigma_{c}\)) increased linearly with respect to the bond strength (\(\sigma_{b}\)). The normalized strength was constant for given simulation conditions. This was the key relationship for predicting the simulated flexural strength. The influence of the relative particle size ratio (\(h/d\)) was investigated to obtain the converged value. The simulated Young's modulus for the three-point bending tests tended to converge to the constant ratio (\(E_{s}/E_{b}\)) of 1.5 at a sufficiently high \(h/d\). The simulated Young's modulus for the uniaxial compressive tests increased as the bond Young's modulus increased. As per the results, the normalized flexural strength and compressive strength were 1.55 and 4.04, respectively. From the ice modelling in the Bohai Sea, the obtained parameters of the contact and bond models could be used to assess and predict the mechanical properties of the sea ice. In future research, ice breaking by a ship will be carried out.  
Conceptualization, S.S. and S.P.; simulation, S.S. and W.J.; formal analysis, S.S. and W.J.; writing--original draft preparation, S.S. and S.P.; writing--review and editing, S.S. and S.P.; visualization, S.S. and W.J.; supervision, S.P. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the National Research Foundation of Korea (NRF-2021R11A3044639) and the grant from Endowment Project of \"Development of Evaluation Technology for Ship's Performance in Extreme Environment\" funded by Korea Research Institute of Ships and Ocean engineering (PES3910).  
Not applicable.  
The authors declare no conflict of interest.