## 3 Verification of Numerical Simulation Method
### Vehicle Breaking Ice Experiment
#### 3.3.2 Experiment Analysis  
The length, width, and thickness of the ice in the experiment were 600 mm, 400 mm, and 200 mm, respectively. The ejection pressure was 3 MPa, 4 Mpa, and 5 Mpa for the vehicle to break ice vertically. The phenomenon in the experiment is illustrated in Figures 15-17. Evidently, some small pieces of broken ice were generated when the head of the vehicle hit the lower surface of the ice. The upper surface of ice at the contact area reached upwards and cracks appeared in the ice. As the vehicle continued to move, the cracks in the ice expanded and a large amount of broken ice was generated. The broken ice splashed upwards along with the vehicle, and eventually the ice was bent and broke off.  
Figure 16: Process of vehicle breaking ice with ejection pressure of 4 MPa: (**a**) ejected; (**b**) vehicle head touched ice; (**c**) vehicle body penetrated ice; (**d**) vehicle head passed through ice slightly; (**e**) vehicle head passed through ice completely.  
Figure 15: Process of vehicle breaking ice with ejection pressure of 3 MPa: (**a**) ejected; (**b**) vehicle head touched ice; (**c**) vehicle body penetrated ice; (**d**) vehicle head passed through ice slightly; (**e**) vehicle head passed through ice completely.  
As shown in Table 3, the initial velocity of the vehicle increased with the ejection pressure. The higher the initial velocity of the vehicle, the larger the residual velocity after breaking ice and the lower the velocity loss rate.  
Based on the experiment model, a numerical simulation model for the vehicle breaking ice at a high velocity was established to further examine the accuracy of the JH-2 sea ice constitutive model, the FEM-SPH adaptive algorithm, and the critical strain value used in this paper. The initial velocity was 13.08 m/s, which was consistent with the initial velocity of the vehicle when the ejection pressure was 3 MPa in the experiment. The experimental result was compared with the numerical simulation results, and the critical strain values (\(\varepsilon_{c}\)) used in the numerical simulation were 0.15, 0.25, 0.35, and 0.45.  
As revealed in Figure 18, the value of the critical strain has an impact on the results. When the critical strain value is 0.35, the numerical simulation result shows a high degree of similarity with the experimental result. As shown in Figure 19, the crack growth and fracture phenomena of ice obtained from numerical simulation are highly similar to the experimental results. This could prove that the sea ice constitutive model, FEM-SPH adaptive algorithm and the critical strain value adopted in this paper are reasonable and reliable.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Ejection Pressure (MPa)** & **Ice Thickness (mm)** & \begin{tabular}{c} **Velocity Before** \\ **Breaking Ice (m/s)** \\ \end{tabular} & \
\begin{tabular}{c} **Residual Velocity** \\ **After Breaking Ice (m/s)** \\ \end{tabular} &
\begin{tabular}{c} **Velocity** \\ **Loss Rate** \\ \end{tabular} \\ \hline
3 & 200 & 13.08 & 7.80 & 40.37\% \\
4 & 200 & 15.44 & 10.62 & 31.22\% \\
5 & 200 & 16.63 & 11.53 & 30.67\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Velocity of the vehicle breaking ice under different ejection pressures.  
Figure 17: Process of vehicle breaking ice with ejection pressure of 5 MPa: **(a)** ejected; **(b)** vehicle head touched ice; **(c)** vehicle body penetrated ice; **(d)** vehicle head passed through ice slightly; **(e)** vehicle head passed through ice completely.