# In Situ Experimental Study of the Friction of Sea Ice and Steel on Sea Ice
## 5 Conclusions  
To obtain a better understanding of the ice friction during ice navigation, a series of field experiments on sea ice, stainless steel (SS), and coated steel (CS) sliding on natural sea ice cover was conducted. The effects of normal stress, contact material, ice columnar grain orientation, and sliding velocity on the kinetic friction coefficient (\(\mu_{\mathrm{k}}\)) were investigated under air temperatures higher than \(-5.0\)\({}^{\circ}\)C for the test period. The results showed that \(\mu_{\mathrm{k}}\) decreased with increasing normal stress. While \(\mu_{\mathrm{k}}\) showed no significant difference for sliding parallel or perpendicular to columnar grain orientation, indicating that \(\mu_{\mathrm{k}}\) is independent of grain orientation. Sliders of sea ice, SS, and CS sliding on the same ice track showed relatively large scatter in \(\mu_{\mathrm{k}}\), partly because of the different surface roughnesses of the materials. An increase in \(\mu_{\mathrm{k}}\) wfith increasing velocity was found in the velocity regime investigated for ice-ice contact and steel-ice contact because of the viscous resistance of water film. The velocity dependence of \(\mu_{\mathrm{k}}\) was quantified using the rate- and state-dependent model [35], and the results showed that \(\mu_{\mathrm{k}}\) logarithmically increased with increasing velocity in the range investigated. Stick-slip motion was observed in this experiment, not only on ice-ice contact, but also on steel-ice contact. A tendency that low machine stiffness enhances the stick-slip motion at high sliding velocity was found by comparing the velocity ranges of stick-slip in present study with previous reports. The frequency of load oscillations in stick-slip was also found to increase with increasing sliding velocity, but remained independent of normal stress. With the anticipated future boom in Arctic navigation in summer, the data collected in this study provide insights into the friction between sea ice and a vessel's hull, as well as other offshore structures. It must be recognized, however, that the experiments in this study were only an approximation to real-world ice navigation and that the full natural process would be more complex. Ocean waves, crushing and fracture of sea ice, and variations in temperature, salinity, and ice surface morphology may further affect friction. Restricted by the limited experimental conditions in field, some effects were not or not detailed investigated in current work such as sea ice salinity, surface morphology, and normal stress. These effects will be detected in a laboratory experiment in future. Figure 13: The approximate comparisons between experimental data and estimation of model [43] for (**a**) ice-ice friction and (**b**) steel-ice friction. The correlation coefficient between measured and modelled values was 0.84 for ice–ice friction. For steel–ice friction, the model underestimated and overestimated the experimental data at velocity greater and lower than 0.75 m\(\cdot\)s\({}^{-1}\) respectively, and the correlation coefficients were 0.12 and 0.55 respectively. **Author Contributions:** [PERSON] and [PERSON] conceived and designed the experiments; [PERSON] and [PERSON] performed the experiments; [PERSON] analyzed the data and wrote the paper; [PERSON], [PERSON], and [PERSON] contributed to discussions and to revising the manuscript. **Acknowledgments:** This work was supported by the National Key Research and Development Program of China (2016 YFC1402702), the Global Change Research Program of China (2015 CB953901), the National Natural Science Foundation of China (51639003, 51579028), and the High Technology of Ship Research Project of the Ministry of Industry and Information Technology (350631009). We thank [PERSON] and [PERSON] for their contributions to the field work. We thank [PERSON] for the help in completing the paper and [PERSON] for helpful discussions. We are grateful to anonymous reviewers of this manuscript for helpful comments.