Friction of sea ice on sea ice
Introduction
Ice friction plays an important role in a number of engineering applications. It affects the performance of icebreakers in ice-covered waters (Liukkonen, 1988, Valanto, 2001). Knowing the sea ice friction on different materials (including sea ice) is necessary to calculate the ice loads on sloping offshore structures (Croasdale and Cammaert, 1994, Palmer and Croasdale, 2013, Tikanmaki et al., 2011). According to Schulson and Duval (2009), friction is a fundamental process during the brittle compressive deformation of cold ice. Friction is the largest sink of energy during the rafting and ridging processes of sea ice. Therefore, the results of the numerical simulations describing these processes are significantly affected by the choice of the input for the friction coefficient (Hopkins et al., 1991, Hopkins and Tuhkuri, 1999, Marchenko and Makshtas, 2005).
Numerous studies have been performed to investigate the friction between ice and different materials (Calabrese et al., 1980, Forland and Tatinclaux, 1985, Frederking and Barker, 2002, Liukkonen, 1988, Oksanen and Keinonen, 1982, Ryvlin, 1973, Saeki et al., 1986, Tatinclaux and Murdey, 1985, Tusima and Tabata, 1979). Several friction models and theories (Akkok et al., 1987, Evans et al., 1976, Liukkonen, 1992, Oksanen and Keinonen, 1982) were developed and verified using the results obtained in small-scale laboratory tests. Until recently, fewer studies have focused on the sliding of ice on ice. To date, most ice–ice friction studies have employed small-scale laboratory tests (Fortt and Schulson, 2007, Fortt and Schulson, 2009, Fortt and Schulson, 2011, Kennedy et al., 2000, Maeno and Arakawa, 2004, Maeno et al., 2003, Repetto-Llamazares et al., 2011, Schulson and Fortt, 2012). Most of these laboratory tests were performed with artificially formed and very smooth ice surfaces (Kennedy et al., 2000, Maeno et al., 2003). Other tests on ice–ice friction were conducted when sliding occurred along Coulombic shear faults (Fortt and Schulson, 2007, Fortt and Schulson, 2009, Fortt and Schulson, 2011). In their tests, the authors used very small samples, and sliding of several millimetres occurred. Such well-controlled small-scale laboratory tests help to understand the physics of the ice friction and the effect of various parameters on the friction coefficient (e.g., sliding velocity, temperature, normal load), but the results may not be fully applicable to larger scales. Lishman et al. (2011) performed ice–ice friction tests in the Hamburg Ice Basin (HSVA) and used an analogy with the friction in rocks (Dieterich, 1978, Gu et al., 1984, Ruina, 1983). These authors proposed a rate- and state-dependent friction model for saline ice. A similar approach was used by Fortt and Schulson (2009). From an engineering perspective, it is important to compare how well the dependences obtained in the laboratory and basin tests describe friction processes in the field. To the best of our knowledge, only a limited amount of field data is available for sea ice–sea ice friction (Gavrilo, 1984, Pritchard et al., 2012, Ryvlin, 1973). In all of these tests, the authors used an elastic cable to pull ice blocks and studied the effect of the velocity, normal load, and presence of snow on the surface of the level ice.
This paper presents results from the field tests performed during two field seasons (March–April 2011 and 2012) at Spitsbergen and in the Barents Sea on sea ice–sea ice friction. The main purpose of the experiments was to determine the most important factors that affect the friction of sea ice on sea ice in field conditions and to determine whether the existing friction models (Evans et al., 1976, Oksanen and Keinonen, 1982) are in agreement with these data. The influences of the sliding velocity, air and ice track temperature, normal load, and ice block sliding direction in relation to the ice grain orientation were studied. Furthermore, the presence of sea water in the sliding interface on the friction coefficient was investigated and discussed.
Section snippets
Ice friction models
Ice friction is a very complex process, and different friction regimes may occur depending on the properties of the sliding materials and test parameters (Kennedy et al., 2000, Kietzig et al., 2010). Therefore, there is no universal model that satisfactorily describes ice friction under all possible conditions. We will briefly present several existing ice friction models.
Evans et al. (1976) quantitatively developed a frictional heating theory proposed by Bowden and Hughes (1939). It was assumed
Experimental method
Field experiments on the friction of sea ice on sea ice were performed in March and April of 2011 and 2012. In 2011, the tests were performed in the Adventfjord (78°13.604 N, 15°38.637 E) at Spitsbergen. In 2012, some of the tests were conducted in the Van Mijenfjord at Spitsbergen, and the remainder was performed near Edgeøya Island (77°21.784 N, 24°05.743 E) in the Barents Sea.
Results and analysis
Two distinctive sliding regimes were observed in the tests. The first regime (shown in Fig. 3) is associated with steady sliding. The first peak load corresponds to the force needed to overcome static friction. After sliding was initiated, the pulling force had to balance the kinetic friction force. The static and kinetic friction coefficients were calculated using the well-known expressionwhere Ff is the static or kinetic friction force and Fn is the normal load. The kinetic friction
Discussion
Two sliding regimes were observed in our field tests: steady sliding (Fig. 3) and stick–slip (Fig. 4). The stick–slip regime occurred when the ice block temporarily adhered to the sliding track until the pulling force exceeded a certain threshold value sufficient to initiate slip, and the process was repeated. In this case, the graph of the measured frictional force versus the time (or displacement) had a sawtooth shape. Stick–slip was observed in most ice–ice friction tests reported earlier (
Conclusions
A number of field tests on the friction of sea ice on sea ice were performed. The effects of the sliding velocity, air and ice track temperatures, normal load, presence of sea water in the interface, and ice grain orientation with respect to the sliding direction on the friction coefficient were highlighted. The findings can be summarised as follows:
- 1.
Ice surface roughness is an important parameter that determines the value of the friction coefficient. Repeated sliding over the same track led to
Acknowledgements
The authors wish to acknowledge the support from the Research Council of Norway through the Centre for Research-based Innovation SAMCoT and the support from all SAMCoT partners. We thank Prof. Mauri Määttänen for his helpful discussions and to Marat Kashafutdinov for his assistance in the tests. We are grateful to anonymous reviewers of this manuscript for helpful comments.
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