A Theoretical Analysis of Sea-Ice Strength

For the first time an attempt is made to derive a theoretical relationship between sea-ice strength and the controlling factors of salinity, temperature, and density. A geometric model of the ice-brine relationship is constructed from photographs and used to calculate tensile strength of warm (above 20°C) sea ice. The theoretical results compare well with experimental data. The model developed can be extended to colder temperatures by considering the effect of solid salts. Background-When sea water freezes, small flat plates of pure ice form, leaving behind a concentrated brine which tends to drain out of the ice. However, a certain amount of the brine is retained between the ice plates in layers or pockets, causing the sea ice as a whole to be salty. In general, the faster the ice grows, the more brine is trapped. When the ice first forms, the flat ice plates float on the surface of the water with their c axes vertical, forming a very weak, highly saline mush of overlapping plates. As the ice thickens the plates grow at an angle to the surface, and, at about 1.5 cm from the top, depending on the freezing conditions, vertical plates, with the c axes horizontal, predominate. In lake ice, on the other hand, the c axis often remains vertical throughout the thickness of the ice, and long, candle-shaped crystals are formed. The small plates alternating with layers of brine occur in bundles which appear as single crystals under crossed polaroids. The temperature and salinity of the ice determine the amount of brine and hence the thickness of the brine layers. The salinity of the brine is much greater thal). that of the original sea water and depends on the temperature of the surrounding ice with which it is in thermal equilibrium. As the sea ice becomes colder, more ice freezes out of the brine, which becomes more concentrated. With a temperature rise, ice melts and the brine becomes diluted. These brine layers shrink as the temperature decreases and finally 'neck' and separate into vertical cylinders which often extend entirely through the ice sheet. These brine cylinders are separated by ice 'bridges' which connect the original plates. The separation of the layer is controlled predominantly by surface tension. The cylinders are therefore circular or elliptical in horizontal section. The process of the brine-layer separation into cylinders is shown diagrammatically in Figure 1. The hatched area is brine. Figure la is a horizontal section (plan view) showing ice plates separated by brine layers. In 632 Figure lb the brine layers have begun to 'neck,' and in le the brine layer has separated into cylinders. Figure ld shows the orientation of elliptical cylinders-the short axis of the ellipse is always perpendicular to the ice plates. With a further temperature drop the radii of the cylinders decrease. In the case of elliptical cylinders the long axis shrinks faster than the short, and the cross section approaches a circle. Figure 2a is a photograph of a horizontal section of sea ice in which the layers have begun to 'neck.' In Figure le and 2b the layers have split into rows of cylinders. Figure 2d is a vertical section of the same ice. Note the length of the brine pockets. Figure 1f is a three-dimensional schematic sketch of the icebrine relationship. Fig. 2c shows badly deteriorated · ice. Ideally, a row of equally spaced, equal-diameter, circular cylinders will be formed. Actually, ellipses are more common, and spacing and dimensions vary widely. Often the brine layer splits into two or more parallel rows of cylinders. The possible complexity of the broken brine layer is evident in the photographs. These cylinders stay long in relation to their diameter because of gravity and the thermal gradient across the ice. They are unstable and migrate to the warmer temperature, which in winter is the lower surface of the ice [see V einberg, 1940]. This causes brine to drain out of the ice even under very cold conditions. The salinity of the ice therefore decreases from its initial value of 15 to 20%o to about 5%o late in the first season. The various constituents of the brine crystallize out as their eutectic point is exceeded. Sea ice probably never becomes completely solid under natural conditions. The presence and geometry of these brine pockets are the controlling factors in the strength of the sea ice. The present analysis is limited to warm ice. No attempt is made to determine the quantitative effect of solid salts. When sea ice breaks in tension or flexure, it THEORETICAL ANALYSIS OF SEA-ICE STRENGTH 633 ~--r• ~ ~ w J_. ~ ~a