Digitally processed Seasat synthetic aperture radar images from the Beaufort Sea, recorded during August 1978, were analyzed to determine ice-floe displacements and floe-size distributions. Combining data on displacements with those on floe area and thickness yields floe kinetic energies which can then be used as input into design criteria for offshore Arctic structures. Floe-size distributions are needed to determine probabilistically the “design” mass of Ice for an offshore structure.

Vectors of floe movement show the influence of surrounding floes and the compactness of the ice. Floes nearer to more open water showed more movement in the prevailing wind direction while floe movement within the ice pack was primarily affected by floe interaction.

Different cutoff criteria in terms of number of resolution cell sizes were applied to the data on floe size. It was found that the numbers of floes dropped by up to 50% of the original count at ten resolution cells (250 m). Exponential and log-normal probability distributions were fitted to the original counts of floe size. The log-normal fit was better but this is based on one dataset at one time of year in one location. More datasets need to be analyzed to investigate this further. If a probability distribution to floe size can be generalized then only a subset of all the floes would need to be analyzed to determine numbers of floes in each size range. This would greatly speed up a tedious task and be beneficial for design and operational purposes.

A time-dependent numerical model of ice accretion is used to simúlate the growth of ice loads on wires. Both dry growth (rime) and wet growth (glaze) are modelled in order to examine the dependence of the growth rate of ice load on atmospheric conditions.

The results show that during dry growth under constant atmospheric conditions the growth rate of an ice load slightly decreases. In conditions of wet growth, however, the growth rate increases until the process turns to dry growth after reaching the critical deposit diameter. The effect of air temperature on the growth rate in dry growth turns out to be rather small. However, the final ice load after long-term rime formation is temperature-dependent, because the limiting deposit diameter, at which the collection efficiency becomes practically zero, is reached at different ice masses depending on the ice density.

The modelled relationships between the growth rate of ice load and the atmospheric variables are compared with observational data and with proposed formulae for the calculation of the intensity of wire icing. The possibilities of estimating the formation of ice loads for practical purposes with a simple method, using the routinely measured meteorological parameters only, are discussed.

A collapse of the West Antarctic ice sheet due to warming by atmospheric carbon dioxide is a potential threat to mankind because low-lying land would be flooded by rising sea-level. Intervention would be possible by creating one or several artifical ice rises on the floating ice shelves surrounding the West Antarctic ice sheet. Ice rises are places where the ice shelf has run aground locally on the sea bed. Existing ice rises obstruct ice flow and are responsible for maintaining the ice sheet in its present stable condition. An artificial ice rise could be created by (1) drilling a hole through the ice shelf in a choice position such as over a sea-bed ridge, (2) pumping large volumes of sea-water from beneath the ice shelf so as to flood the surface, and (3) continuing to pump until the frozen sea-water has thickened the ice shelf by 100 m over an area of 100 km2. Approximately 1.6 × 106 kW of power would be required to accomplish the task in ten years. This would cost approximately 20 × 109 US dollars.

The US Geological Survey was asked to predict the rate of retreat of the terminus of Columbia Glacier, Alaska, which is a large (1 100 km2), grounded, iceberg-calving glacier, and to estimate the time distribution of the attendant discharge of icebergs. An extensive field program, using 1 September 1977 through 31 August 1978 as the principal year of study obtained ice-surface altitudes and velocities, mass-balance values and thickness changes, and bed topography estimated from radio echo-sounding for Columbia Glacier. These data were subjected to complex one- and two-dimensional adjustment programs to assure consistency with the equations of continuity and glacier flow.

A one-dimensional numerical model based on the continuity equation was used to make the initial prediction, issued in June 1980. The continuity equation is applied to the lower 14 km of the glacier to deter mine the ice flux to the terminus, and the speed of iceberg calving is taken to he proportional to the average water depth at the terminus. Instead of calculating the dynamics of glacier flow independently, the model requires that a sequence of longitudinal profiles be supplied. Through the calving relationship and other applications of the continuity equation, the model then determines the times at which the glacier assumes each of the supplied profiles. The effect on the predicted rate of retreat caused by the arbitrary nature of the longitudinal profiles is less than the effect of other uncertainties in the data used. A one-dimensional finite-difference dynamic model using the same calving relation gave similar results to those of the continuity model.

A two-dimensional, time-dependent, finite-element computer model was also developed. It describes the dynamics of glacier flow along the centerline of the lower glacier using a calving law that relates calving speed to water discharge and to the height of the ice column unsupported by water buoyancy.

The retreat predicted by the continuity model slowly accelerates from the initial observed rate of 45 m a−1 until January 1983 ± 10 months, when the retreat rate increases to about 4 km a−1. At some time between October 1933 and July 1986, the terminus is expected to retreat 9.5 km. An annual iceberg-calving flux of about 10 km3 a−1, which is 6 to 8 times the 1978 flux, is expected to occur in 1984; daily or weekly peaks will be much higher. The two-dimensional dynamic model gives similar results, suggesting that retreat will accelerate in 1983, and that a maximum calving flux will be attained in 1984 (see Fig.1.). Fig. 1.

Predicted retreat based on the continuity equation model, and observed retreat to 3 September 1982.

In the summer of 1980, calving was much less than that observed in previous years, probably due to low amounts of run-off, the fact that the stream discharged in an area of shallow water, and an unusually positive mass-balance year. Thus, the observed retreat is slower than that predicted. However, on 3 September 1982, the observed retreat was within the bounds of error of the original prediction.

The monitoring of the number of acoustic seismic impulses arising from snow instabilities is regarded as a relative indicator of an unstable snow slope but has not yielded a qualitative, predictive indicator. Until now, the source parameters (fracture area and length), seismic moment, energy released, stress drop, and location of acoustic seismic emissions arising from the snowpack have been neglected. A comprehension of these parameters leads to a better understanding of the event and may help in avalanche prediction.

The location of a seismic event is derived from time differences between P-wave arrivals at four sensors located at the snow-ground interface. Three methods confirm the location of an acoustic seismic snow event to within 2 to 4 cm when the event is inside a seismic net.

Spectral analyses of body waves from seismic snow events yield estimates of source parameters, stress drop and energy released. Equivalent dislocation surface radii range from 4.8 to 9.0 cm, which give stress drops of 0.20 to 0.29 bar, with a dissipated energy in the range of 0.0205 to 0.0632 J.

Spectral analysis of the acoustic seismic snow event with application of dislocation theory provides several likely methods to predict avalanches of a climax type.

The two-parameter equation of motion for snow avalanches proposed by Voellmy in 1955 was later formally derived by Perla in 1979. It has been the object of numerous investigations, mainly to its applications. It has been solved for tracks approximated by straight lines, and this solution has, in some countries, been used extensively with a two-segment approximation. Perla and Cheng programmed such a solution for digital computation by matching an arbitrary number of straight line segments. This solution can also include impact losses due to abrupt changes in the track.

In the first part of this paper a formal integration of the Voellmy/Perla equation is carried out for the general case of a track. The averaged values of the different terms are discussed and evaluated as to their relative orders of magnitude. It is shown that the “centrifugal” effect, which is, of course, automatically omitted in the straight-line solution, can be neglected in most cases. As a conclusion it is shown that all avalanche motions governed by the Voellmy/Perla equation will have the same average velocity on all tracks having the same vertical drop H, the same horizontal extension L, and the same set of “friction” parameters, as long as the length S of the track is the same, regardless of the shape of the tracks. The shape will only determine the velocity profile along the track.

The second part of the paper shows the exact solution of the equation for the special case of tracks with constant curvature, i.e. circular arcs. If the conclusion of the first part of the paper holds true, this solution can be used to determine the average velocity on other shaped tracks of the same length, etc.

It is finally shown that a number of well-known avalanches described in the literature can well be approximated by a circular arc. In these cases even the velocity profile is determined by the exact solution.

Structure/property relationships, while well-researched in metallic and in some ceramic materials, have been essentially ignored 1n studies on the mechanical properties of ice. To rectify this situation, experiments have been designed and have been underway for the past two years to investigate one mechanical property, i.e. tensile strength, and the effect of one structural feature, i.e. grain size, on this property. A clear relationship has been established, and is reported here. Other work is in progress and will also be reported in due course.

Equiaxed and randomly oriented aggregates of freshwater ice, of grain size (as seen in two-dimensional sections) varying from 1.0 to 7.3 mm, were prepared in the form of large cylinders (91 mm diameter × 231 mm length). The aggregates were deformed to fracture under uniaxial tension, using a specially designed ball-joint and yoke assembly to ensure axial loading. Data were obtained at -10 ±0.2°C (i.e. at 96% of the melting point) at a strain-rate of 10−6 s−1.

Figure 1 shows that the tensile strength decreases with increasing grain size, from 1.25 MPa for d = 1 mm to 0.80 MPa for d = 7 mm. Moreover, this figure illustrates that the data are highly reproducible; i.e. that strength is reproducible to within ±5% for a given grain size over the complete range. Fig. 1.

Graph showing the decrease in the tensile strength of ice with increasing grain size.

Concerning the functional relationship between tensile strength of and grain size, analysis shows that the following equation is well obeyed:

Where σj is 0.6 MPa and k is 0.02 MPa m½ at -10°C and 10−6 s−1. This point is illustrated in Figure 2. Fig. 2.

Hall-Petch plot showing the relationship between the tensile strength and the grain size of the ice.

The d−½ character of this relationship, which is of the classical Hall-Petch form observed frequently in metallic materials, indicates that the tensile strength of ice is controlled by some process involving stress concentration, possibly the propagation of microcracks nucleated by the interactions of dislocations or the propagation of pre-existing defects. Of these, the former is the more probable. The reason is that processes involving dislocation motion, when expressed by the difference of σf – σi, are expected to increase linearly with increasing d−½, whereas processes involving the propagation of pre-existing defects predict a linear relationship between σf and d−½ which extrapolates through the origin. The former behavior is the one observed.

It is thus concluded: (i) that the tensile strength of equiaxed and randomly oriented freshwater ice, when deformed slowly at -10°C, decreases with increasing grain size, (ii) that the functional relationship between tensile strength σf and grain size d is σf = σj + kd−½, where σj and k are materials parameters, and (iii) that the tensile strength of polycrystalline ice is controlled by the propagation in a brittle manner of microcracks nucleated by dislocation interactions.

Acknowledgement

This work was funded by the US Army Research Office, Contract No. DAA G-29-80-C-0064.

The problem of vertical lifting ice forces caused by a rising water level, and their action on a vertical slender structure (pile), has been studied by use of the classical theory of an elastic plate resting on an elastic support, in order to calculate the moments and normal forces in the sheet that cause rupture and thus produce cracks in the sheet (Nevel 1974). When cracks are formed, the continuous rise of the water level tends to widen them further, and the theory of elasticity is no longer valid. Usually, formation of cracks in structural members results in complete failure, but this may not be the case here. If the temperature of the air is below zero, the water penetrating the cracks will freeze when it meets with the upper part of the ice and with the air, both having a temperature far below the freezing point of water. Thus the cracks will be continuously healed up, as they are widened by the rising water level. A material healing its own cracks along the rupture zone gives a completely changed stress/strain situation during the deformation.

This new approach may lead to a theory which is able to predict the uplift forces of ice as a function of time, of frequency and amplitude of water-level fluctuations, and of air temperature. It appears that the pile is lifted only a short distance with each cycle of water-level fluctuation. Since the downward ice force is smaller than the upward force, and the pile has a larger resistance to compression than to pulling, the pile may eventually, in the course of repeated cycles, be lifted several metres.

This essay is not a scientific paper in the usual sense; it is rather a personal retrospective view, presented as an oral account of a period of snow research spent almost in isolation. For this printed version a few adaptations have been made, including a reduction in the number of figures. Original illustrations from the Interval Reports of the Institute of Snow and Avalanche Research were used to illustrate the talk and have been retained for publication. Although some information is in German, the essential content of the figures is repeated in English in the captions.