The study of crevasse formation and propagation provides information on the overall flow of the glacier and the tensile properties of glacier ice. The earliest theoretical contribution was that ofReference HopkinsHopkins (1862) who, from considerations of statics, related crevasse orientation to the forces causing motion. More recently,Reference NyeNye (1952) used Glen’s flow law in a laminar flow model to investigate the occurrence of crevasse patterns and was able to predict realistic crevasse depths.
Field measurements were made by Meier (Reference Meier and MeierMeier and others, 1957; Reference MeierMeier, 1960) who investigated the formation of transverse crevasses on the Saskatchewan Glacier and on the Greenland ice sheet. Meier measured the motion of stakes spaced at distances varying from 50 to 200 m, these distances being of the order of the existing crevasse spacing. He concluded that the critical extending strain-rate for the initiation of a transverse crevasse was 0.01 year-1.Reference HoldsworlhHoldsworth (1969) confirmed the results obtained by Meier.Reference LachenbruchLachenbruch (1961) constructed a model of tension cracks in geological materials; this model predicts reasonable depths and spacings of crevasses in glaciers.
The purpose of this note is to discuss small-scale surface strain measurements made on the Blue Glacier, Washington, during the summers of 1967 and 1968. The apparatus used for these measurements is described in some detail elsewhere (Reference Colbeck and EvansColbeck and Evans, 1969) and will not be discussed here. Large spatial variations of surface strain were found and these results lead to conclusions which are considered to be relèvent to the study of small-scale glacier flow phenomena. Local flow phenomena considerably different from regional phenomena have previously been recorded. Reference MeierMeier (1960) measured large velocity fluctuations on the Saskatchewan Glacier over short time intervals and even measured backward motion; similarly, large fluctuations in the rate of basal sliding have been measured in ice tunnels on the Blue Glacier.Reference LliboutryLliboutry (1969) states that study of glacier dynamics necessitates smoothing over local fluctuations and that small-scale information is not pertinent to regional flow phenomena. The lower limit of the gage length for deformation measurements which will provide useful information for glacier analysis is certainly an important consideration.
Fig. 1. Fig. 1. Position of stakes and marginal crevasses.
A transverse crevasse field exists on the lower Blue Glacier in which the crevasse spacing is consistently 12 m over a total distance of about 150 m. The regularity of the spacing suggests that crevasse formation is associated with a definite state of déformation. Accordingly, it was decided to attempt to measure the state of deformation of the glacier surface on a small scale and in the immediate vicinity of a forming crevasse by securing wood slakes in the surface at an initial spacing of 3 m and measuring their relative displacement directly.
Fig. 2. Fig. 2. Position of stakes and transverse crevasses.
A pilot project was planned for the summer of 1967; however, due to the late melt, the transverse crevasse field, although below the equilibrium line, was still covered with snow by the end of July. Since the technique for securing the stakes in the surface required that the ice be free of snow, measurements were made in a snow-free marginal crevasse field. A single line of five stakes was placed up-stream from the last crevasse so that, if the existing spacing were continued, the next crevasse should form between stakes 3 and 4 (see Fig, 1). For three weeks no strain-rates greater than the inherent errors (± 1 mm) in the measuring techniques were computed. Subsequently, however, a large extension between stakes 3 and 4 occurred, corresponding to a strain-rate of about 0.8 year-1. After two days a new fracture was found between stakes 3 and 4. One year later, during the summer of 1968, this fracture had opened to form a crevasse.
On the basis of this pilot project we were encouraged to plan a more complete investigation for the summer of 1968. The measuring technique was improved so that distances between stakes could be measured to an accuracy of o. 1 mm using dial micrometers mounted on a rigidly supported invar bar. The pattern of stakes placed at the upper end of the transverse crevasse field is shown in Figure 2. Stakes were placed so that, if the regularity of the spacing were continued, the next crevasse would open between stakes 4 and 5.
Measurements were taken over a period of 3 weeks, one week of which was needed to secure the stakes firmly (see Reference Colbeck and EvansColbeck and Evans (1969) for details). During this first week the measurements were not considered to be accurate. Subsequently, consistent yet unusual results were obtained.
Fig. 3. Fig. 3. Deformation between stakes 1 and 2.
Figures 3, 4, and 5 represent three typical strain results. Figure 3 shows the strain between stakes 1 and 2; the strain-rate is linearly extensional and undergoes an abrupt increase at day 8. Concurrently, a fracture developed between these stakes. Figure 4 shows the strain between slakes 8 and 9, which is uniformly compressive while Figure 5 shows that the strain between stakes 6 and 7 is extensional for the first 6 days and then changes to become compressive. It should be noted that, although these local strain-rates are an order of magnitude greater than the regional strain-rates measured by Meier, the same is not necessarily the case for stresses. Use of an appropriate flow law, in fact, gives stresses approximately twice those given by regional values.
Fig. 4. Fig. 4. Deformation between stakes 8 and 9.
We feel that the unusual results obtained are not due to errors of measurement. The deformation measurements between each pair of stakes are consistent and do not suggest that large random errors occurred. Nor can a consistent motion of the stakes relative to the ice explain the deformations measured over the entire network of stakes. A description of the nature of the ice in this locality and other observations lend credibility to the data.
Fig. 5. Fig. 5. Deformation between stakes 6 and 7.
When seen on an aerial photograph, the crevasse field appears to be reasonably orderly. However, a large number of small fractures appeared and subsequently disappeared during the period of the experiment. These had a typical fracture spacing of 3 m and were apparently randomly oriented. Additionally the fracture observed between stakes 1 and 2 healed without developing into a crevasse. The surface was further complicated by the presence of another transverse crevasse field some 400 m up-stream of the site. Crevasses from this field had healed long before they reached the test site. J. Weertman (personal communication) has postulated that crevasses may close at the surface though not at depth and, in fact, such crevasses have been found on the Blue Glacier (Reference LaChapelleLaChapelle, 1968). Moulins were present near the test site; these were thought to be a rémanent feature of the crevasse field up-stream and, since they were large enough to be draining surface melt water, they probably had a definite effect on the stress distribution around the test site. The nature of the surface and the opening and closing of surface fractures is in fact consistent with the data, namely that the state of stress and deformation changes significantly over a distance of a few meters and changes in character over short time intervals.
Such variations on a small scale are consistent with the observations of Reference MeierMeier (1960) and have been detected in other materials. For example, large fluctuations in surface strain have been measured on concrete specimens after the occurrence of microcracks (Reference HsuHsu, 1968).
The conclusions we draw from the 1968 results are that strain measurements pertinent to the overall glacier flow and to the formation of crevasses cannot be obtained from readings over such small gage lengths as were used here because the presense of surface cracks leads to discontinuous displacement fields which undergo large variations over small distances. Thus, although the strain-rate readings may have some significance with regard to stress distribution, strain-rates meaningful to a continuum analysis of regional flow phenomena must be determined by averaging displacement gradients over distances which are large compared with local phenomena, e.g. surface fractures. A reliable estimate of minimum gage length would require a statistical study of surface fracture spacing and orientation as well as knowledge of the effect of such fractures on the distribution of stress and strain-rate. It seems clear, however, that the gage length must be an order of magnitude greater than fracture spacing. i.e. on the order of 30 m.
We do not suggest that such a conclusion is valid for all surface strain measurements. At the transverse crevasse field, as stated above, the structure was complicated by previous fracturing. Although data from the marginal crevasse field in 1967 are not of sufficient accuracy to draw definite conclusions, it appeared that meaningful results could be obtained using a 3 m gage length. At this location, the ice up-stream from the crevasses was fracture-free and it is suggested that a continuum approach would be meaningful here over dimensions smaller than those for the transverse crevasse field.
