On Ice Arches

Understanding ice flows in the Nares Strait

Today an article on the BBC website caught my interest, but perhaps not for reason the author intended. The article describe the premature disintegration of an ice arch that bridges between Greenland and Ellesmere Island. The arch had blocked the so called Nares Strait, much like the damming of a river, thus preventing the southern migration of the ice flow. Viewed from space the arch is spectacular. The images below show before and after disintegration.

The point of the BBC article was to highlight the effect of a changing climate and what might result from increased ice flow. I have no interest in discussing this; it doesn’t remotely fall within my expertise and I don’t have anything new or novel to bring to the topic. 

Instead, what initially crossed my mind was whether this, and similar structures, I assume other examples must exist, might be the largest arches on the planet. I have no idea whether this is the case or not, but one has to think that they must be contenders.

My mind then turned to the question of why such arches form and whether they were in fact true arches at all. As it turns out I think the two questions could be linked. Not that I really know anything about this subject either, but I do at least feel more comfortable to speculate on the basis of structural principals.

The ‘before’ photo shows the ice flow firmly interlocked with the coast of each land mass. The interlocking extends over a distance, which exceeds the width of the strait and that seems significant to me. The reason I view this as important is that a member whose depth exceeds half its width fits the definition of a deep beam. A deep beam is one that is of sufficient depth that its behaviour is no longer governed by bending effects. I therefore wondered whether what we actually had was a deep beam rather than an arch. That gave me cause to think about how a deep beam actually works. It was this that lead me to postulate how, and I suppose why, an ice arch might form.

The effective depth of a deep beam is roughly equal to its span. It follows that there is little load resisting contribution from the ice flow beyond that point. Normally within a deep beam’s effective depth the stresses behave a bit like an imaginary tied arch with a compression zone at the top, which pushes outwards towards the sides. There must also be a corresponding tension zone at the bottom of the beam, the tie, which prevents the internal ‘arch’ from spreading and tension cracks from forming.

The trouble is that this isn’t what we see in the satellite image. The tension zone is completely missing, leaving the observed arch profile at the base of the ice flow. The obvious reason for this would be that ice is an anisotropic material; it is strong in compression, but has little or no strength on tension. Self-evidently, since there is is an absence of tension capacity, the section of ice exposed to tension has, presumably, cracked and floated away prior to the picture being taken, thus leaving behind an arch profile.

That said, while this may explain the formation of an arch profile it can’t be the whole story. If there is no tie stopping the ice arch from spreading why hasn’t the arch itself collapsed? The answer must be that the land mass on either side of the ice flow provide strong buttresses, which contain and resist the outward thrusts. 

This, however, still doesn’t entirely explain what is going on, because if the buttresses are secure then no tension can be present in the ice flow and if that is so why did the bottom of the ice flow fall out.

Assuming the buttress theory to be correct I can think of several potential mechanisms, but I am not sure which, if any, are contributory.

My first thought would be that perhaps the ice formation takes time to interlock with the land mass and the arch is able to spread while it is still forming. Perhaps during the formation process ice at the land interface cracks and breaks, as the ice flow moves south only becoming solid and immovable as it is slowly pushed and squashed into all the available gaps. Perhaps there is also undulation in the ground and some of the ice rides up over the shallow flat parts until it is is resisted by projections.

Maybe, despite the appearance of static resistance, even the arch is moving slowly southwards and the buttresses gradually shift and adjust. Not enough for the arch to fail, but enough for tension cracks to form at the base of the ice flow.

These would seem, at least to me, plausible explanations for the formation of an arched profile. The question is whether what we are actually seeing is in fact a true arch. We had been considering the possibility of deep beam behaviour, but have, without noticing, slipped back into describing the structure as an arch.

I think it would be just as correct to view the structure as a buttressed deep beam with the effect of rigid coastlines replacing the beam’s tension zone. Though this is perhaps an unusual description I happen to think it is a better description than a true arch. I have three reasons for this.

Firstly, I don’t think the ‘arch profile’ forms without the ice flow first trying to behave as a deep beam. Secondly, due to the re-distribution of forces within the depth of the structure, caused by the buttresses adjusting I don’t think you can avoid the conclusion that stresses are set up across the full width and effective depth of the ice flow. Thirdly, using classical arch theory, which has been discussed in prior posts about masonry arches, I don’t think you could stop the thrust line leaking out of the optimal arch shape due to the depth of the structure and the behaviour of the abutments...actually I’m not sure that’s not just another way of stating reason two.

So, that would be my answer. I think that the base of the ice flow has the appearance of an arch, but is in fact a buttressed deep beam, or maybe that’s just a speculative folly on my part. 

One notable point is that I have offered no comment on the ‘after’ picture. I guess that’s because I wanted to talk about the apparent arch itself, it seems obvious that it would start to fail if the ice melts. Maybe the ‘after’ scenario shows what the ice flow looks like as the structure is forming and the ice is being squashed together. I have no idea if that is true, but aesthetically I am drawn to the idea of a circular process. Perhaps if the temperature is lower at higher latitudes a new wider ‘arch’ will form further north.