17 February 2014
Context: fatigue in rock
The concept of fatigue in material science is well-established. It describes a process in which structural damage accumulates as a material is subjected to repeated loading. This process is perhaps best known in metals (so-called metal fatigue); it came to the attention of the world in a series of crashes of the first jet airliner, the de Havilland Comet, in 1953 and 1954. In this case the repeated stress cycles applied to the fuselage of the aircaft as it was pressurised and depressurised caused cracks to grow from the corners of the windows in the fuselage; eventually this caused catastrophic failure and in-flight break-up of the aircraft. This image shows a window of one of the aircraft recovered after a crash in 1954 (from the Royal Society); note the cracks radiating from the corners of the window of the aircraft:
The key idea behind fatigue is that failure of the material develops though the growth of cracks. Under dynamic stresses (i.e. stresses that repeatedly increase and decrease) the local stress at the tip of the crack can exceed the strength of the material, allowing the crack to grow. Eventually the cracks join together to cause failure. This can occur even when the applied stress is lower than the ultimate strength of the material. In aircraft, this is avoided partly by ensuring that the materials are sufficiently strong to prevent this process, and partly by shaping the windows so that stress cannot concentrate in the corners. These are the windows and doors on an Airbus A380 – note the lack of sharp corners:
Two other things to bear in mind about fatigue. First, the rate of fatigue depends upon the stresses applied – i.e. fatigue can be quite fast when the applied load is close to the ultimate strength of the material, but is much slower when stresses are lower. And second, in many materials there is a fatigue limit – i.e. a stress below which fatigue does not occur. Thus, the process only starts once the fatigue limit is exceeded.
Fatigue in rocks
Whilst best known in metals, fatigue occurs in other materials too, and there is good evidence that brittle rocks can undergo fatigue processes. This of course leads to an interesting question as to when it might be important, and one obvious potential setting is that of rockfalls in which release is controlled by the fracture of the rock. In 2005, Peter Adams and some colleagues from the USA (Adams et al. 2005) proposed that fatigue processes might be important in the generation of rockfalls on coastal cliffs. The idea was that repeated wave impacts on the cliff toe regenerates a cyclic load on the cliff itself. They used a set of seismometers located on the cliff to show that the wave impacts generated small magnitude movements of the cliffs themselves – termed microseismic ground motions . Given that waves strike the cliffs every five to 25 seconds (i.e. about 3 million times per year) they proposed that this might induce a fatigue process that might eventually lead the rock to failure, and thus to the generation of rockfalls. It is a very neat idea, and I like the way that it accounts for progressive weakening of the cliff. They key question of course is whether it is a viable mechanism.
Are microseismic ground displacements a significant geomorphic agent?
In our paper (Brain et al. 2014), for which the work was led by my Post-Doctoral Researcher Dr Matthew Brain, we set out to investigate whether fatigue is a viable mechanism for the generation of rockfalls. We used our long-established field site at Boulby in North Yorkshire, at which we have been measuring rockfall activity since 2002:
At Boulby we have used seismometers to measure the delivery of energy to the cliffs from wave impacts – this work is described in detail in a PhD thesis (Norman 2012), available online, by my former student and now Post-Doctoral Researcher Dr Emma Norman. In Brain et al. (2014) we looked in detail at the microseismic motions that we recorded at the cliff top, showing very clearly that the motions were related to the magnitude of the wave impacts, with the biggest motions being recorded during storms. In te largest events we recorded ground motions of about +/-16 microns. However, during calmer periods (which of course is most of the time), the ground motions were typically only about +/-12 microns – i.e. much smaller. So the key conclusion that we have drawn is that fatigue is likely to be a highly episodic process, and indeed we suggest that ground motions as low as 2 microns would be highly unlikely to cause a fatigue process, primarily because this would be unlikely to exceed the fatigue limit. Given that this reduces dramatically the number of cycles to which a cliff is subject, it is unlikely that coastal cliffs would fail in this way.
Of course the greatest microseismic motions also occur when the cliff is subject to a range of other processes that can induce failure, such as high pore water pressures and wind loading. Thus, it is more likely that one of these other processes would lead to detachment. We do recognise though that the progressive weakening of the rock mass caused by microseismic motions might contribute to the failure process.
Adams, P.N., Storlazzi, C.D. and Anderson, R.S. 2005. Nearshore wave-induced cyclical flexing of sea cliffs. Journal of Geophysical Research, 110: F02002 http://dx.doi.org/10.1029/2004JF000217
Brain, M.J., Rosser, N.J., Norman, E.C. & Petley, D.N. Are microseismic ground displacements a significant geomorphic agent?. Geomorphology 207:161-173. http://dx.doi.org/10.1016/j.geomorph.2013.11.002
Norman, E.C. 2012 Microseismic monitoring of the controls on coastal rock cliff erosion. Doctoral thesis, Durham University.