Physicists take a crack at rocks
Apr 2, 2007
Sandstone and granite are very different types of rock, so it might come as a surprise that both materials appear to crack in the same way -- at least according to physicists in Canada and Germany who have measured the sounds given off by rocks before they shatter. What’s even more curious is that sounds from the small samples of rock studied by the group have similar characteristics as those detected after an earthquake, suggesting cracking is a universal process that occurs in many different materials over a wide range of size and time scales (Phys. Rev. Lett. 98 125502).
Humans have been cracking rocks for at least one million years – first to make tools and then to quarry and shape building materials. While both stone-age toolmakers and modern-day mechanical engineers have developed a practical understanding of the cracking process, a microscopic theory of cracking has remained elusive. The problem is that most rocks are made of grains that come in many different shapes and are arranged in many different ways. This makes it very difficult to predict when and where a crack will begin and how it will propagate.
Despite these structural variations, Jörn Davidsen of the University of Calgary and colleagues at the GeoForschungsZentrum Potsdam have found that a collection of different rock samples (two sandstones, two granites and a basalt) appear to crack in a very similar manner.
The rocks were fractured by subjecting them to external pressure and detecting the sounds emitted during microcracking events. Microcracks are tiny ruptures that occur in the rock before it shatters.
The team then analysed the sounds to determine the magnitude of the microcracks and the “waiting times” between successive events. Waiting times are important because they reveal how successive microcracks lead to the large-scale structural failure of a material.
Davidsen and colleagues then took the waiting times for each sample and divided them by the average waiting time for that sample. Amazingly, the probability distribution of these normalized waiting times could be described by the same mathematical formula known as a gamma function -- which gives a high probability for short waiting times, with the probability dropping rapidly for longer waiting times.
The waiting times shared the same probability distribution despite the fact that the average waiting times of the rocks differed by a factor of almost 100 from sample to sample. The team also showed that normalized waiting times associated with sounds emitted after an earthquake are described by the same distribution – suggesting that the cracking of rock on a massive scale is associated with earthquakes.
Davidsen told Physics Web that the universal nature of the probability distribution suggests that the precise microscopic details of the material may not play a significant role in the cracking process after all. This could mean that a successful model of rock cracking could be developed without having to worry about the rocks at a microscopic level. The researchers are now busy trying to develop a model of cracking that can reproduce the observed universality.
About the author
Hamish Johnston is editor of Physics Web