Scaling and Universality in Rock Fracture

Abstract

We present a detailed statistical analysis of acoustic emission time series from laboratory rock fracture obtained from different experiments on different materials including acoustic emission controlled triaxial fracture and punch-through tests. In all considered cases, the waiting time distribution can be described by a unique scaling function indicating its universality. This scaling function is even indistinguishable from that for earthquakes suggesting its general validity for fracture processes independent of time, space and magnitude scales.PACS numbers: 62.20. Mk,91.30.Dk,89.75.Da,05.65.+b The fracture of materials is technologically of enormous interest due to its economic and human cost [1]. Despite the large amount of experimental data and the considerable efforts undertaken [2], many questions about fracture have not yet been answered. In particular, there is no comprehensive understanding of rupture phenomena but only a partial classification in restricted and relatively simple situations. For example, many material ruptures occur by a "one crack" mechanism and a lot of effort is being devoted to the understanding, detection and prevention of the nucleation of the crack [3,4,5,6,7,8]. Exceptions to the "one crack" rupture mechanism are heterogeneous materials such as fiber composites, rocks, concrete under compression and materials with large distributed residual stresses. In these systems, failure may occur as the culmination of a progressive damage involving complex interactions between multiple defects and microcracks.In particular, acoustic emission (AE) due to microcrack growth precedes the macroscopic failure of rock samples under constant stress [9,10] or constant strain rate loading [11,12]. This is an example of the concept of "multiple fracturing" -the coalescence of spontaneously occurring microcracks leading to a catastrophic failure -which is thought be applicable to earthquakes as well [13,14,15]. Due to this and the similarity in their statistical behavior, acoustic emissions can be considered analogous to earthquake sequences. The temporal [16,17], spatial [18] and size distribution [11] of AE events follow a power law, just as it is commonly observed for earthquakes [19,20]. Such power-law scaling can be considered indicative of self-similarity in the AE and earthquake source process [16].The time evolution of AE and earthquake data also display considerable differences. Laboratory rock fracture is dominated by a large number of foreshocks while seismicity in the Earth's crust is characterized by an abundance of aftershocks [21]. Here, we show that despite this difference the probability density function (PDF) for the time interval between successive events is the same in both cases if they are rescaled with the mean waiting time or equivalently with the mean rate of occurrence. In particular, the PDF for laboratory rock fracture neither depends on the specific experiment nor on the specific material. These observations strongly suggest a universal character of the waiting time d...

Triggering Processes in Rock Fracture

“…Our analysis of other experimental data over a wide range of rock types and under different loading conditions [19,35] confirms this. Our findings are consistent with the (direct or indirect) observation of triggering in other AE experiments.…”

“…This is consistent with the picture that the b value depends on the differential stress [55,56] as triggering should preferentially occur in areas that are closer to failure during prepeak loading. Nevertheless, the overall b values are similar to those observed in a variety of different AE experiments [19,23,24] such that b values alone are not generally indicative of the presence or absence of triggering.…”

“…Many explanations involve the picture of an earthquake as a purely frictional sliding event [16,17]. In the lab, earthquakelike stick-slip sliding on rough granite surfaces produces acoustic emission (AE) events-related to the nucleation and growth of microcracks corresponding to mini earthquakes [18,19] often considered a special type of crackling noise [20,21]-that show statistical behavior similar to tectonic seismicity. This includes Omori-type aftershock decay as well as Gutenberg-Richter (GR) frequency-magnitude distributions [22].…”

Fluctuations of Global Energy Release and Crackling in Nominally Brittle Heterogeneous Fracture

“…Such dynamics are e.g. revealed by the acoustic emission accompanying the failure of various materials [3][4][5][6] and, at much larger scale, by the seismic activity going along with earthquakes [7,8]; A generic observation in this field is the existence of scalefree statistics for the event energy [9].These avalanche dynamics [10] have attracted much recent attention. They were originally thought to be inherent to quasi-brittle fracture, where the solid starts by accumulating diffuse damage through microfracturing events before collapsing when a macroscopic crack percolates throughout the microcrack cloud [11].…”

Scaling properties of planetary calderas and terrestrial volcanic eruptions

“…This type of global approach has been proven successful at defining scaling laws for the occurrence of other natural hazards such as forest fires (Corral et al, 2008), earthquakes (Corral, 2003;Shcherbakov et al, 2005), solar flares (Baiesi et al, 2006) and tropical cyclones (Corral et al, 2010). This approach was also successfully used in analyzing the fracture of rocks (Davidsen et al, 2007). Despite their complexity, volcanic processes can also be approximated by a point process in space and time.…”