# Acoustic Emission Spectroscopy: Applications in Geomaterials and Related Materials
## 3 Collapse Predicting  
Tectonic materials are generally inhomogeneous, anisotropic and show nonlinear elastic responses. Non-linearities often lead to sudden collapses under elastic constrains and to catastrophic failure. The catastrophic failure is not continuous, and the evolution of strain fields is not smooth, but abrupt, and displays typical avalanche characteristics. Earthquakes and mine collapses are examples of such catastrophic failures. The development of methods which can serve as early warning systems of such disasters has been the focus of disaster prediction research for many years [39; 40; 41; 42]. Progress has been very limited due to the complexity of the nonlinear time evolution during failure, the hidden triggering mechanisms and insufficient theoretical models [43; 44; 45]. Compared with the traditional mechanical constitutive model and failure criterion, statistical physics provides an alternative research framework for disaster research [46; 47; 48]. They are based on elastic responses, as measured by seismic waves in the geological context, while acoustic emission (AE) spectroscopy is used on an engineering and laboratory time and length scale. A series of acoustic emission studies of geological materials such as shales [49], porous quartz [50], berlinite [51], corundum [52] and goethite [32] show that the acoustic emission signals released during the failure process characterize well the statistical features of the collapse with the following characteristic features: the acoustic emission signal (amplitude and energy of the 'jerks' or burst signals) follow power law statistics. In addition, the waiting time distribution between events, and the aftershock distribution of these geomaterials, are indeed very similar to observations of earthquake so that it may be assumed that the underlying principles of the statistical processes are very similar [53]. [PERSON] et al. [54] explored early warning AE signals of compressed geological materials before they collapse. The probability for an event with energy E is a power law P(E) dE\(\sim\)E\({}^{-\epsilon}\)dE. Compared with previous attempts, they used larger samples and higher pressure to observe the change of power law exponents in AE energy distributions. Dry and wet sandstone and coal samples were studied under uniaxial compression. Initially, the damage centers are almost randomly distributed with little spatial correlation between them. Closer to the final collapse, the damaged areas interact and form fracture zones,  
Figure 1: Schematic typical AE experiment and AE signals. The setting of the Peak Definition Time (PDT) ensures correct identification of the signal peak for rise time and peak amplitude measurements. If the PDT is smaller than the rise time, the amplitude captured by AE system would be smaller than the truth value. Proper setting of the Hit Definition Time (HDT) ensures that each AE signal from the structure is reported as one and only one hit. If the HDT is larger than (T2-T1), hit 1 and hit 2 will be detected by AE system as just one hit. AE system needs HLT to get ready for the next signal detection, with proper setting of the Hit Lockout Time (HLT), spurious measurements during the signal decay are avoided and data acquisition speed can be increased. which leads to the final catastrophic failure (Figure 2). The power law exponents \(\varepsilon\) show different values in these two stages. For example, for sandstone, the energy exponent during the early stage is \(\varepsilon\) = 1.77, while near failure it reduces to 1.53 (Figure 3). The time evolution of avalanche exponents is well understood by the tendency to assume some 'critical values' near failure points [35]. Experimental results in coal [55] and sandstone [50] confirm this picture. Discrete element computer simulations [56; 57] show variable power law exponents. Variable exponents were previously observed in several physical systems.