# Acoustic Emission Spectroscopy: Applications in Geomaterials and Related Materials

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## Abstract

**:**

## 1. Introduction

## 2. Avalanches and Acoustic Emission Spectroscopy

^{−18}V

^{2}s (i.e., in the attojoule regime, aJ) referred to sensor signal at 34 dB preamplifier gain. A previous study showed simultaneous measurements of the avalanche of stress and AE during mechanically induced twin boundary motion in a shape memory alloy. It showed that the probability of finding an AE event during a stress drop is ~100 times higher than between stress drops. Additionally, the relations between mechanical energy drops and the lower bound of the acoustic emitted energy is approximately proportional [34]. The common drawback of AE is that the local signal is first locally transferred into an acoustic signal inside the sample which then propagates as an acoustic wavelet to the noise detector. The wave profile of AE is hence determined only indirectly by the initial signal and great care has to be taken not to confuse the measured signal with that of the initial atomic event. This problem has been analyzed in great detail [35], the analytical techniques highlight the strong similarity with the deconvolution procedure to analyze propagating waves in the context of geophysical seismology. The current statistical analysis of AE signals, especially its energy probability distribution function (PDF) and the interevent times, are not much affected by wave profiles and there is a large amount of literature which elucidates some of the intricacies of AE spectroscopy [35,36,37,38]. The AE signal is in the form of a wave in Figure 1, and the important parameters of AE waves are their amplitude, duration, rise time, absolute energy, and waiting time.

_{max}. The duration is the time period over which an avalanche survives. Experimental time scales typically extend from a few microseconds to many milliseconds. Absolute energies are obtained by numerical integration of the square voltage of signals E = 1/R ${{\displaystyle \int}}_{\mathrm{ti}}^{\mathrm{tj}}{\mathrm{U}}^{2}\left(\mathrm{t}\right)\mathrm{dt}$, where t

_{i}and t

_{j}are starting and ending times of the signal and R = 10 kΩ is a reference resistance. The rise time is the time difference between starting time of a wavelet and time of the wave peak. The waiting times are the times between consecutive events, also called ‘interevent times’.

## 3. Collapse Predicting

^{−ε}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, which leads to the final catastrophic failure (Figure 2). The power law exponents ε show different values in these two stages. For example, for sandstone, the energy exponent during the early stage is ε = 1.77, while near failure it reduces to 1.53 (Figure 3).

_{2}) nanoporous materials. The variations in the activity rate are sufficient to explain the presence of multiple periods of accelerated seismic release leading to distinct brittle failure events [64].

## 4. Avalanche Mixing

## 5. Applications

#### 5.1. Biocementation

#### 5.2. Hydroxyapatite (Human Teeth) Cracking

#### 5.3. Sandstone Creep

#### 5.4. Damage of Wetting–Drying Cycles in Sandstone

#### 5.5. Avalanches in Sugar Lumps

## 6. Supplementary Discussion on Båth’s Law

_{AS*}= 1.2, where Ms is the magnitude of main shock, and M

_{AS*}is the magnitude of the largest aftershock [83].

_{10}(E

_{MS}/E

_{AS*}), but the calculation code is incorrectly written as ΔM = log

_{10}(E

_{MS})/log

_{10}(E

_{AS*}), E

_{MS}and E

_{AS*}are the energy of main shock and the largest aftershock normalized by 1 aJ which is approximately the minimum detectable energy. Figure 14 shows the comparison results of Båth’s law of different samples calculated by two formulas. Blue is the correct Båth’s law result and red is the ratio result of the incorrect calculation. There are three points to be pointed out. First, why does the correct Båth’s law formula not yield a result of 1.2? Secondly, the results of Båth’s law indicate that the relationship between the main shock and the largest aftershock is independent of the magnitude of the main shock, but the results of Figure 14 show that the Båth’s law analysis does not show a constant index in the low energy range. Thirdly, why does the wrong formula achieve better results than the correct one and what does it represent? These problems may be caused by the choice of the largest aftershock. The influence of time is not considered in this selection scheme, which may lead to the result that the so-called largest aftershock may be far away from the main shock: and indeed, the so-called ‘largest aftershock’ is registered as an independent event rather than as an aftershock. Its energy is not different from the previous main shock, which results in the small relative magnitude of the aftershock. This effect is more obvious in the low energy range because of the limited statistics of the potential aftershocks. Therefore, it is very important to improve the way to select the relevant aftershock to correctly analyze Båth’s law in acoustic emission tests. We are conducting further work to combine information from Omori’s law and the Båth’s law to explore whether a better analysis of aftershocks is possible.

## 7. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**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.

**Figure 2.**Evolution of AE centers. (

**a**) A few AE centers appear in the top and bottom areas of a sandstone sample since friction between sample faces and loading faces; (

**b**) some AE centers occur randomly; (

**c**) AE centers form the final crack; and (

**d**) the image of the cracked sample. Reproduced with permission from [54]. De Gruyter, 2016.

**Figure 3.**Distribution of avalanche energies for sandstone samples in the different time windows. The inset shows the maximum likelihood estimation fitting exponent ε as a function of a lower threshold. Reproduced with permission from [54]. De Gruyter, 2016.

**Figure 4.**Time sequence of jerk events in coal under uniaxial stress. The spectrum contains 18,968 jerks (blue) and 21 superjerks as record–breaking events. Superjerks are more energetic than any of the previous jerks. Reproduced with permission from [59]. American Physical Society, 2017.

**Figure 5.**Energy exponent as a function of the lower energy cut-off determined by maximum likelihood (ML) estimate. (

**a**) Energy exponents determined by the maximum likelihood method for k-intervals 13–14 and 20–21 with error bars and estimate values; (

**b**) energy exponents for all intervals between k = 13 and k = 21. Sparse data sets lead to a less defined plateaus. We used data near 103 aJ to determine the energy exponents. (

**c**) Evolution of the waiting time renormalization factor λ and the energy exponent ε with increasing rank k of superjerks. Two plateaus can be distinguished for large and small λ and exponents near ε = 1.5 and ε = 1.32. Reproduced with permission from [59]. American Physical Society, 2017.

**Figure 6.**(

**a**) Experimental arrangement for high stress measurements. (

**b**) Energies of AE hits, detected by the transducers attached to coal and sandstone as indicated by their color as function of time. This experiment contains 1001 events in coal, and 4875 events in sandstone. The shadowed areas indicate time intervals from 790 s to 1100 s and from 1460 s to 1635 s. Reproduced with permission from [71]. American Physical Society, 2019.

**Figure 7.**Log–log histogram of energy distributions (

**a**), and ML analysis of the power law exponent as a function of a moving threshold (

**b**) for sandwiches of sandstone and coal. ‘Setup A’ indicates low stress measurements, ‘Setup B’ high stress measurements. Reproduced with permission from [71]. American Physical Society, 2019.

**Figure 8.**(

**a**) Distribution of avalanche absolute energies for different temperatures. (

**b**) The ML-fitting exponent ε as a function of a lower threshold E

_{min}. (

**c**) Damping and pure power fitting for the distribution of avalanche absolute energies of 100 °C and 700 °C. Reproduced with permission from [72]. De Gruyter, 2019.

**Figure 9.**Compression arrangement for (

**a**) grain, (

**b**) sands without cementation, and (

**c**) biocemented sand sample crushing. Reproduced with permission from [77]. Elsevier, 2021.

**Figure 10.**(

**a**) The distribution of AE energy (double logarithmic scales) was fitted by P(E)~E

^{−ε}with ε = 1.4. (

**b**) Maximum likelihood estimates the plateaus indicates the estimation for the energy exponent. The dashed black line indicates the slope of the PDF. (

**c**) Maximum likelihood estimate for the energy distribution exponent at different strain levels. Reproduced with permission from [78]. Elsevier, 2021.

**Figure 11.**(

**a**) AE energy spectra with a series of active periods, n = 1, 2, 3, and 4. The red continuous curve represents the energy average of 30 consecutive events. (

**b**) Distribution of avalanche energies for n = 1 and n = 4 in creep experiments. (

**c**) The ML-fitting exponent ε as function of the lower threshold E

_{min}for n = 1, 2, 3, and 4. The horizontal dashed line (ε = 1.39) indicates the result from Vycor compression. Reproduced with permission from [79]. AIP Publishing, 2018.

**Figure 12.**(

**a**) AE spectra corresponding to stress curve in damaged sandstone. (

**b**) The AE energies distribution of sandstone samples with different number of wetting–drying cycle in log–log scale. (

**c**) the ML-fitting curves as a cutoff E

_{min}, the plateau value is consistent with the slope in log–log scale. (

**d**) the relationship between the energy exponent and the number of cyclic wetting events. Reproduced with permission from [82]. Springer Nature, 2018.

**Figure 13.**(

**a**) Jerk spectrum showing the peak amplitude vs. time with a threshold of 23.6 dB. Each peak in this spectrum is attributed to an avalanche in the sugar lump. (

**b**) ML-fitting exponent ε as a function of energy. The plateau shown by the horizontal black line is an indication of ε = 1.47 from compressing the sugar lump.

**Figure 14.**The relationship between relative magnitude and mainshock energy for all samples, blued results are calculated by ΔM = log

_{10}(E

_{MS}/E

_{AS*}), and red results are from ΔM = log

_{10}(E

_{MS})/log

_{10}(E

_{AS*}).

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**MDPI and ACS Style**

Salje, E.K.H.; Jiang, X.; Eckstein, J.; Wang, L.
Acoustic Emission Spectroscopy: Applications in Geomaterials and Related Materials. *Appl. Sci.* **2021**, *11*, 8801.
https://doi.org/10.3390/app11198801

**AMA Style**

Salje EKH, Jiang X, Eckstein J, Wang L.
Acoustic Emission Spectroscopy: Applications in Geomaterials and Related Materials. *Applied Sciences*. 2021; 11(19):8801.
https://doi.org/10.3390/app11198801

**Chicago/Turabian Style**

Salje, Ekhard K. H., Xiang Jiang, Jack Eckstein, and Lei Wang.
2021. "Acoustic Emission Spectroscopy: Applications in Geomaterials and Related Materials" *Applied Sciences* 11, no. 19: 8801.
https://doi.org/10.3390/app11198801