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The elastic wave propagating in rock has velocity dispersion characteristic that holds an imperative significance in rock engineering. This paper aims at study elastic wave velocity dispersion characteristic in limestone dynamic fracture process. For this purpose, the experiment of elastic wave propagates in the limestone when cyclic loading and unloading process is conducted, and elastic wave velocity dispersion characteristic is analyzed. Based on multifractal theory and Raiga model, the influence of fracture degree on velocity dispersion characteristic is discussed qualitatively and quantitatively with evolution characteristic of the AE event. The research results indicate that there is velocity dispersion characteristic when elastic wave propagates in the limestone sample, which presents positive correlation between velocity and frequency. The variation of wave velocity dispersion characteristic is consistent with that of AE activities and both of them show a nonlinear increase trend with an increase of loading. The reason for velocity dispersion characteristic is that the retarding effect of microcracks on elastic wave velocity with different frequencies is different, and the effect is enhanced with the microcrack scale increasing. According to the variation of multifractal parameter [Formula: see text] of the AE event energy series, the limestone sample under loading experiences a transformation process from small-scale microcrack to large-scale microcrack and small-scale microcrack dominance to multi-scale microcrack coexistence, and this complex transformation process results in nonlinear variation of velocity dispersion characteristic. Further, the multifractal parameter [Formula: see text] is introduced into Raiga model to establish the velocity dispersion quantitative model. The model can describe well elastic wave velocity dispersion characteristic, and indicates quantitatively that there is an obvious nonlinear positive correlation between the dispersion characteristic and the fracture degree. The research results have important theoretical and practical significance for understanding elastic wave velocity dispersion characteristic in limestone dynamic fracture process. It can provide important support for characterizing rock fracture process using elastic wave velocity dispersion characteristic.

Coal failure behavior under dynamic loading is significant for dealing with the failure issues encountered in underground coal mines. In this study, the crack propagation and internal fracture process of coal under dynamic loading were investigated by a split Hopkinson pressure bar (SHPB) experimental system and numerical approach, respectively. The experimental and numerical results show that the coal crack propagation and internal fracture surface manifest significant multifractal features. Further, multifractal analysis suggests that the multifractal feature becomes more and more significant during the dynamic loading. The formation mechanism of the multifractal features was further discussed, and the result demonstrates that the crack propagation path within coal is essentially a multifractal structure, thus causing the total fracture behavior of coal to show multifractal features under dynamic loading. Moreover, the multifractal spectrum parameter [Formula: see text] was proved to be closely related to the brittle fracture property of coal, which transpires that the multifractal feature is feasible to evaluate the coal brittleness under dynamic loading and also applicable to predict the coal failure risk in underground coal mines.

During coal and rock loading, a significantly large number of electromagnetic signals are generated as a result of fracture appearance and crack expansion. The generation of electromagnetic signal is the comprehensive embodiment of the coal rock failure behavior. Therefore, the generated signals contain complex and rich messages that can reflect the damage process and degree of coal and rock. In this work, the multifractal theory is applied to analyze the nonlinear characteristics of the electromagnetic wave and its spectrum induced during coal rock, which present good correlation with failure process. The failure process of coal rock is non-uniform, non-continuous and nonlinear, during which, there is a good synchronization and correlation between the electromagnetic pulses and the stress drop, rather than the stress. Both waveform and its spectrum of electromagnetic signal have multifractal characteristics, the larger the fracture scale is, the more significant the multifractal characteristic of electromagnetic signal is, and the multifractal characteristic of electromagnetic signal from coal is higher than that from sandstone. The difference of fracture energy and size can be represented by the maximum of the multifractal dimension [Formula: see text] of the electromagnetic wave and its spectrum during coal rock failure. In the electromagnetic spectrum, small signals are always dominant, and the dominant frequency is only a few isolated points. What is more, with the increase of fracture size, the difference between the dominant frequency and the non-dominant frequency is gradually enhanced.

Coal fractography is a powerful tool for interpreting coal fracture behaviors, which is significant for dealing with failure issues encountered in deep coal mining. However, the accuracy of coal fractography highly depends on the method of quantitatively characterizing coal fracture surfaces. In this study, coal fractography under dynamic impact loading was investigated based on a multifractal method, the multifractal spectrum parameters were proposed to quantitatively describe the coal fracture surfaces. The width of the multifractal spectrum [Formula: see text] characterizes the uniformity of the surface asperity distribution, and the spectrum parameter [Formula: see text]–[Formula: see text] characterizes the proportion of dominant asperities on fracture surface. The coal fractography results indicate that larger loading rate leads to more asperities on the coal fracture surfaces, i.e. rougher fracture surfaces, and the fracture surfaces are dominated by small asperities induced by dynamic impact loading. In addition, significant anisotropy effect was found on the fracture surfaces under dynamic impact loading by the spatial distributions of multifractal spectrum parameter [Formula: see text]. The parameter [Formula: see text] was further utilized to determine the macrocrack direction and microfracture markings on the coal fracture surfaces, the results transpire that the multifractal method is feasible for coal fractographic analysis under dynamic loading conditions.

Ultrasonic receiving wave can reflect physical properties and damage degree of coal samples. Therefore, it is of great significance to deeply study the parameters of ultrasonic. In this paper, time-domain characteristics of receiving wave are analyzed systematically, which present good correlation with stress. The frequency spectrum of receiving wave is obtained using Fast Fourier Transform (FFT), and peak frequency and centroid frequency are calculated. During the entire loading process, peak frequency fluctuates around 110[Formula: see text]kHz, but corresponding centroid frequency decreases obviously at the end stage of loading. According to multifractal theory, the multifractal spectrum of wavelet packet energy characteristics is calculated. The results show that wavelet packet energy distribution has obvious multifractal characteristics, and multifractal parameter [Formula: see text] presents downward trend before coal samples buckling failure. Based on damage process of the coal samples, the reason of change in [Formula: see text] value is related to damage degree of coal samples. This research is of great significance for understanding the deformation and failure process of coal samples using ultrasonic technology.

To study the damage evolution mechanism of gas-bearing coal and formation causes of acoustic emission signals during this process, the loaded experiments of gas-bearing coal were performed, and acoustic emission (AE) data radiated in this process were collected. Based on the multifractal theory, the causes of AE were explored in various loaded phases. The results showed that at the low stress stage, the fractures close and the friction/slip could cause low-energy acoustic emission events, and the multifractal spectrum had a smaller width. By contrast, at the high stress stage, the cracks expand, penetrate, and rupture, which would lead to AE events with the release of high energy, reflecting an increase in the width of the multifractal spectrum. At the initial loading stage, the time-varying multifractal spectrum was characterized by a chaotic behavior, but as the loading progressed, it gradually became orderly. In the elastic stage, coal experienced elastic deformation without damage, the ratio of strong and weak AE signals was almost the same, and both [Formula: see text] and [Formula: see text] were close to 0. In the plastic fracture stage, coal body consumed huge amounts of energy and suffered fracture. This also caused the coal body to radiate a large amount of AE signals. An analysis of these signals indicated that strong signals dominated and showed an increasing trend, and [Formula: see text] was less than 0 and continued to decrease. The time-varying multifractal characteristics reveal the formation mechanism of AE signals from gas-bearing coal, which contributes to improve our understanding of the mechanism of gas-bearing coal damage.

During coal oxidation and temperature rise, a significantly large amount of electromagnetic radiation (EMR) signals are generated as a result of thermal deformation and thermal cracking. The generation of EMR signal is the comprehensive embodiment of the physical and chemical changes in coal during its oxidation and subsequent heating. Therefore, the generated signals contain complex and rich messages that can reflect the changes in the internal structure of coal. In this work, the characteristics of EMR signal were analyzed by multifractal theory. Multifractal analysis was used to deconstruct EMR signals. Our preliminary study indicated that the multifractal spectrum of the EMR signal had a feature of small probability event. Further analysis demonstrated that the characteristic parameters of EMR signal are quite different at the later heating stage from those at the early heating stage. At the initial stage of coal spontaneous combustion, the multifractal spectrum of the signal is wider, but when coal combustion is reached, the scale range of EMR signal increases significantly, and its structure changes at different temperature ranges. The research results presented provide a basis for monitoring and presenting an early warning of coal spontaneous combustion risk.

In this paper, acoustic emission (AE) signal of coal and rock samples during the heating process are measured. The results show that AE energy of coal samples is higher than that of rock samples. Based on the multifractal theory, the multifractal characteristics of AE signal are researched. The multifractal spectrum width ([Formula: see text]) of coal samples is wider than that of rock samples, which means AE signal of coal samples is more complex than AE signal of rock samples during the heating process. Multifractal parameter ([Formula: see text]) is more than zero, illustrating that small AE signal is dominate. The time-varying multifractal characteristics are analyzed, and the change trend of multifractal spectrum width ([Formula: see text]) of coal and rock samples is consistent. At the stage of 40–50[Formula: see text]C, multifractal spectrum width ([Formula: see text]) gets the maximum value, whereas multifractal spectrum width ([Formula: see text]) gets the minimum value at the stage of 80–100[Formula: see text]C. For coal samples, multifractal parameter ([Formula: see text] is more than zero except at the stage of 40–50[Formula: see text]C. However, multifractal parameter ([Formula: see text] of rock samples is always more than zero during the entire heating process. By [Formula: see text] analytical method, Hurst exponent of AE signal is calculated. The results show that Hurst exponent of coal and rock samples are more than 0.5, which indicate that AE signal presents persistence, and there is a positive correction between AE signal and temperature. In different temperature levels, Hurst exponent curve presents an increase trend after the initial decrease.

A microseismic (MS) monitoring system in a mine can monitor the MS signals generated by coal rock rupture and blasting waves and can distinguish the two types of waves more clearly to monitor and analyze the rupture and evolution process of coal rock. According to the nonlinearity characteristics of the waveform, the fractal characteristics of a mine’s MS and blasting waves are analyzed by simple fractal and multifractal theory, and the simple fractal dimension [Formula: see text] and multifractal parameters are obtained, respectively. Results show that the simple fractal dimension [Formula: see text] reflects the complexity and frequency structure of the wave. The simple fractal dimension [Formula: see text] of a blasting wave is larger than that of a mine MS wave, which indicates that the blasting wave is relatively complex with higher frequency, while the mine MS wave is relatively simple with lower frequency. However, the simple fractal dimension [Formula: see text] can only describe the wave integrity features, not the local features. The multifractal parameters can describe the local characteristics of the wave more finely, and the multifractal spectrum describes the probability information of the singularity exponent [Formula: see text]. The singularity exponential range and multifractal spectral width [Formula: see text] of the blasting wave are smaller than those of the mine MS wave, which indicates that the probability measure of distribution unevenness and the degree of partial parameter fluctuation of the blasting wave are more severe than those of the mine MS wave. Wave signal analysis based on simple fractal and multifractal methods can not only obtain the characteristics of the wave strength and spectral structure but also other important information, such as local singularity. Therefore, it is possible to more clearly and conspicuously identify mine MS and blasting waves, so that coal rock rupture can be monitored more accurately.

In order to explore the causes of acoustic emission (AE) signals during coal failure, the coal samples with original joints were subjected to uniaxial compression experiments, and the AE signals were monitored by AEwin Test for Express-8.0. Based on the multifractal theory, the multifractal characteristics of AE were analyzed. The results showed that the AE counts and accumulative counts change over time corresponded well with the load-time, which reflected the degree of crack evolution and loading. During the initial loading stage, the cracks expanded gradually along the trace of the original cracks, which could induce a few AE events, while with the increase of load, the cracks enlarged gradually and then joined together to form a macroscopic fracture, which would cause much more AE events within a larger value. Multifractal spectrum [[Formula: see text]] of AE was more concentrated in the right side, illustrating that the frequency of small signals was greater than that of the large signals in AE sequences, which revealed cracks expanding and microfracture events dominated during the loading process. The greater the multifractal spectrum width ([Formula: see text] was, the larger the AE signals differences were, which reflected that AE varied more intensely. The more developed the original cracks, the more obvious the multifractal characteristics. This research revealed the causes and percentage of the AE events within small or large signals, which would help us to recognize crack evolution of coal and generation mechanism of AE.