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Article

Experimental Study of the Self-Potential Response Characteristics of Anisotropic Bituminous Coal during Deformation and Fracturing

by
Jun Zhang
1,
Shengdong Liu
1,
Cai Yang
2,3,4,* and
Juanjuan Li
1
1
State Key Laboratory for Deep Geomechanics and Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China
2
The National Joint Engineering Laboratory of Internet Applied Technology of Mines, China University of Mining and Technology, Xuzhou 221116, China
3
Internet of Things Perception Mine Research Center, China University of Mining and Technology, Xuzhou 221116, China
4
School of Resource and Earth Science, China University of Mining and Technology, Xuzhou 221116, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2023, 13(2), 1095; https://doi.org/10.3390/app13021095
Submission received: 23 December 2022 / Revised: 10 January 2023 / Accepted: 11 January 2023 / Published: 13 January 2023
(This article belongs to the Special Issue Mining Safety: Challenges and Prevention of Mine Disasters)
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Abstract

The deformation and fracturing of coal rock is a crucial part of coal and rock dynamic disasters and is accompanied by variations in the electrical field of the rock. In this study, the self-potential characteristics of coal rock were measured to dynamically monitor the spatiotemporal evolution of coal rock deformation and fracturing. By using an MTS816 rock mechanics test system, an AE acoustic emission system and a self-developed SEMOS-LAB experimental system, synchronous measurements of the self-potential, stress and acoustic emission of anisotropic bituminous coal under uniaxial compression were obtained. The self-potential of anisotropic bituminous coal exhibited a good correspondence with the stress and acoustic emission counts during the damage and fracturing. As the stress gradually increased, the bedding-perpendicular coal samples exhibited a stronger linear relationship with the stress during initial loading than the bedding-parallel samples. The amplitude of the self-potential and stress of the bedding-perpendicular samples were higher than those of the bedding-parallel samples. Anisotropy is an important factor that affects the variation in the self-potential of a rock mass under loading. The results of this study can be applied to evaluate the stress state of coal by measuring its loading-induced electrical potential; thus, this work is important in the field for the monitoring and warning of coal and rock dynamic disasters.

1. Introduction

Coal mining depths continue to increase. Deep coal rock masses are located in harsh environments with high ground stress, abundant gas deposits, a high temperature and high osmotic pressure [1], resulting in frequent coal and rock dynamic disasters such as rock bursts and coal and gas outbursts. The mechanisms controlling these disasters are complex [2,3,4], posing a major threat to the safe mining of deep resources. In response to such geological issues, a number of technical methods based on geophysical electrical exploration have been developed such as monitoring of electromagnetic radiation [5], charge inductions [6] and surface potentials [7]. By measuring changes in the electrical properties of coal and rock, the evolution of coal and rock dynamic disasters can be monitored. The related methods have been the subject of considerable research [8,9,10].
The study of charged phenomena on the surface of rock materials began in the early 20th century. In 1933, Stepanov studied electrical phenomena during the fracturing of halide crystals. He believed that the charge appeared in the non-uniform deformation of the crystal sample and at the crack surface [11]. In the 1970s, Chen et al. [12], at the Department of Geophysics at Peking University, studied changes in a natural electric field during rock pressure experiments and found that there was a sudden change in the potential difference between electrodes whenever there was a rupture that caused a pressure drop. Furthermore, before the rupture occurred, almost all rock samples exhibited an accelerated potential change rate or potential “jitter” in at least one direction. Wu et al. [13] conducted an experimental study on the surface charge properties of granite specimens under uniaxial pressure by measuring the micro-current. They analyzed the possible causes of such surface charges and ruled out the piezoelectric effect as the only cause of a surface charge. Enomoto et al. [14] studied potential changes during the deformation and fracture of granite and marble under uniaxial compression. Yoshida et al. [15] found that conspicuous potential changes occurred before the dynamic rupture of both dry sandstone and saturated sandstone. Hao et al. [16] carried out a rock fracture experiment with a servo-controlled biaxial loading system and found that the self-potential and strain field showed correlated pulse changes with a pronounced spatiotemporal variation under conditions of sudden loading and unloading, viscous slips and rock sample fractures. Eccles et al. [17] observed that potential signals were generated in dry and water-saturated quartz-rich sandstone and water-saturated limestone before a sample failure. Takeuchi et al. [18] carried out instantaneous loading experiments on granite and gabbro plates and measured an instantaneous potential of approximately 40 mV and a current signal of approximately 35 pA at the moment of loading. Aydin et al. [19] studied the voltage signal caused by the failure of marble and granite under compression and observed a polarity reversal of the voltage signal at the instant before the rock fractured. Triantis et al. [20] conducted uniaxial compression tests on cement mortar specimens to obtain electrical signal characteristics, which provided clear information on the fracture stress of the specimens. They found that the change in the strain rate was correlated with the electric emission.
Li et al. [21] systematically studied the effect, rule, influencing factors and generation mechanism of the surface potential of coal under loading and determined the spatiotemporal variation and response mechanism of the surface potential of the coal under loading. Archer et al. [22] pointed out that the pressure excitation voltage was related to micro- and macro-scale ruptures. Yin et al. [23] established a coupling relationship between coal rock damage and a potential signal through experiments on the evolution of damage of coal rock under loading. Liu et al. [24] described the discharge mechanism of deep rock-mass damage from the crack tip and systematically analyzed the response characteristics of the self-potential from field detection data with this discharge mechanism. Yang [25] studied the characteristics of the self-potential response during the whole stress–strain process of loaded coal, sandstone and limestone and found that the fluctuations in the self-potential were greatest when the rocks were subjected to a maximum load. In addition, the surface potential signal generated by the coal rock mass under a load failure exhibited a good agreement with the stress. Wang et al. [26] found that the surface potential generated by coal under loaded breaking had a good positive correlation with the load. Yang [27] preliminarily studied the one-to-one correspondence between the self-potential and the stress of coal under uniaxial compression. The stress and acoustic emission also exhibited a good correlation under uniaxial compression [28].
The electrical properties of rock samples under uniaxial compression are affected by the moisture content, loading mode, loading rate and anisotropy [25,29,30,31]. Anisotropy is important for rock physical properties; however, the effect of anisotropy on the self-potential response characteristics of coal under compression has been little studied. Therefore, by conducting uniaxial compression tests with an MTS816 rock mechanics test machine, we explored the self-potential response characteristics of anisotropic bituminous coal and their relationship with the stress and acoustic emission. The aim of this study was to answer the following two questions. First, what are the synchronous response characteristics of the self-potential, stress and acoustic emission of anisotropic bituminous coal? Second, what is the relationship between the self-potential and stress of anisotropic bituminous coal? In this study, we attempted to understand the response of the self-potential of anisotropic bituminous coal during uniaxial compression; the results helped to elucidate the mechanism of the self-potential induced by rock fractures.

2. Materials and Methods

2.1. Experimental System

A SEMOS-LAB experimental system, which was independently developed by our research group, was used for self-potential data collection. The sampling interval of the self-potential data collection was set to 1 ms. The uniaxial compression instrument used for the rock samples was an MTS816 rock mechanics test system (MTS Systems Corporation, Eden Prairie, MN, USA). The uniaxial loading rates were 0.001, 0.002 and 0.005 mm/s and the sampling interval of the mechanical parameters was 1 s. An AE21C system (Shenyang Computer Technology Research and Design Institute, Shenyang, China) was used for the acoustic emission acquisition. In the uniaxial loading process, the self-potential, stress and acoustic emission parameters were synchronously collected and in real-time. The MTS816 rock mechanics test system, SEMOS-LAB experimental system and acoustic emission test system are shown in Figure 1.

2.2. Coal Sample Preparation

Bituminous coal from a coal mine in the middle of the Jungar coalfield, Ordos City, Inner Mongolia, was used in the experiment. Basic information on the bituminous coal samples is provided in Table 1 and photographs of the samples are shown in Figure 2. All the coal samples were drilled from a large-sized lump of coal. A rock cutting machine and a double-sided grinding machine were used to process pieces of the coal into cylindrical specimens. The coal sample specifications met the International Society of Rock Mechanics standard. To study the self-potential response of anisotropic bituminous coal during damage and fracturing, the coal samples were prepared perpendicular to and along the direction of the rock bedding. Bituminous coal samples A1 to A6 were obtained along the bedding direction and samples B1 to B6 were obtained perpendicular to the bedding.

2.3. Experimental Procedure

Electrodes were arranged on the surface of the coal samples in a regular array. Considering the influence of the conductive properties and the contact resistance of the coal sample, a copper electrode (8 mm long and 4 mm wide) was selected as the potential electrode. A conductive adhesive was used for the coupling. The surface electrode observation system is illustrated in Figure 3a. Four electrode lines were arranged on each coal sample with eight electrodes in three electrode lines and seven electrodes in one electrode line. The distance between the adjacent electrodes was 10 mm. The placement of the inner electrode was determined in consideration of the feasibility of the experiment and the reliability of the collected data. An electric drill was used to drill a hole (diameter of 3.8 mm and depth of 4 cm) in the middle of each coal sample (Figure 3b). The inner electrode and electrode line were buried in the hole and the hole was sealed with pulverized coal and conductive glue (the glue thickness was approximately 10 mm).

3. Results

3.1. Response Characteristics of Self-Potential, Stress and Acoustic Emission

The response characteristics of the self-potential and acoustic emission counts with time for the coal during uniaxial fracturing are illustrated in Figure 4. The variation in the self-potential was clearly related to the stress during the deformation and fracture process of the bituminous coal. There was also a correlation between the stress turning point and the acoustic emission count. In addition, the variation in the self-potential and stress of samples B1 to B6 was greater than those of samples A1 to A6. At the elastic deformation stage, the stress showed a gradual increase, but the self-potential of samples A1 to A6 at the elastic deformation stage showed marked fluctuations compared with samples B1 to B6.
The loading rates for the bituminous coal A-samples were 0.001 mm/s for samples A1 and A2; 0.002 mm/s for samples A3, A4 and A6; and 0.005 mm/s for sample A5. The loading rates for the B-samples were 0.001 mm/s for sample B1; 0.005 mm/s for samples B2, B3 and B4; and 0.002 mm/s for samples B5 and B6. The different loading rates had a weak influence on the amplitude of the self-potential variation.

3.2. Response Characteristics of Self-Potential Difference and Stress

The curves of the stress and axial and radial self-potential difference with time for samples A1 to A6, which were obtained parallel to the bedding, are illustrated in Figure 5 and Figure 6; the same curves for samples B1 to B6, which were drilled perpendicular to the bedding, are shown in Figure 7 and Figure 8. The variation in the self-potential difference between the two electrode lines of the anisotropic bituminous coal was consistent with the stress variation in the coal samples under loading. At the inflection point, where the stress markedly changed, the self-potential difference between the two electrode lines also showed a distinct inflection point.
For the bedding-parallel samples (A1 to A6), the range of the axial self-potential difference was −61.51 to 59.44 mV; that of the radial self-potential difference was −56.38 to 79.67 mV. For the samples perpendicular to the bedding (B1 to B6), the range of the axial self-potential difference was −78.84 to 51.45 mV; that of the radial self-potential difference was −94.98 to 53.43 mV.
The compressive strength of the bituminous coal sampled perpendicular to the bedding was conspicuously higher than that of the samples obtained parallel to the bedding. The variation in the self-potential difference was larger for the samples obtained perpendicular to the bedding than for the bedding-parallel samples.

3.3. Variation in Self-Potential with Time for Bituminous Coal Samples

The Kriging interpolation method was used to calculate the self-potential on four electrode lines at the same time to obtain the self-potential profiles for samples A2 and B4 (Figure 9 and Figure 10). The coordinates of the electrode lines are shown in Figure 9 and Figure 10. The distance between the two adjacent electrode lines was 3.93 cm (one-quarter of the circumference of a 5 cm-diameter circle).
Profiles of the self-potential variation with time during the uniaxial loading of bituminous coal sample A2 are shown in Figure 9. The initial uniaxial loading occurred at 1 s and 200 s; at this time, the sample was at the linear elastic stage. Peak stresses occurred at 588.4 and 588.5 s. The maximum peak point before the stress burst took place at 1076.3 s. Macroscopic fracturing of the rock sample after the stress drop occurred at 1076.5 s. As the uniaxial loading proceeded, the amplitude of the self-potential in the region above 40 mV gradually decreased.
Profiles of the self-potential variation with time during the uniaxial loading of bituminous coal sample B4 are illustrated in Figure 10. At 1 s and 100 s, the sample underwent the initial stage of uniaxial loading. At these times, the sample experienced elastic deformation and did not break. The maximum load point occurred at 278.2 s; the time point after the second stress peak point was at 310.1 s. The load dropped below 0 at 325.2 s. The stable stage after the macro-rupture commenced at 340.6 s. As uniaxial loading proceeded, the self-potential amplitude in the region above 20 mV gradually rose and then fell. The self-potential amplitude between line 1 and line 2 gradually increased.

4. Discussion

The results of the uniaxial loading experiments clearly demonstrated that the changes in the self-potential were related to the stress changes that occurred during the damage and fracturing of the anisotropic bituminous coal. There was also a correlation between the stress turning point and the acoustic emission count. The effects of anisotropy on the self-potential could be described as follows. During the elastic deformation stage, as the stress gradually increased, the self-potential of samples A1 to A6 showed marked fluctuations whereas the curves for samples B1 to B6 were relatively stable. The variations in the self-potential and stress of the bedding-perpendicular samples were greater than those of the bedding-parallel samples. In addition, the compressive strength of the samples obtained perpendicular to the bedding was markedly higher than that of the samples obtained parallel to the bedding. The variation amplitude of the axial and radial self-potential during uniaxial loading was greater for the samples that were cut perpendicular to the bedding.
During the initial stage of uniaxial compression, as the uniaxial stress gradually increased, the self-potential of the bituminous coal exhibited a linear increase or linear decrease. Taking sample A3 as an example, the relationship between the self-potential and the stress of the sample (Figure 11) indicated that there was a marked relationship between the self-potential measured from electrode CH25 to electrode CH32 and the stress during the elastic deformation stage. The correlation coefficients (R2) of the linear fitting between the self-potential and the stress of bituminous coal samples A1 to A6 and B1 to B6 at different loading rates are listed in Table 2. Statistical analyses demonstrated that the probability of R2 > 0.5 was 58.3% and the probability of R2 > 0.8 was 55.3%. Of the 12 bituminous coal samples tested, only sample A5 exhibited a correlation coefficient between the stress and the self-potential of electrodes CH25 to CH32 of less than 0.5. From these results, we obtained the constitutive relationship between the self-potential and stress at the elastic deformation stage, which was Sp = a·S + b, where S denotes the stress (MPa) and Sp denotes the self-potential (mV). The samples perpendicular to the bedding (B1 to B6) exhibited a stronger linear relationship with the stress during initial loading than the bedding-parallel samples (A1 to A6). Anisotropy can lead to different self-potential response characteristics during the deformation and fracture of a rock mass.
The main mechanisms giving rise to the self-potential in coal rock are the redox electric field, filter electrical field, diffusion–adsorption electrical field, piezoelectric effect, triboelectric effect, grain boundary/dislocation charge separation and crack tip discharge. The piezoelectric effect, tribological electrification, grain boundary/dislocation charge separation and fissure-tip discharge are the main causes for self-potential changes induced by the deformation and fracturing of a coal rock mass under loading [7,25,26,27], not considering gas-bearing and water-bearing rock masses. The tensile fracturing of coal rock leads to a separation of the charge at the tip of the expanding crack.
Due to differing charges on the new surfaces on either side of a propagating crack, the formation and expansion of a large number of cracks lead to the accumulation of the charge and finally generate an electrical field. There is a positive association between higher potential amplitude increases and a faster crack formation rate. This mechanism is the main reason why a coal rock mass produces a higher potential and a sudden change of potential during the rapid instability stage of fracturing. The results demonstrated that anisotropy was an important factor affecting the variation in the self-potential of a rock mass under loading; the influence of anisotropy on the compressive strength of a rock mass may be directly related to the variation amplitude of the self-potential during rock damage and failure. This topic requires further study.

5. Conclusions

Changes in the self-potential, stress and acoustic emission of anisotropic bituminous coal samples in a complete stress–strain process were obtained through uniaxial compression experiments. The experimental results clearly showed a relationship between the self-potential changes and the stress changes that occurred during the damage and fracturing of anisotropic bituminous coal. In addition, there was a good correlation between the stress and acoustic emission counts. At the initial stage of loading, the samples of bituminous coal obtained perpendicular to the bedding exhibited a stronger linear relationship with the stress as the stress gradually increased than the samples obtained parallel to the bedding. The variations in the self-potential and stress of the bituminous coal sampled perpendicular to the bedding were greater than those of the samples cut parallel to the bedding, indicating that anisotropy was an important influencing factor of the self-potential of bituminous coal under loading. Furthermore, the influence of anisotropy on the compressive strength of a rock mass may be directly related to the variation amplitude of the self-potential during the process of rock-mass damage and failure. The mechanism controlling the relationship between the stress and self-potential needs to be studied further. Research achievements can be applied in future to evaluate the stress state of a coal mass, which has an important field application value for the monitoring and warning of coal and rock dynamic disasters.

Author Contributions

Conceptualization and methodology, S.L., J.Z. and C.Y.; data curation, J.L.; writing—original draft preparation, J.Z. and C.Y. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded in part by the National Natural Science Foundation Project of China, grant numbers 42104133 and 41974149, in part by the Natural Science Foundation of Jiangsu Province, grant number BK20190643, in part by the Open Lab Project of CUMT (NO 2021SYF83) and in part by the Fundamental Research Funds for the Central Universities.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Experimental system for collection of stress, self-potential and acoustic emission data. MTS816 rock mechanics test machine (1), SEMOS-LAB experimental system (2) and acoustic emission test system (3).
Figure 1. Experimental system for collection of stress, self-potential and acoustic emission data. MTS816 rock mechanics test machine (1), SEMOS-LAB experimental system (2) and acoustic emission test system (3).
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Figure 2. Photographs of the rock samples used in the study. Bituminous coal samples A1 to A6 were obtained along the bedding direction and bituminous coal samples B1 to B6 were obtained perpendicular to bedding.
Figure 2. Photographs of the rock samples used in the study. Bituminous coal samples A1 to A6 were obtained along the bedding direction and bituminous coal samples B1 to B6 were obtained perpendicular to bedding.
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Figure 3. Diagram of the observation system used to measure self-potential (a) and photograph of drilling of the inner hole (b). 1#–32# stand for the electrode 1 to electrode 32.
Figure 3. Diagram of the observation system used to measure self-potential (a) and photograph of drilling of the inner hole (b). 1#–32# stand for the electrode 1 to electrode 32.
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Figure 4. Response characteristics of bituminous coal self-potential and acoustic emission counts with time during uniaxial fracturing. Samples A1 to A6 were obtained parallel to the bedding and samples B1 to B6 were drilled perpendicular to the bedding.
Figure 4. Response characteristics of bituminous coal self-potential and acoustic emission counts with time during uniaxial fracturing. Samples A1 to A6 were obtained parallel to the bedding and samples B1 to B6 were drilled perpendicular to the bedding.
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Figure 5. Curves of stress and axial self-potential difference with time of bituminous coal samples A1 to A6 under uniaxial loading.
Figure 5. Curves of stress and axial self-potential difference with time of bituminous coal samples A1 to A6 under uniaxial loading.
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Figure 6. Curves of stress and radial self-potential difference with time of bituminous coal samples A1 to A6 under uniaxial loading.
Figure 6. Curves of stress and radial self-potential difference with time of bituminous coal samples A1 to A6 under uniaxial loading.
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Figure 7. Curves of stress and axial self-potential difference with time of bituminous coal samples B1 to B6 under uniaxial loading.
Figure 7. Curves of stress and axial self-potential difference with time of bituminous coal samples B1 to B6 under uniaxial loading.
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Figure 8. Curves of stress and radial self-potential difference with time of bituminous coal samples B1 to B6 under uniaxial loading.
Figure 8. Curves of stress and radial self-potential difference with time of bituminous coal samples B1 to B6 under uniaxial loading.
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Figure 9. Profiles of the variation in self-potential with time for coal sample A2. Areas of significant change in self-potential are indicated by red dashed lines. 1#–32# stand for the electrode 1 to electrode 32.
Figure 9. Profiles of the variation in self-potential with time for coal sample A2. Areas of significant change in self-potential are indicated by red dashed lines. 1#–32# stand for the electrode 1 to electrode 32.
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Figure 10. Profiles of the variation in self-potential with time for coal sample B4. Areas of significant change in self-potential are indicated by red dashed lines. 1#–32# stand for the electrode 1 to electrode 32.
Figure 10. Profiles of the variation in self-potential with time for coal sample B4. Areas of significant change in self-potential are indicated by red dashed lines. 1#–32# stand for the electrode 1 to electrode 32.
Applsci 13 01095 g010
Applsci 13 01095 g011
Figure 11. Scatter diagram of the relationship between self-potential and stress of bituminous coal sample A3 at the initial stage of uniaxial compression.
Figure 11. Scatter diagram of the relationship between self-potential and stress of bituminous coal sample A3 at the initial stage of uniaxial compression.
Applsci 13 01095 g011
Table 1. Basic information on the bituminous coal samples.
Table 1. Basic information on the bituminous coal samples.
Sample NameDiameter (mm)Height (mm)Quality (g)Loading Rate (mm/s)
A149.7999.31246.60.001
A249.7999.69244.50.001
A349.8099.56238.30.002
A449.8099.62250.70.002
A549.7999.49247.80.005
A649.7499.67244.10.002
B149.8499.45275.30.001
B249.4399.81242.00.005
B349.3599.78239.50.005
B449.5899.70250.90.005
B549.8399.97254.30.002
B649.4699.96241.50.002
Table 2. Correlation coefficient parameters of self-potential and stress of all studied bituminous coal samples.
Table 2. Correlation coefficient parameters of self-potential and stress of all studied bituminous coal samples.
R2 *CH25CH26CH27CH28CH29CH30CH31CH32Loading
Rate (mm/s)		Stress
Interval
(MPa)
R2 (A1)0.5270.4210.0550.00060.0870.6060.9310.1240.001≤4.899
R2 (A2)0.4650.6580.8170.7780.7070.3200.2490.8820.001≤5.523
R2 (A3)0.0170.2800.3880.9020.9560.8530.9580.7830.002≤11.352
R2 (A4)0.0550.4900.1830.0410.9080.9320.9410.8820.002≤3.853
R2 (A5)0.3620.1530.2470.0020.0070.0160.1260.1240.005≤2.833
R2 (A6)0.3040.4470.7780.7690.7800.6380.1680.9420.002≤4.585
R2 (B1)0.0910.7860.9540.9350.5800.6310.9420.9640.001≤31.251
R2 (B2)0.3470.9770.9100.6640.1590.5860.1940.5820.005≤20.303
R2 (B3)0.9810.9020.1860.6320.8900.6200.7980.8480.005≤14.706
R2 (B4)0.8940.6580.0300.9330.890.9030.1450.6500.005≤18.660
R2 (B5)0.0010.1990.0610.0210.470.6580.7270.7840.002≤17.518
R2 (B6)0.3880.9580.9600.1250.8740.8200.0650.8210.002≤20.486
* Correlation coefficients R2 marked in red were greater than 0.5. Samples A1 to A6 were drilled parallel to bedding and samples B1 to B6 were drilled perpendicular to bedding.
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Zhang, J.; Liu, S.; Yang, C.; Li, J. Experimental Study of the Self-Potential Response Characteristics of Anisotropic Bituminous Coal during Deformation and Fracturing. Appl. Sci. 2023, 13, 1095. https://doi.org/10.3390/app13021095

AMA Style

Zhang J, Liu S, Yang C, Li J. Experimental Study of the Self-Potential Response Characteristics of Anisotropic Bituminous Coal during Deformation and Fracturing. Applied Sciences. 2023; 13(2):1095. https://doi.org/10.3390/app13021095

Chicago/Turabian Style

Zhang, Jun, Shengdong Liu, Cai Yang, and Juanjuan Li. 2023. "Experimental Study of the Self-Potential Response Characteristics of Anisotropic Bituminous Coal during Deformation and Fracturing" Applied Sciences 13, no. 2: 1095. https://doi.org/10.3390/app13021095

APA Style

Zhang, J., Liu, S., Yang, C., & Li, J. (2023). Experimental Study of the Self-Potential Response Characteristics of Anisotropic Bituminous Coal during Deformation and Fracturing. Applied Sciences, 13(2), 1095. https://doi.org/10.3390/app13021095

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