To explore the energy dissipation mechanism and damage evolution characteristics of rock specimens under compressive loading, we performed the acoustic emission (AE) testing under uniaxial compression in intact rock specimens and those with large-scale prefabricated cracks. The basic mechanical properties of both types of specimens were analyzed comprehensively, and the evolution patterns of strain energy indicators (total strain, elastic, and dissipative energies) in rock specimens before the peak on the stress-strain curve were identified. We further revealed the effect of the prefabricated crack dip angle, which controlled the surplus energy conversion of the following peak deformation and failure in the rock specimens. Using the modified equation of rock specimen damage evolution characterized by the AE energy and examining the fracture surface morphology via the scanning electron microscopy (SEM), the AE distribution law for rock specimen damage was revealed. An increase in the prefabricated crack dip angle was shown to reduce the peak stress and strain of rock specimens, which experienced a transition from the tensile and splitting failure mode to shear and slip one. Cracked rock specimens exhibited strain energy accumulation at the elastic deformation stage of the stress-strain diagram and rapid energy consumption at the plastic stage. By contrast, the intact rock specimens had a smoother energy evolution pattern. As the prefabricated crack dip angle increased, the dissipated and surplus strain energies’ shares increased. Moreover, the first peak of the AE energy occurred earlier, and the stress needed for its occurrence decreased as the dip angle increased. According to the damage evolution equation for rock specimens, their damage process can be subdivided into the initial damage, stable damage increase, and the accelerating damage increase stages. An increase in the prefabricated crack dip angle accelerated the damage accumulation in rock specimens. The locking effect of the sawtooth-like structures on the fracture surface was less conspicuous, and the fracture surface roughness increased. Thus, microcracks gradually developed, and rock specimens became more susceptible to sudden unstable failure.
Coal mining involves roadway tunneling and stoping of working face, which usually leads to the exposure of such macroscopic geological structures as faults and joints. These structures are sources of crack initiation and propagation, in which processes jeopardize the mining production safety and require in-depth analysis. In particular, multiple studies of these phenomena have been reported in China, where coal is considered the primary source of energy in the foreseeable future [
Zhao et al. [
Besides the energy input and dissipation observed during the loading of rock specimens, their damage occurs continuously. The damage accumulation finally induces the overall failure of the rock specimen. There are many ways to define the damage variable of rock specimens [
In the present study, intact rock specimens and those with large-scale prefabricated cracks were taken as the research objects. The uniaxial compression tests and AE monitoring were performed to analyze the prepeak total strain, elastic, and dissipative energy components during the stress-strain evolution. Evolutions of postpeak released energy and surplus energy under different prefabricated crack dip angles were also monitored and analyzed. The equation of rock specimen damage evolution characterized by the AE energy parameters was refined. SEM was employed to analyze the damage features of the intact and precracked rock specimens. The research findings provide theoretical guidance for disaster prevention and control of mining production safety.
All rock specimens used in the experiments were collected from the fine sand strata in the roof of the 11513 working face of the Panbei Coal Mine located in Huainan city, Anhui Province of China. The large-scale rock specimens collected on-site were processed into standard cylindrical rock specimens with a diameter of 50 mm and a height of 100 mm by using laboratory rock core drill, rock cutter, and grinding machine. The unevenness at both end faces of rock specimens did not exceed 0.05 mm. A total of twelve standard rock specimens were prepared and divided into four groups. Group 1 consisted of three intact rock specimens (R1, R2, and R3) while each of the remaining three groups contained three precracked rock specimens with crack dip angles of 30, 45, and 60°, respectively. The precrack dip angle was the included angle between the crack line and the end surface of the rock specimen. The precracks were made by cutting with a diamond-tipped cutter. The rock specimens in group 2 were numbered as 30°−R1, 30°−R2, and 30°−R3, respectively. The same intuitive numbering principle was used for specimens in groups 3 and 4. The rock specimen preparation results are depicted in Figure
Rock specimen’s processing and preparation.
The experimental setup included the loading control system, AE monitoring system, digital monitoring system, and SEM monitoring system, as shown in Figure
Loading and monitoring system.
The loading control system used an RMT-150B multifunction automatic rigid rock material testing servo machine. This system could realize conventional uniaxial and triaxial compression test modes, along with automated data collection, processing, and display of the stress-strain curve. The load was increased at the loading rate of 0.5 kN/s until the final fracture of rock specimens.
A DS5-16B multichannel full-wave AE signal analyzer was equipped for the AE monitoring system. This system could extract such characteristic parameters as AE energy and ring-down count. Four AE transducers were installed, and the coupling agent was applied between the AE transducers and the rock specimens. Before the tests, the system calibration was performed several times to adjust its accuracy. Finally, the AE transducers’ resonance frequency of 100–600 kHz, sampling rate of 3 MHz, preamplifier gain of 40 dB, and monitoring threshold value of 35 dB were preset.
A FlexSEM1000 scanning electron microscope, which could achieve a 60–300 K magnification and a 0.3–20 kV accelerating voltage, with a resolution of 4 nm, was applied in SEM examinations. A Nikon camera was provided for the digital monitoring system to capture the fracture morphology during the loading process.
Using the RMT-150B rock testing machine, stress-strain curves of the intact and precracked rock specimens were monitored and constructed during the loading process. For brevity sake, only four stress-strain curves of typical intact and precracked rock specimens are shown in Figure
Stress-strain curves of typical intact and precracked rock specimens.
As shown in the figure, stress-strain curves of typical intact and precracked rock specimens exhibited similar variation patterns. All of them underwent the compaction stage, elastic stage, plastic stage, and residual deformation stage. As the prefabricated crack dip angle increased, the peak strength and strain of rock specimens decreased. The stress-strain curves of the intact and precracked rock specimens presented the left-shifting and compression trend. This can be attributed to the fact that the prefabricated cracks were large-scale, which affected the structural integrity of rock specimens and increased the initial damage. As the prefabricated crack dip angle increased, the axial stress component acting on the rock specimens along the dip of the prefabricated cracks increased. Under the action of the intense shear stress at the crack tip, the original cracks propagated while new ones were formed as well, thus leading to the overall failure of rock specimens. As a result, the rock specimens’ peak strength and strain decreased, leading to a progressive aggravation of their brittle fracture on the macroscopic scale.
Taking a typical intact rock specimen as an example, the assessment of prepeak and postpeak strain energies can be based on the calculation principle illustrated by Figure
The energy conversion process of typical intact rock specimens: (a) strain energy calculation principle and (b) strain energy area.
It is assumed that the energy conversion between the RMT-150B rock testing machine and rock specimens does not involve heat exchange with the environment. Then, according to the first law of thermodynamics [
The averages of
According to the curve of one loading-unloading cycle of the uniaxial compression test, the prepeak unloading path is consistent with the loading curve slope. According to Hooke’s law [
The prepeak total energy consists of the elastic
The postpeak released energy
Some part of the prepeak elastic energy
The surplus energy can be converted into kinetic energy for rock ejection, inducing dynamic disasters. Based on the above calculation idea, the prepeak (total strain, elastic, and dissipative) energies, as well as postpeak (released and surplus) energies in typical intact rock specimens, were derived, as shown in Figure
Figure
The relationships between stress, prepeak strain energy, and strain in typical intact (a) and precracked rock specimens with crack angles of 30° (b), 45° (c), and 60° (d).
At each prepeak stage of the stress-strain curve, intact and precracked rock specimens also had similar variations in the prepeak strain energy components. Compaction stage: The dissipative energy in intact and precracked rock specimens increased nonlinearly as the rock specimen deformation was aggravated. Its value was higher than the elastic energy of rock specimens because the original cracks in rock specimens developed, consuming the absorbed energy. Elastic stage: As the original cracks closed, the elastic energy of the intact and precracked rock specimens gradually increased. After the elastic energy curve intersected with the dissipative energy curve (i.e., their values become equal), the elastic energy of precracked rock specimens increased at an accelerating rate. In contrast, the dissipative energy curve showed an inflection point for the downward trend. In intact rock specimens, both the elastic and dissipative energies increased stably. The reason was that the prefabricated cracks changed the initially uniform bulk stress state of rock specimens. The tips of the prefabricated cracks were more likely to store elastic energy, leading to the stress concentration phenomenon. Besides, at this stage, the total strain energy increased at a constant rate, and the dissipative energy decreased. Plastic stage: When the elastic energy accumulating at the prefabricated crack tips was larger than the surface free energy needed for crack development, the original cracks propagated. In the meantime, new cracks were formed, and an inflection point for an upward trend appeared on the dissipative energy curve. As the original and new cracks continued to propagate at the prefabricated crack tips, the elastic energy stored in rock specimens was consumed, leading to a sudden dissipative energy jump.
Figure
Curves depicting the relationship between the strain energy and precrack dip angle in typical intact and precracked rock specimens: (a) peak strain energy and (b) strain energy ratio (share).
Figure
As the precrack dip angle increased, the peak elastic energy share before the peak decreased while that of the dissipative energy increased. This implies that, with an increase in the precrack dip angle, the damage accumulates more intensively at the precrack tips. As a result, cracks propagate more rapidly, and rock specimens become more susceptible to failure. The surplus energy is mainly spent on the ejection failure of rock specimens. As the precrack dip angle increases, the peak surplus energy drops while the peak surplus energy share is increased. This happens because the brittle failure of rock specimens is intensified, and the postpeak released energy drops at larger precrack dip angles. Consequently, the main part of the elastic energy accumulated at the precrack tips is converted into surplus energy. In other words, rock specimens acquire higher kinetic energy upon failure, which is accompanied by severe ejection of the chipped and fragmented rock specimens. Thus, the cracking sounds are emitted and recorded by the AE system.
The prepeak dissipative energy peak value shares increase at larger precrack dip angles. Therefore, rock specimens are more susceptible to failure. The peak surplus energy share increases and rock specimens are more susceptible to ejection failure. In actual roadway excavation and stoping of the coal mine working face, when large-scale and large-dip-angle defects (geological structures, such as faults and joints) are exposed, the following precautions should be taken. The fragmentation of the surrounding defective rock masses should be prevented to ensure the safe advance of the roadway and working face; energy variation near the defects should be carefully monitored; and other appropriate countermeasures should be adopted to reduce the structural impact hazards.
Figure
The AE energy evolution during the entire loading process of intact (a) and precracked rock specimens with a dip angle of 30° (b), 45° (c), and 60° (d).
The occurrence of the first AE energy peak in intact and precracked rock specimens with dip angles of 30, 45, and 60° was revealed after 153, 101, 73, and 37 s, respectively. The corresponding axial stresses were 38.9, 25.7, 18.6, and 9.4 MPa, respectively. The first macroscopic crack (corresponding to the first peaks of AE energy and ring-down count) has appeared earlier, and the axial stress level required for the fracture was reduced with the dip angle. This result confirms the fact that the presence of prefabricated cracks significantly accelerates the failure of rock specimens.
The AE energy value is highly sensitive to the damage and fracture of rock specimens. It can intuitively reflect the initiation, propagation, and coalescence of cracks in rock specimens. Therefore, in this study, the AE energy was used as a characteristic parameter to reflect the damage evolution in intact and precracked rock specimens.
The equation of rock specimen damage evolution under uniaxial compression was elaborated based on the statistical damage theory:
Assuming that the strength of microbodies in rock specimens obeys the Weibull distribution [
In the triaxial compression test, rock specimens do not undergo complete failure due to the confining pressure, which contributes to their residual strength. However, in the uniaxial compression test, the rock specimens might still retain residual strength after the peak. The theoretical model depicting the relationship between the damage factor and AE parameters based on the Weibull distribution does not consider the residual strength after the failure of rock specimens under loading. Instead, it assumes that the complete failure of rock specimens occurs when
By incorporating the residual strength,
By introducing formulas (
The normalization method was used to convert the damage variable characterized by the cumulative AE energy in typical intact and precracked rock specimens. Thus, the damage evolution process of rock specimens under uniaxial compression was obtained, as shown in Figure
Damage evolution curves of typical intact and precracked rock specimens characterized by the AE energy.
It can be observed that the damage evolved in both types of rock specimens follows a similar trend, which can be subdivided into three stages. The initial damage stage: At this stage, rock specimens exhibit low damage degree, and the damage variable is approximately zero. The reason is that it corresponds to the compaction stage and early elastic stage of the stress-strain curve. The energy input into rock specimens is mainly consumed by the closure of precracks. The bulk stress state of rock specimens is relatively uniform, without the formation or propagation of new cracks. The stable damage increase stage: At this stage, the rock specimen damage increases nonlinearly with a high variation rate. This happens because it corresponds to the middle and late elastic and early plastic stages of the stress-strain curve. At this time, the original cracks in rock specimens are closed. As the stress imposed by the test machine gradually increases, the original cracks further propagate after reaching the ultimate state while new cracks are formed and start to propagate. The accelerating damage increase stage. This stage, characterized by a sharp increase in rock specimen damage, is very short. The reason is that it corresponds to the middle and later plastic stage and residual deformation stage of the stress-strain curve. Microcracks in rock specimens propagate and coalesce rapidly, forming a crack network with the interpenetration of cracks. Thus, rock specimens undergo macroscopic failure.
The comparative analysis of the damage evolution processes in typical intact and precracked rock specimens revealed that an increase in the precrack dip angle reduced the initial damage stage duration. The damage accumulated more rapidly, promoting the evolution of rock specimens toward a “sudden instability.”
Figure
SEM images of fracture morphology and fracture surfaces of typical intact (a) and precracked rock specimens with a dip angle of 30° (b), 45° (c), and 60° (d).
As the precrack dip angle is increased, the fracture mode of rock specimens changed from the tensile and splitting one to shear and slip fracture. There was a certain consistency in the macrofracture morphology and mutual conversion between different strain energy forms in rock specimens. Larger precrack dip angles promoted the ultimate energy storage ability exhaustion and increased the shear stress concentration at the precrack tips. Therefore, precracked rock specimens underwent fast shear and slip failure.
The morphological features of the fracture surfaces of typical intact and precracked rock specimens were instrumental in determining the damage and failure evolution patterns on the microscopic scale. The intact rock specimens had flat fracture surfaces with multiple sawtooth-like (jagged) structures. The latter structures could lock into and rub against each other, thus inhibiting the rock specimen’s failure to a certain degree. As the precrack dip angle increased, sawtooth-like structures became smaller, and fracture surfaces became uneven, with developed microcracks. The above results confirm that larger precrack dip angles make specimens more susceptible to “sudden” failure, which is in concert with the damage evolution characteristics of rock specimens characterized by the AE energy.
During the uniaxial compression tests of rock specimens with small-scale prefabricated cracks [
The results obtained made it possible to draw the following conclusions. Rock specimens with inclined precracks exhibited alterations in the compressive strength and deformation features, as compared to intact ones. With an increase in the precrack dip angle, their fracture mode changed from the tensile and splitting one to shear and slip fracture. In precracked rock specimens, the energy storage at an accelerating rate was observed at the elastic deformation while rapid energy dissipation occurred at the plastic stage. Both the prepeak dissipative energy and postpeak surplus energy shares in the total energy increased with the precrack dip angle. This indicates higher kinetic energy for the ejection of rocks, causing rock specimen fragmentation. Meanwhile, the kinetic energy in intact rock specimens rose more gradually. Based on the derived damage evolution equation, the rock specimens’ damage process was subdivided into (i) the initial damage stage, (ii) stable damage increase stage, and (iii) the accelerating damage increase stage. As the precrack dip angle increased, the first peak of AE energy occurred earlier, and the corresponding stress level provided by the test machine was reduced. The damage in rock specimens accumulated at an accelerating rate. The sawtooth-like structures on the fracture surface were less likely to lock into each other. The fracture surface became uneven, and microcracks gradually developed. As a result, the rock specimens were more susceptible to the “sudden” failure.
The data used for conducting classifications are available from the corresponding author authors upon request.
The authors declare that they have no conflicts of interest.
The authors acknowledge the financial support for this work provided by the National Natural Science Foundation of China (Grant no. 51634007) and the Graduate Innovation Fund Project of Anhui University of Science and Technology of China (2019CX1003).