Gaining a comprehensive understanding of the dynamic mechanical properties of deep coal rock is highly important for ensuring the safe design and evaluation of coal rock engineering. This paper conducted triaxial coal samples using SHPB loading experiments on deep Using the split Hopkinson pressure bar to test coal samples test equipment, under various situations. The findings indicate that the stress-strain curves of coal subjected to coupled triaxial dynamic-static loading exhibit a consistent pattern. The stress-strain curves did not exhibit a compaction phase because of the initial axial prestress. Furthermore, the dynamic peak stress and secant modulus of the deep coal samples exhibited a linear increase as the constraint pressure and strain increased, followed by a decrease as the axial prestress increased. The threshold pressure for alterations in axial prestress is approximately 8 MPa (equivalent to 44% of the compressive strength). Amount of energy taken in by the deep coal samples during impact loading varies with the rise of axial static prestress at the same strain rate and confining pressure. Initially, it increases and then declines. Axial static tension grows as increased, the coal samples transitioned from experiencing shear damage to experiencing a combination of shear and tension damage. This study aims to provide guidance for preventing coal rock dynamic disasters and assessing the stability of mining engineering.
Research Article
Dynamic mechanical properties of deep coal rocks under three-dimensional dynamic and static loading
https://doi.org/10.21203/rs.3.rs-4974693/v1
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Deep coal rock
Dynamic mechanical properties
SHPB
Axial static prestress
As a result of the depletion of superficial mineral resources, mining operations have expanded to deeper levels at With an annual pace of 10 to 25 meters [1–3]. Consequently, deep coal and rocks go through a process of significant axial the pre-stress of static and circumferential stress prior to being disrupted by mining activities, earthquakes, and other dynamic forces [4–5].The occurrence circumstances of deep coal and rock are highly complicated, leading to an increased frequency of dynamic disasters such as rock explosions and roadway collapses during the mining process [6–7]. It is illogical to immediately apply the theory of shallow rock mechanics to deep coal and rock mining for the purpose of prevent deep calamities caused by coal and rock dynamics and assess the stability of deep coal and rock mining engineering [8]. Hence, it is highly valuable in the field of engineering and holds significant scientific importance to pursue a rational explanation regarding the features of the dynamic mechanical system and constitutive relationships of deep coal and rock.
Recently, several international conferences have started to focus on the field of "dynamic rock mechanics". There has been significant interest in this field and many research findings have been obtained [9]. Multiple research findings suggest that the dynamic the rock's mechanical characteristics include: dynamic peak strength, elastic modulus, absorbed energy, and other dynamic parameters, are subject to a substantial amount of impact from Multiple research findings suggest that the dynamic the rock's mechanical characteristics include: dynamic peak strength, elastic modulus, absorbed energy, and other dynamic parameters, are subject to a substantial amount of impact from the rate at which the material is deforming and the pressure applied to the material from all sides.Specifically, these properties tend to increase as the rate at which the material is deforming and the pressure applied to the material from all sides increase [10–14]. However, as the extraction of natural resources reaches greater depths, the composition and structure of the in-situ stress on deep coal and rock will undergo alterations. Vertical stresses are above horizontal stresses when mining operations are carried out at too great a depth [15–16]. Hence, in following the completion of a research of the dynamic mechanical component characteristics of deep coal and rock, it is crucial to take into account not only the impact of elevated confining pressure but also the early axial static pre-stress. Li [17] summarized the engineering challenges in deep coal rocks as rock mechanics in static and dynamic environments. The advancement of dynamic rock mechanical test methods has significantly facilitated the study of deep rock dynamics of the mechanical system and its characteristics under combined dynamic and static loads, as evidenced by recent studies [18–20]. Interestingly, in the course of conducting the study, it was found that the mass of rock materials subjected to a mixture of static and dynamic loads is affected by axial pre-stresses It has been found that if the axial static pre-stress is below a critical value, it will impede fractures in coal and rock that have grown larger over time. As a result, this enhances the rate at which the material is deforming and the pressure applied from all sides, including peak strength that is dynamic, elastic modulus, dissipated energy, and fractal dimension. On the contrary, if the axial static state is too large or even exceeds a specific value, it will lead to the continuous expansion of the gaps in the coal rock and ultimately reduce its dynamic mechanical properties. [21–24]. Numerous researchers have conducted corresponding studies, and the results have shown that the dynamic mechanics of deep rocks are individually affected by a variety of factors such as axial static progression and strain rate According to the research, it is found that the dynamic mechanical properties of deep rocks in actual engineering are affected by the combined effect of many factors, rather than a factor acting alone. Historically, numerous studies disregarded the impact of axial Static pre-stress applied to the dynamic mechanical system characteristics of deep coal and rock. This implies that the previous research theory is not effectively applicable to engineering practice. This study utilized an enhanced Hopkinson (SHPB) experimental system to conduct impact load experiments on deep coal and rock. The objective is to observe how factors such as strain rate, axial static stress, and residual strength interact with each other to affect the dynamic mechanical properties of the coal rock at depth under three-dimensional combined dynamic and static conditions Furthermore, utilizing the statistical damage theory and viscoelastic model, we developed a comprehensive three-dimensional dynamic constitutive model for deep coal and rock subjected to impact loads. The model systematically analyzed the impact of axial static pre-stress, strain rate, residual strength, and putting strain on the dynamic mechanical characteristics of deep coal yet limiting their range and rock. This analysis provides valuable insights for preventing catastrophes that are dynamic in deep coal and rock formations and evaluating the stability of mining engineering projects in these formations.
2.1 Coal sample preparation
Samples of coal that were used in this experiment were chosen from a coal mine located in Guizhou Province, China. The coal samples belonged to the coking coal category. In order to reduce experimental error, the coal samples were collected from a consistent depth of 400 meters. Ultimately, the coal samples in the shape of a cylinder fifty millimeters in diameter and thirty millimeters in height were acquired. Figure 1 displays the coal sample.
In order to examine the variations in dynamic mechanical characteristics of coal samples, the test was conducted with three distinct groups. Each group consisted of 5 coal samples, resulting in a total of 15 coal samples. The variations were analyzed under varied axial static pre-stress, strain rates, and confining pressures. Group A exhibits varying levels of axial static pre-stress while maintaining same confining pressure and impact speed. Group B exhibits varying impact velocities while maintaining identical confining pressure and axial static pre-stress. Conversely, group C demonstrates variable confining pressures while maintaining the same impact velocity and axial static pre-stress. Group A has a confining pressure of 6MPa, an impact velocity ranging from 7.389m/s to 7.757m/s, and axial static pre-stress values of 4MPa, 6MPa, 8MPa, 10MPa, and 12MPa, respectively. The axial static pre-stress values correspond to the static compressive strengths of 22%, 33%, 44%, 55%, and 66% correspondingly. Group B has a confining pressure and axial static pre-stress of 6MPa, and an impact velocity ranging from 7.689 to 14.568 m/s. Group C exhibits an axial static pre-stress of 10MPa, an impact velocity ranging from 6.539-7.647m/s, and varying confining pressures of 4MPa, 6MPa, 10MPa, and 12MPa. However, the C-1 coal sample is subjected to standard impact conditions.This is the link between the rate of strain and the velocity of impactis linear, meaning that increasing the impact velocity will result in a corresponding change in strain rate [26].
Before the three-dimensional static and dynamic test, the sample is first tested statically. The results of this test revealed that the uniaxial compressive strength was 18 MPa, the elastic modulus was 4.164 GPa, and the Poisson's ratio was 0.33.
2 Experimental system and operation procedure
This experiment utilized a modified separate Hopkinson pressure bar (SHPB) triaxial dynamic and static test setup. The bullet, incident bar, and reflect bar of the device are constructed from alloy steel. The bullet has a length of 400mm, the incident bar has a length of 3000mm, and the reflect bar has a length of 2500mm. All three components have a diameter of 50mm. The alloy steel used has an elastic modulus of 206GPa and a density of 7.74 g/cm3. Figure 2 depicts the physical system.
Different stress states have an impact on the dynamic mechanical properties should be considered of deep coal and rock. By methodically investigating the dynamic mechanical characteristics and constitutive connections between coal and rock at various strain rates, confining pressures, and axial static prestresses, it is possible to mitigate the risk of dynamic disasters such as rock bursts and roadway collapses. The preceding experiments provide data on the dynamic peak strength and secant modulus of coal samples under various conditions. The results of these tests are presented in Table 1.
| Sample number | Confining pressure/(MPa) | Axial static prestress/(MPa) | Mean strain rate/(s− 1) | Peak stress /(MPa) | Secant modulus /(GPa) |
|---|---|---|---|---|---|
| A-1 | 6 | 4 | 91.780 | 44.404 | 27.971 |
| A-2 | 6 | 6 | 71.010 | 52.457 | 19.573 |
| A-3 | 6 | 8 | 79.455 | 63.679 | 51.058 |
| A-4 | 6 | 10 | 81.450 | 57.576 | 35.620 |
| A-5 | 6 | 12 | 89.844 | 45.369 | 11.257 |
| B-1 | 6 | 6 | 74.535 | 59.298 | 28.861 |
| B-2 | 6 | 6 | 111.437 | 76.361 | 16.162 |
| B-3 | 6 | 6 | 148.645 | 91.241 | 34.101 |
| B-4 | 6 | 6 | 155.321 | 102.659 | 38.662 |
| B-5 | 6 | 6 | 236.154 | 110.454 | 94.729 |
| C-1 | 0 | 0 | 94.808 | 33.160 | 10.285 |
| C-2 | 4 | 10 | 86.986 | 41.718 | 16.695 |
| C-3 | 6 | 10 | 91.780 | 44.404 | 26.950 |
| C-4 | 10 | 10 | 80.287 | 49.761 | 48.884 |
| C-5 | 12 | 10 | 99.116 | 62.699 | 81.949 |
The data in this test was processed using the three-wave approach with the SHPB data processing program. The test data's validity relies on two fundamental hypotheses: the hypothesis of pressure in a single dimension waves and the premise of Place an emphasis on homogeneity. The stress wave that is just one-dimensional theory is mostly utilized to mitigate the dispersion impact of stress waves during propagation. This is achieved by incorporating a pulse shaper and modifying the width of the incident bar [27–28]. To validate the quality of the test data, the stress uniformity hypothesis was examined using Eq. (1). This equation states that the combined value of strain that is reflected and strain that is incident should be equal to the transmitted strain [29]. The data from coal sample A-1 are utilized for the purpose of verification, and the outcomes of the verification are depicted in Fig. 3.
Where εi(t), εr(t), and εt(t) are the incident strain, reflected strain, and transmitted strain at a certain time, respectively.
3.1 Strength characteristics
The strength quality of coal is mainly affected by strain rate, confining pressure and axial static prestress [30–31]. [30–31]. According to the findings of experiments, The stress-strain curves of coal rock subjected to many different factors are shown in Fig. 4.
Figure 4 illustrates the stress-strain curves of coal rock when subjected to both three-dimensional dynamic and static loads. These curves exhibit a consistent pattern, which may be categorized into three distinct phases: the phase of elastic motion, the period of plastic motion, and the post-peak damage period. During the elastic stage, the stress exhibits a linear relationship with the strain, meaning that as the strain grows, the stress also increases proportionally. During the plastic phase, the tension gradually rises as the strain increases, leading to permanent plastic deformation of the coal sample. With the increasing stress, at the end of the plastic movement stage,, the tension reaches its maximum level. During the post-peak damage stage, the stress does not completely decline to zero as the strain increases. However, there is still some bearing capacity, which suggests that The strength that is still present should be taken into consideration. While studying the dynamic constitutive connection of coal rock. The stress-strain curves exhibit variations when both confining pressure and axial static prestress are applied, as compared to typical impact circumstances observed in the C-1 coal sample. During typical circumstances of impact, the stress-strain curves were observed.exhibit a phase of compaction, meaning that the curves are concave upwards. The phenomenon occurs due to the compaction of coal samples when they are subjected to impact loading, which is caused by the presence of confining pressure and axial static prestress. Consequently, the coal sample undergoes no compaction phase when subjected to three-dimensional combined dynamic-static pressure, and instead instantly transitions into the stage of elastic deformation.
By analyzing the information presented in Table 2, we can derive the graphs illustrating the link between the dynamic peak and the stress and axial static prestress, as seen in Fig. 5, the strain rate and the confining pressure are both represented. Figure 5 (a) demonstrates that as the axial static prestress increases from 4 to 8 MPa (equivalent to 22%σc to 44%σc), the fractures in the coal are consistently compressed, resulting in an improvement in dynamic compressive strength. Hence, the use of axial static prestress enhances the dynamic peak strength. Furthermore, when the axial static prestress is within the range of 8 to 12MPa (equivalent to 44%σc to 66%σc), the dynamic peak compressive strength falls as the axial static prestress increases. Additionally, the axial static prestress facilitates increases the dynamic peak compressive strength while simultaneously causing crack expansion. Hence, the coal samples exhibit a critical axial static prestress of 8MPa, which corresponds to 44% of the compressive strength (σc). Figure 5 (b) demonstrates a direct correlation between the strain rate and the dynamic peak stress of the coal rock, indicating that the strain rate is increased, the stress rises in a linear fashion. This phenomenon is a result of the coal samples being loaded quickly, leading to numerous fissures in the coal that do not have enough time to grow when the rock breakup occurs. By observing Fig. 5(c), it is evident that the dynamic peak stress of coal and rock exhibits a linear increase as the confining pressure increases. The presence of restricting pressure during impact loading limits the expansion of internal fissures in the coal rock. Thus, when subjected to both dynamic and static loading in three dimensions, the dynamic peak stress of coal and rock rises proportionally to the increase in confining pressure. Based on the study conducted, it is evident that the dynamic compressive strength of coal is significantly influenced by axial static prestress, strain rate, and confining pressure.
3.2 Deformation characteristics
The deformation properties of rocks are typically described using parameters such as elastic modulus and secant modulus [32]. However, the subjective nature of the elastic modulus value is a limitation. Figure 6 illustrates the variation of the secant modulus under various stress conditions.
As depicted in Fig. 6(a), the correlation coefficient is merely 0.507 when using a quadratic function of one variable to fit the relationship between the secant modulus and the axial static pre-stress. However, it is evident that the secant modulus generally exhibits When the axial static pre-stress was altered, there was an initial rise, which was then followed by a drop. Figures 6 (b) and 6 (c) illustrate a linear relationship between the secant modulus and both the rise in confining pressure and strain rate. Additionally, the fitting coefficient shows a relatively high value. Through the analysis of the correlation between the dynamic secant modulus of coal and rock under various stress conditions, it can be inferred that coal's dynamic compressive strength is a measure of its and rock under combined three-dimensional dynamic and static loading is significantly influenced by axial static pre-stress, strain rate, and confining pressure.
3.3 Energy dissipation and failure mode analysis
The Structural changes and destruction of coal rock is a process of energy transfer.. The macroscopic deformation of coal and rock occurs due to the buildup of internal microfracture destruction [33–34]. Hence, it is significant to examine the distortion and harm caused to coal and rock when subjected to three-dimensional dynamic and static forces, taking into account the energy aspect. Given the absence of heat transfer between coal and the surrounding environment during the experiment, the incident energy (Wi), reflected energy (Wr), transmitted energy (Wt), and absorbed energy (Wd) of coal and rock specimens under three-dimensional dynamic and static combined loading can be determined using Eq. (2) [35].
$$\left\{ \begin{gathered} \mathop W\nolimits_{i} =\frac{A}{{{C_0}{\rho _s}}}\int_{0}^{t} {\sigma _{i}^{2}\left( t \right)} dt=\frac{{A{E^2}}}{{{C_0}{\rho _s}}}\int_{0}^{t} {\mathop \varepsilon \nolimits_{i}^{2} \left( t \right)dt} \hfill \\ \mathop W\nolimits_{r} =\frac{A}{{{C_0}{\rho _s}}}\int_{0}^{t} {\sigma _{r}^{2}\left( t \right)} dt=\frac{{A{E^2}}}{{{C_0}{\rho _s}}}\int_{0}^{t} {\mathop \varepsilon \nolimits_{r}^{2} \left( t \right)dt} \hfill \\ \mathop W\nolimits_{t} =\frac{A}{{{C_0}{\rho _s}}}\int_{0}^{t} {\sigma _{t}^{2}\left( t \right)} dt=\frac{{A{E^2}}}{{{C_0}{\rho _s}}}\int_{0}^{t} {\mathop \varepsilon \nolimits_{t}^{2} \left( t \right)dt} \hfill \\ \mathop W\nolimits_{d} =\mathop W\nolimits_{i} - \left( {\mathop W\nolimits_{r} +\mathop W\nolimits_{t} } \right) \hfill \\ \end{gathered} \right.$$
2
Let Wd, represent the absorbed energy, Wi represent the incident energy, Wr represent the reflected energy, and Wt represent the transmitted energy. E0 represents the elastic modulus of both the incident bar and the transmitted bar. C0 is the propagation velocity of the stress wave in the bar. A0 represents the cross-sectional area of both the incident bar and the transmitted bar.
This study focuses solely on examining the correlation between various axial static pre-stress levels and coal and rock crushing energy consumption. It specifically explores this relationship under the dynamic and static loading characteristics that are coupled in three dimensions. Previous studies have already investigated the connection between coal rock crushing energy consumption and strain rate and confining pressure. By inputting the initial test data into Eq. (2), For different axial static pre-stress circumstances, we may determine the incident, reflected, transmitted, and absorbed energies of coal rock.These results are presented in Table 2.
| Axial prestress/(MPa) | Sample number | Incident energy/J | Reflected energy/J | Transmittedenergy/J | Absorbed energy/J |
|---|---|---|---|---|---|
| 4 | A-1 | 380.573 | 167.380 | 28.448 | 184.746 |
| 6 | A-2 | 297.181 | 107.855 | 40.627 | 148.699 |
| 8 | A-3 | 424.328 | 127.353 | 64.688 | 232.287 |
| 10 | A-4 | 414.505 | 119.865 | 52.136 | 242.504 |
| 12 | A-5 | 362.683 | 151.102 | 26.578 | 185.004 |
Controlling the impact velocity of several coal samples to be precisely equal is challenging during the SHPB experiment. Table 3 clearly demonstrates a considerable disparity in the incident energy between the A-2 coal sample and the other 4 coal samples. This indicates a substantial difference in the impact velocity of the A-2 coal sample compared to the other 4 coal samples. Hence, the experimental data from the A-2 coal sample is disregarded when analyzing the correlation between absorbed energy of coal and rock and axial static pre-stress. By analyzing the data shown in Table 3, it is possible to determine the correlation between the absorbed energy of the coal sample and the axial static pre-stress when subjected to both loading in three dimensions is both dynamic and static. This relationship is seen in Fig. 7.
Figure 7 clearly demonstrates that the absorbed energy initially increases and subsequently drops as the axial static pre-stress of coal samples is subjected to combined three-dimensional dynamic and static loads. The fitting curve follows a quadratic function with one variable. At an axial static pre-stress of 4MPa (equivalent to 22% of the compressive strength), the expansion of cracks will be impeded because to the relatively low magnitude of the axial static pre-stress. The fissures in the coal and rock are compressed, and a portion of the energy from the axial impact load is utilized to counteract the axial static prestress. Consequently, the energy received by the coal sample during this phase is comparatively minimal. The energy absorbed by the coal sample reaches its greatest value when the axial static pre-stress is 8MPa (44% of the compressive strength) and 10MPa (55% of the compressive strength), and the axial static pre-stress approaches the critical value. Moreover, if the axial static pre-stress of the coal sample surpasses the critical threshold, the existence of such pre-stress will facilitate the propagation of cracks during this phase. As the axial static pre-stress increases, the coal sample absorbs less energy from the impact load over time.
So that we may look into the correlation between failure modes of coal and rock and various levels of axial static pre-stress, both three-dimensional dynamic and static loading were used. Figure 8 illustrates the distinct failure modes of coal and rock at varying levels of axial static pre-stress. From Fig. 8, it is evident that when the axial static pre-stress increases, the failure degree of the coal sample initially rises and then declines, whereas the crushed particle size initially reduces and then grows. When the axial static pre-stress is 4MPa (equivalent to 22% of the compressive strength), the primary failure mode observed in the coal sample is shear failure. Due to the low axial pressure of the coal sample, the stored strain energy is also minimal, resulting in a limited degree of fracture. When the axial static pre-stress is 8MPa (44% of the compressive strength) and 10MPa (55% of the compressive strength), the primary failure mode of the coal sample is a combination of shear and tensile failure. Here, the coal sample experiences a significant axial pressure, leading to a higher amount of strain energy being stored in the sample. When the coal sample is exposed to an impact load, the degree of damage is likewise greater. Furthermore, when the axial static pre-stress reaches 12MPa (equivalent to 66% of the compressive strength), the primary form of failure observed in the coal sample is a combination of shear and tensile failure. While the axial static pre-stress is currently the highest, the coal sample absorbs a relatively little amount of energy from the impact load. As a result, the damage to the coal sample diminishes and the level of fragmentation increases.
The SHPB test equipment was utilized to perform impact testing in three dimensions, both dynamic and staticon deep coal rocks, varying the strain rates, axial static prestresses, and confining pressures. The dynamic mechanical characteristics of deep coal and rock were measured. This study examines the dynamic properties of deep coal and rock under various stress conditions, including strength, deformation, energy dissipation, and damage patterns. The primary findings of this document can be summarized as follows:
(1) The stress-strain curve of coal rock under the combined three-dimensional dynamic and static loads follows a similar variation trend, which may be categorized into three stages: elastic stage, plastic stage, and post-peak failure stage. Additionally, the presence of initial axial static pre-stress and confining pressure eliminates the compaction stage in the stress-strain curve.
(2) The peak stress and modulus of deep coal rock grow in a linear manner as the confining pressure and strain rate increase, respectively. They exhibit an initial increase followed by a drop when the axial static pre-stress increases, indicating a variation consistent with a quadratic equation. When the axial static pre-stress is within the range of 4 to 8 megapascals (equivalent to 22–44% of the compressive strength), it can enhance the dynamic peak strength. When the axial static pre-stress is within the range of 8 to 12 megapascals (44–66% of the compressive strength), it enhances the propagation of cracks and reduces the peak compressive strength under dynamic conditions. Hence, the crucial axial static pre-stress of deep coal and rock amounts to 8MPa, which is equivalent to 44% of the compressive strength (σc).
(3) When the rate of strain and the confining pressure are both remain constant, the energy absorbed by deep coal rock after dynamic impact the initial rise is followed by a drop as the quantity axial static pre-stress increases. Additionally, the failure mode of deep coal rock transitions from shear failure to shear.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Author Contribution
Ren feng：Investigation, Data curation, Methodology, Writing – original draft. Yao chunlei：Supervision, Conceptualization, Funding acquisition, review & editing. Wang jie：sources, Project administration, Funding acquisition, Supervision. Bao jiming：Investigation. Shilang. Chen hua: Software, review & editing.Guangchao Wei: Software, review & editing
Acknowledgments
This paper was supported by the Guizhou Provincial Program on Commercialization of Scientific and Technological Achievements [2023] general 108, China.
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No competing interests reported.