Experimental Study on Pressure Relief Mechanism of Variable-Diameter Borehole and Energy Evolution Characteristics of the Surrounding Rock

Abstract

Conventional borehole pressure relief can meet the requirements for preventing rock bursts, but it can also easily destroy the roadway, resulting in system support failure. Taking coal-like samples with boreholes as the research object, the pressure relief effects of the same-diameter boreholes and variable-diameter boreholes are compared and analyzed by a uniaxial compression test. The joint pressure relief mechanism of the variable-diameter drilling hole is discussed. The experimental results show that the stress–strain curve of variable-diameter drilling sample occurred the phenomenon of pre-peak stress drop and post-peak stress plateau, which indicates that the variable-diameter drilling hole can enhance the plastic characteristics of coal-like samples. The borehole size dramatically influences the variation of various pressure relief indexes. The evolution law of AE counting the pre-peak and post-peak of borehole samples verified the abovementioned law. Variable-diameter drilling can enhance the plasticity of samples, weaken the brittleness and reduce the impact tendency. Under the maximum size of the variable-diameter drilling hole and the same-diameter drilling hole is same, the pressure relief effect is more significant. The results obtained in this paper can provide a new theoretical basis and technical guidance for borehole pressure relief and roadway support.

1. Introduction

With the depletion of shallow underground coal resources, the development of coal resources in China turned to deeper sources. However, rock bursts become frequent in the deep underground environment [1,2,3]. Borehole pressure relief technology has the advantages of simple on-site construction, fast construction speed, and strong adaptability to geological conditions. It has been widely used in rock burst mines [4,5]. Many scholars have carried out a lot of research on borehole pressure relief technology. Li et al. [6] simulated the strain energy distribution characteristics of coal bodies under different borehole pressure relief parameters and optimized the borehole pressure relief parameters in the step area. Lu et al. [7] studied the composite dynamic disasters by the new proper triaxial test methods; the results have guidance value for the prevention and control of composite dynamic disasters in deep coal mines. Cai et al. [8] proposed a new evaluation index by analyzing the strain energy transfer laws during coal impact in coal mining. Zhai et al. [9] believe that large-size boreholes are more suitable for stressing elimination. Wu et al. [10] found that borehole shape could change mechanical properties and affect the crack initiation and propagation characteristics of samples. Zhang et al. [11] proposed a new monitoring technology while drilling, which is of great value for the monitoring of deep wells, the abutment pressure distribution, and the evaluation of the pressure relief effect. Liang et al. [12] found that the larger the diameter, the better the pressure relief effect and the drilling changed the failure mode of samples. Peng et al. [13] studied the arrangement of boreholes on rock’s mechanical behavior, and the results proved that the arrangement of boreholes can change the evolution characteristics of AE and the failure mode of rock. Zhang et al. [14] conclude that the more significant the drilling density, the better the pressure relief effect by uniaxial compression of drilling samples; on this basis, a new method for the optimal layout parameters of borehole pressure relief is proposed. Zuo et al. [15] analyzed the deformation and failure behavior of rock–coal–rock assemblage containing weak coal interlayer, and the mechanism affecting the failure of the assemblage was revealed.

Meng et al. [16] studied the energy evolution characteristics of sandstone treated by different loading rates and proposed a method of the effective equivalent energy surface. Huang et al. [17] conducted uniaxial compression tests with different loading rates on composite coal–rock, and the influence law of loading rate on each stage of the sample was obtained. Wang et al. [18] studied the change law of impact propensity of drilled coal samples; they found that drilling methods changed the failure mode of samples, and the more rows of drilling holes, the weaker the tendency of rock bursts. Zhang et al. [19] studied the layout parameters of large-diameter boreholes and established multiple evaluation index systems for evaluating the layout of drilling holes with different diameters on the effect of reducing rock bursts.

The above scholars have conducted a lot of research on the mechanism and the effect of borehole pressure relief, the results of which are significant to prevent rock bursts. However, there are few reports on the research of variable-diameter drilling to prevent rock bursts. In fact, the surrounding rock of the deep roadway can be seriously damaged by excavation [20,21,22,23]. Even conventional borehole pressure relief can prevent the occurrence of rock bursts, but it can easily damage the roadway support system, resulting in support failure. Reducing the damage to the roadway support system while ensuring the pressure relief effect occurs is a significant problem in deep safety mining. Therefore, the mechanical tests and theoretical analysis of coal-like samples with the same-diameter drilling and variable-diameter drilling were carried out respectively. The pressure relief effect and mechanism of variable-diameter drilling boreholes was analyzed and discussed. It lays a foundation for researching the prevention and control of rock bursts by variable-diameter drilling. The results obtained in this paper can provide a new theoretical basis and technical guidance for borehole pressure relief and roadway support.

2. Materials and Methods

2.1. Test Program with Coal-like Methods

Because coal samples obtained on-site have many natural cracks, holes, and other defects, discreteness provides poor conditions for repeated tests. Therefore, coal-like materials are used in this paper. The feasibility of coal-like samples to simulate raw coal was proved by many scholars [14,18]. After numerous proportioning test results, it is found that the mechanical properties of coal-like samples are similar to that of raw coal when the water–gypsum ratio is 0.45 (water–gypsum ratio refers to the mass ratio of water to gypsum), so a water–gypsum ratio of 0.45 makes for the most suitable test sample. (For the convenience of description, the sample from the side with small-size drill holes is referred to as part A, and the sample from the side with large-size drill holes is referred to as part B.)

Manufacturing steps of coal-like materials:

• Put the gypsum material with the ratio of 0.45 into the mold and use the vibrating screen to drive out the air from gypsum materials (50 mm × 100 mm × 200 mm).
• In order to make the surface of the sample flat, using a scraper to scrape off the excess gypsum material above the mold.
• Demold the preliminary formed coal-like samples, and place the molded coal-like samples in a curing box (25 °C) for 28 days.
• Polish the samples’ upper and lower end faces to make the flatness difference of the end faces less than 0.05 mm.
• GSB600RE electric drill is used to drill holes with different sizes; stick the drilling samples into composite samples of same-diameter drilling and variable-diameter drilling with different sizes through a strong viscous adhesive. Typical samples are shown in Figure 1, and the specific parameters are shown in

  Table 1. Experimental design.

  Borehole Shape	Borehole Size (mm)	Number of Drilling Samples of Each Size	Number of Boreholes	Drilling Depth (mm)
  $\mathrm{Same-}\mathrm{diameter} \mathrm{drilling} ({\Phi }_1–{\Phi }_1$)	8–8, 14–14, 18–18, 22–22	3	1	100
  $\mathrm{Variable-}\mathrm{diameter} \mathrm{drilling} ({\Phi }_1–{\Phi }_2$)	8–14, 8–18, 8–22

  (notes: 8–8 represents the same-diameter borehole sample with a borehole diameter of 8 mm; 8–14 represents the variable-diameter borehole sample with a borehole diameter of 8 mm and 14 mm, and other samples are the same as above). The schematic diagram of the drilling sample is shown in Figure 1, mold as shown in the Figure 2 and specific borehole parameters are shown in Table 1.

We considered the effect of bonding on the mechanical properties of samples, so we compared the mechanical properties of intact and composite samples. It is found that bonding has little effect on the mechanical properties of the samples.

As shown in Figure 3, the compressive strength of the intact sample was 15.2 MPa and the peak strain was 0.0083. The compressive strength of the composite sample was 14.6 MPa and the peak strain was 0.0092. It can be seen that the bonding has little effect on the mechanical properties of the samples.

2.2. Test Loading Scheme

Shimadzu AG-X250 rock mechanics testing machine was used for the uniaxial compression test, as shown in Figure 4. Displacement loading mode was adopted, and the loading rate is 0.02 mm/s. The test is equipped with the AE system for synchronous monitoring, and the monitoring threshold of the AE system was set to 45 dB. Before the experiment, apply an appropriate amount of couplant on the contact surface between the sample and the AE probe to ensure the accurate acquisition of AE signals. The samples are shown in Figure 5.

3. Pressure Relief Effect of Borehole Pressure Relief with Variable-Diameter

3.1. Evaluation Index of Pressure Relief Effect

The pressure relief effect of the sample cannot be judged only by the strength of the sample, which lacks strictness. The loading and failure process of the specimen is the process of energy input and dissipation. Therefore, to better evaluate the pressure relief effect of variable-diameter boreholes, this paper introduces energy-related indicators to comprehensively evaluate the pressure relief effect of boreholes.

(1)

Pre-peak strain energy [14].

The pre-peak strain energy can better reflect the sample’s ability to accumulate elastic energy before the peak stress, the lower the ability of the sample to store elastic energy, and the lower the possibility of generating larger impact energy during a failure. The curve in Figure 6 is the stress–strain curve of the sample, and U is the pre-peak strain energy, which is given by:

$$U={{\displaystyle \int }}_0^{{\epsilon }_1}{\sigma }_{1}d\epsilon$$

(1)

(2)

Energy dissipation index.

According to the research needs, the energy dissipation index is redefined in this paper. Where $K_E$ is the ratio of the difference between the pre-peak strain energy ($U_a$) of the small borehole sample and the pre-peak strain energy ($U_b$) of other borehole samples to the pre-peak strain energy of the small borehole sample, which is given by:

$$K_E=\frac{U_a-U_b}{U_a}$$

(2)

where: $K_E$ represents the amount of energy dissipation during the loading process of the sample. In the case of excluding other energy losses, the larger the $K_E$, the better the pressure relief effect of the sample.

(3)

Strength reduction index.

The strength reduction index is defined as the ratio of the difference between the compressive strength of small borehole samples and that of other borehole samples to the compressive strength of small borehole samples (in this paper, samples numbered 8–8 are defined as small borehole samples), which is given by:

$$K_{\sigma }=\left({\sigma }_2-{\sigma }_o\right)/{\sigma }_2$$

(3)

where: ${\sigma }_2$ is the compressive strength of small borehole sample; ${\sigma }_3$ is the compressive strength of other drilled samples.

(4)

Post-peak strain energy release rate.

In order to better compare the effect of variable-diameter drilling on the post-peak strain energy of the sample, the post-peak strain energy release rate is used to characterize the post-peak energy evolution of the sample, which is given by:

$$U_t={{\displaystyle \int }}_{{\epsilon }_1}^{{\epsilon }_2}{\sigma }_{1}d\epsilon$$

(4)

$$W_t=\frac{\Delta U_t}{\Delta t}$$

(5)

where: ${\epsilon }_1$ is the peak strain of the sample, ${\epsilon }_2$ is the strain corresponding to the residual strength of the sample, $U_t$ is the post-peak strain energy of the sample, and $W_t$ is the post-peak strain energy release rate of the sample.

3.2. Result and Discussion

As shown in Figure 7, the stress–strain curves of samples with the variable-diameter borehole and the same-diameter borehole can be divided into four stages: compaction stage, elastic stage, yield stage and failure stage. However, the pre-peak curve of sample with the variable-diameter drilling fluctuates more intensely than that of the sample with the same-diameter drilling. In the yield stage, the stress-strain curve of sample with variable-diameter borehole shows apparent stress reduction and the decrease of elastic modulus, resulting in the curvature of curve greater than that of the same-diameter drilling. The decline rate of stress–strain curve of sample with variable-diameter borehole is slower than that of the same-diameter drilling in the failure stage, and the phenomenon of stress platform appeared; these results indicate that the plasticity characteristics of sample with variable-diameter drilling are more evident than that of sample with same-diameter drilling.

Figure 7 and Figure 8 show that the compressive strength, peak strain, elastic modulus, and pre-peak strain energy of samples with the same-diameter drilling and variable-diameter drilling decrease with the increase of drilling size, but the strength reduction index and energy dissipation index gradually increase. It can be seen from Figure 8 that the compressive strength of drilling sample numbered 8–14 is 11.78 MPa, a 9.38% lower than that of drilling sample numbered 14–14; the compressive strength of drilling sample numbered 8–22 is 8.32 MPa, a 26.24% lower than that of drilling sample numbered 22–22. Among them, the compressive strength of borehole sample numbered 8–22 is 29.37% lower than that of borehole sample numbered 8–14. With the increase of borehole size, the decreasing latitude of compressive strength of sample with the variable-diameter drilling decreases nonlinearly. The variation trend of peak strain is the same as that of compressive strength: the variable-diameter drilling makes the plastic characteristics of sample more significant compared with the same-diameter drilling, which is not conducive to be accumulated before peak stress of sample, as the less elastic energy is accumulated, the more pronounced the pressure relief effect is. With the increase of the borehole size, the elastic modulus generally shows a downward trend. The decrease of elastic modulus represents the decrease in the anti-deformation capacity of sample. The decreasing trend of elastic modulus of sample numbered 8–22 is the largest, 39.62% lower than that of sample numbered 8–14. It can be seen from Figure 7b that a small amplitude of stress fluctuation occurs in the variable-diameter borehole samples before the peak stress is reached. Observing the video of the experiment process, it is found that cracks first appear around the large-diameter drilling at the yield stage, and stress fluctuations occur due to the appearance of cracks.

It can be seen from Figure 8 that the pre-peak strain energy of samples with variable-diameter drill holes is generally lower than that of samples with the same-diameter drill holes. The pre-peak strain energy of sample 8–22 is 16.03% lower than that of sample 22–22, indicating that the ability to accumulate elastic energy before peak stress is weakened. The change trends of energy dissipation index and strength reduction index are opposite to that of pre-peak strain energy, and the overall trend is upward. The increase in energy dissipation index and strength reduction index indicates that both the decreasing range of dissipated energy and compressive strength increase. It shows that the impact tendency of sample cannot be judged only by the compressive strength. The changing trend of pre-peak strain energy, energy dissipation index and strength reduction index are also very significant in evaluating the impact tendency.

To sum up, the pauperization of physical and mechanical parameters of the sample by variable-diameter drilling is more evident than that by the same-diameter drilling. When the maximum size of the variable-diameter borehole is the same as that of the same-diameter borehole, the resistance deformation and storage elasticity energy ability of the variable-diameter borehole samples are significantly lower than that of the same-diameter borehole samples, and its plastic characteristics are more obvious. This shows that the pressure relief effect is more evident in variable-diameter drilling than in the same-diameter drilling.

3.3. Analysis of Mechanical Properties Post-Peak

The fracturing form and energy evolution characteristics of the post-peak stress can also be used to evaluate the pressure relief effect of samples with different sizes and forms of drilling. The greater the energy released in unit time, the faster the release speed, the more prone to dynamic disasters. It can be seen from Figure 9 and

Table 2. Post-peak mechanical parameters of each sample under different borehole sizes.

Sample No.	Secant Modulus/GPa	Residual Strength/MPa	Post-Peak Strain Energy/(J·cm−3)
8–8	1.79	7.08	0.0346
14–14	1.54	6.83	0.0297
18–18	1.32	5.63	0.0296
22–22	1.3	5.5	0.0293
8–14	1.46	5.96	0.0287
8–18	1.28	5.12	0.0236
8–22	1.22	4.67	0.0177

that the residual strength, secant modulus, and post-peak strain energy of samples with the same diameter gradually decrease with the increase of borehole size. The secant modulus and residual strength of samples are lower than those of samples with the same-diameter drilling. These results show that the variable-diameter drilling has a more significant impact on the post-peak mechanical properties of sample, resulting in the deterioration of residual strength and brittleness characteristics.

3.4. Post-Peak Energy Release Rate

It can be seen from Figure 10 that the post-peak strain energy of sample with same-diameter drilling and the variable-diameter drilling sample both gradually decreases with the increase of drilling size. The maximum post-peak strain energy of sample numbered 8–8 is 0.0346 J·cm⁻³ and of the sample numbered 22–22 is 0.0293 J·cm⁻³, a decrease of 15.32% compared with the sample numbered 8–8, while the minimum strain energy of the sample numbered 8–22 is 0.0177 J·cm⁻³, a reduction of 48.84%. It can be seen that the variable-diameter drilling has a significant impact on the post-peak strain energy of sample: variable-diameter drilling reduces post-peak strain energy in a more pronounced manner compared with same-diameter drilling. The post-peak strain energy release rate of the sample numbered 8–8 is 9.01 × 10⁻⁴ J·cm⁻³·s⁻¹, meaning that the sample numbered 22–22 and sample numbered 8–22 are 30% and 36.74% lower than the sample numbered 8–8, respectively. It can be seen that the variable-diameter drilling can more easily decrease the post-peak strain energy and post-peak energy release rate than that same-diameter drilling, and that the variable-diameter drilling had a better effect on reducing the impact tendency; these results are consistent with the law reflected in the above energy dissipation index and compressive strength.

4. Energy Evolution Characteristics

Figure 11 shows that the AE count curve has an excellent relationship with the stress–strain curve. In the compaction and elasticity stage, the original pores of sample are compacted and closed, there are few new cracks, the AE count level is low, and the cumulative AE count curve increases slowly. In the yield stage, the AE counting rate intensifies, and the AE count rises sharply and reaches the maximum value. The cumulative AE counting curve began to rise significantly simultaneously, indicating that the increase in stress caused a large number of new cracks to be generated, expanded, and penetrated, releasing a large amount of energy. In the failure stage, the continuous loading makes the sample slowly fall to the residual strength. The constant increase of stress aggravates the crushing degree of the sample, resulting in the sliding or closure of the fracture surface. Therefore, the AE count is still relatively active, and the cumulative AE count curve is slowly rising.

Although variable-diameter boreholes with different sizes have little impact on the evolution law of the AE counts compared with the same-diameter drilling, the AE activity in each stage is significantly different in the pre-peak stress stage. AE counting curve has a short quiet period before reaching the compressive strength of the sample with the same-diameter borehole, the AE counting level gradually increases. The AE count of variable-diameter drilling is relatively dense compared to the same-diameter drilling, but the AE count is low. The sample numbered 8–14 has an intense AE count before reaching the compressive strength, well matching the sudden stress drop in the stress–strain curve. In the post-peak stress stage, the AE count of the sample with same-diameter drilling is still maintained at a high level, but the sample with variable-diameter drilling is low. It can be seen that the drilling shapes significantly impact the AE characteristics of the pre-peak and post-peak. The analysis shows that the variable-diameter drilling can promote crack development before the peak stress, and the increase of dissipated energy weakens the ability to store elastic energy before peak stress. There is also a good correspondence between the AE count and the stress curve in the post-peak stage, and low-intensity AE count indicates no violent activity in the sample. This phenomenon shows that the sample has reached a new equilibrium.

It can be seen from Figure 12 that the cumulative AE counts of samples with different sizes and borehole shapes behave pretty differently. The cumulative AE counts of samples with the same-diameter and variable-diameter decrease gradually with the increase of borehole size. There is a negative correlation between borehole size and cumulative AE counts. The cumulative AE count of the sample numbered 8–8 is 15,880 and of the sample numbered 22–22 is 7595, a decrease of 52.17%, while the AE count of the sample numbered 8–22 is 2309, a decrease of 70.63% compared with the sample numbered 8–14. The significant reduction of the AE count indicates the weakening of the sample internal activity intensity. It can be seen from the figure that the AE activity frequency of sample with a variable-diameter borehole is greater than that of the same-diameter borehole, showing the phenomenon of low frequency and high amplitude. It can be seen that variable-diameter drilling can weaken the strength of the sample, which is helpful for the graded release of energy in the process of sample failure and weakening the impact tendency of sample.

5. Failure Mode and Fracture Evolution Characteristics

In Figure 13, 8–22 (8) represents the sample numbered 8–22 and contained an 8 mm drilled part, 8–22 (22) represents the sample numbered 8–22 and contained a 22 mm drilled part. It can be seen from Figure 13a that there are three tensile cracks in the sample, but these do not penetrate to form an effective pressure relief zone, as the failure form is mainly tensile splitting.

It can be seen from Figure 13b that the increase in borehole size intensifies the stress concentration around the borehole, the local stress field reaches the limit of the shear strength and tensile strength of sample, and the sample appears to be a tensile–shear mixed failure. It can be seen that the size of the drill hole can change the final failure form of the sample.

It is found in Figure 13c that the surface of sample is mainly composed of three prominent tensile cracks, which are interconnected but do not penetrate the whole sample, and the damage degree is smaller than that of the sample numbered 8–8.

As shown in Figure 13d, the time for failure of the sample numbered 8–22 (22) is shorter than that of the sample numbered 22–22. This is because the combined pressure relief effect of variable-diameter drilling and the development and through of shear cracks lead to multiple adjustments and changes of the original stress field in the coal sample.

In a word, stress concentration areas can be formed around the upper and lower ends of the drill holes during the loading process, the cracks at the upper and lower ends of drill holes developed and connected with the increase in stress, eventually leading to sample failure. The failure characteristics of the two kinds of samples are also quite different. The failure degree of samples with the variable-diameter samples is smaller than that of samples with the same-diameter drilling. This is because the large degree of stress concentration of the large aperture in the sample with the variable-diameter drilling leads to the formation of an effective pressure relief zone near the drilling holes, most of the elastic energy released, the stress disturbance to the small aperture reduced. The failure process is more complicated and the failure degree is smaller in the small part of the variable-diameter drilling sample. It is beneficial to maintain the stability of the surrounding rock and protect the support system.

6. Conclusions

In this paper, the uniaxial compression test is carried out on the coal-like samples with boreholes, compared and analyzed the difference between the same-diameter drilling and the variable-diameter drilling in pressure relief, and discussed the pressure relief mechanism of the variable-diameter drill. Its superiority and feasibility are verified, and provide a new idea and theoretical basis for solving the problem of preventing rock bursts in deep mining conditions.

(1)

With the increase of borehole size, the compressive strength, pre-peak strain energy, and post-peak strain energy release rate of the same-diameter borehole sample and variable-diameter borehole sample both gradually decrease, and the strength reduction index and energy dissipation index both progressively increase. Under the condition that the maximum size of the variable-diameter borehole is the same as that of the same-diameter borehole, the compressive strength, pre-peak strain energy, and post-peak strain energy release rate of the variable-diameter borehole sample decrease more, and the strength reduction index and energy dissipation index increase more. Indicating that the pressure relief effect of the variable-diameter borehole is better.

(2)

The influence of variable-diameter drilling on the AE characteristics of the samples of the pro-peak and post-peak is significant, which enhances the plastic characteristics of the sample of the post-peak. The cumulative AE count decreases more, and the activity intensity decreases, realizing the graded release of the sample energy, reducing the impact tendency, and verifying the rules mentioned above.

(3)

Different drilling patterns impact the damage mode of samples. When the maximum borehole size is the same, the failure characteristics of the same-diameter borehole sample and the variable-diameter borehole sample are also vastly different. The small size borehole sample of the variable-diameter sample is more complicated due to the stress disturbance at the failure of the large-sized borehole sample. The large-sized borehole sample has a faster failure speed due to the enormous stress concentration degree, which is not conducive to the accumulation of energy before and after the failure, and the pressure relief effect is more pronounced.