Research on influencing factors of rock breaking efficiency under ultrasonic vibration excitation

Underground coal projects frequently deal with hard formations. Their treatment by traditional rock-breaking methods with low energy utilization ratios results in rapid wear of drilling bits. Therefore, it is crucial to develop novel rock-breaking techniques with high efficiency and energy-saving properties.¹ NASA first applied the ultrasonic vibration rock-breaking technique to collect samples and conducted a series of studies regarding ultrasonic vibration drilling (USDC).^2–4 By combining test and theoretical analysis, Wiercigroch et al.⁵ examined the applicability of the ultrasonic vibration rock-breaking technique to underground drilling. They found that introducing high-frequency axial vibration to traditional drilling could significantly enhance the drilling rate. Numerical simulations by Zhao and Sangesland⁶ revealed that the contact force between the drilling bit and the rock was reduced under ultrasonic vibration, thereby reducing the wear between the drilling bit and the rock. Such studies proved the broad application prospects of ultrasonic vibration rock-breaking techniques in hard-rock-breaking domains.

In recent years, scholars have conducted a great deal of research on the damage and fracturing mechanisms of rocks under high-frequency vibration excitation. Zhao et al.⁷ analyzed the propagation rules of microcracks in granite under ultrasonic vibration and concluded that damage to feldspar particles was the main reason for rock failure. In combination with scanning electron microscopy, Wang⁸ investigated the damage mechanisms of four different types of hard rocks under the excitation of ultrasonic vibration. They pointed out that high-frequency vibration can promote the formation of transgranular fractures in the rock. Zhou⁹ employed a two-dimensional particle flow code (PFC-2D) to establish a rock fatigue damage model under ultrasonic vibration excitation and calibrated the model in combination with strain experiments. Zhang¹⁰ performed nuclear magnetic resonance experiments, proving that ultrasonic vibration could effectively promote the initiation and propagation of micropores in rocks. Zhao¹¹ studied the thermal damage of granite during the ultrasonic vibration excitation process and reported that pores expanded significantly when the rock temperature exceeded a certain threshold. Wang¹² examined the dynamic damage process in red sandstone under ultrasonic vibration with the direct current method combined with numerical simulations, yielding the rock’s tensile–shear damage mode. Using a uniaxial compression test, Yin¹³ investigated the damage rules of granite under ultrasonic vibration and proposed the optimal static load corresponding to the most severe damage to rocks. Bai¹⁴ conducted an orthogonal test to investigate the effects of many factors, including bit weight, spring rate, and bit quality, on the drilling efficiency of the ultrasonic bit; according to their results, the bit weight imposed the most significant effect. Zhou¹⁵ measured the deformation rules of granite under ultrasonic vibration using strain gauges. He reported that the rock’s displacement amplitude and crack propagation rate significantly increased when its vibration frequency was close to the inherent frequency. Li¹⁶ analyzed the stress field and the displacement in the rock under high-frequency harmonic dynamic loading via numerical simulation. He found that the rock fracturing range and damage degrees under static–dynamic combined loading exceeded those under static loading. By combining tests and numerical simulations, Han et al.¹⁷ analyzed the effect of vibration amplitude on pores in granite. They reported that the increased vibration amplitude raised the internal stress in crystal defects, promoting the initiation and propagation of microcracks.

Despite a great deal of research on rock damage and fracturing behavior under ultrasonic vibration conditions, scholars mainly focused on rocks under uniaxial stress while ignoring the surrounding rock effect. In addition, the combined impact of many factors on rock-breaking efficiency, which is crucial for engineering applications of ultrasonic vibration rock-breaking techniques, has rarely been reported. To fill this gap, the present study applied several evaluation indices of rock-breaking efficiency for qualitative and quantitative analysis of the effects of vibration parameters and the confining pressure on the efficiency of ultrasonic vibration-assisted rock-breaking of red sandstone samples.

Brittle red sandstone collected from the Sichuan Province of China was machined into cylindrical samples of a height of 100 mm and a diameter of 50 mm, according to the standard formulated by the Internal Society for Rock Mechanics (ISRM), as shown in Fig. 1(a). Then, the wave velocity in the rock was measured using a wave velocity meter. By eliminating rock samples with excessive wave velocities, those with an average rock wave velocity of 4110 m/s were selected for rock-breaking tests. Besides, to avoid bias in the experimental results, the inherent frequencies of varying rock samples were measured with the percussion method.¹⁸ After a fast Fourier transform (FFT) of rock vibration signals, the inherent frequency results were obtained, as shown in Fig. 1(b). Finally, rock samples with an intrinsic frequency of 11650 ± 50 Hz were selected for the rock-breaking tests.

Figure 2 displays the ultrasonic vibration excitation device used. The ultrasonic generator converted commercial electricity into a high-frequency alternate-current (AC) electrical signal. After passing the ultrasonic transducer, the electric energy was converted into mechanical vibration to generate high-frequency axial impact on the lower rock via the connected tool head. The static load within a specific range was applied to the rock sample along the longitudinal direction using the air compressor. Table I lists the ultrasonic excitation parameters.

Rock-breaking tests were performed under different static stress levels of 0.15, 0.2, and 0.25 MPa to examine the combined impact of static load and ultrasonic vibration on the rock-breaking efficiency. As shown in Fig. 3, using the interval vibration excitation mode, rock-breaking conditions were observed every 40 s after the application of excitation. The vibrations were stopped during each observation and repeated until the next examination with the subsequent excitation. The cumulative rock-breaking time was recorded until a volume break occurred.

Figure 4 shows the progressive fracturing process of red sandstone at different static stress levels (0.15, 0.2, and 0.25 MPa). Under the excitation of ultrasonic vibration, the contact area between the exciter and the rock sample gradually underwent local failure. With prolonged excitation time, broken pits with the same shapes as the exciter section were progressively formed in the rock. Accompanied by rock damage around the excitation face, cracks were constantly generated from the exciter face’s edge and gradually developed toward the surroundings. When the exciter penetrated the sample at a certain depth, the adjacent main cracks formed and gradually coalesced, while rock fragments were produced and then shed from the surface. As the static stress increased from 0.15 to 0.25 MPa, the time of macrocrack initiation in the rock samples dropped from 280 to 40 s, with a decreasing ratio of up to 85.7%. Meanwhile, the cumulative rock-breaking time decreased from 960 to 160 s, and the rock-breaking velocity was enhanced by six times.

Figure 5 displays the final failure patterns of rocks under different static loads. The maximum penetration depth into the rock increased with increasing static load. In the meantime, the propagation of macrocracks in the longitudinal direction was promoted under a growing static load, increasing the volume of the finally formed fragments. As shown in Fig. 6, both the maximum penetration depth (H_q) and the maximum propagation depth of macrocracks (H_f) were exponentially related to the applied static stress. As the static stress increased from 0.15 to 0.25 MPa, H_q and H_f increased by 275% and 105.56%, respectively. This implies that the increased static load can effectively accelerate rock damage and fracture velocity and expand the rock fracturing range.

The damage and fracturing process in rocks refers to the cumulative development process of microscopic cracks accompanied by energy transfer. Investigating the rock damage mechanism under the coupling of many vibration parameters from the microscopic perspective can reveal the influencing mechanism of various vibration parameters on rock-breaking efficiency more systematically.

Numerical simulation with particle flow software (PFC-2D) can comprehensively analyze the effects of various vibration parameters on rock-breaking efficiency and monitor the propagation of microcracks, coupled dynamic damage characteristics, and the evolution rules of the energy field in a timely manner, thereby significantly overcoming the shortcomings of laboratory tests.

Based on molecular dynamics, Wang and Cui¹⁹ applied the particle flow theory to the damage and fracturing mechanism of rocklike materials from the perspective of micromechanics. Using particle flow codes based on the discrete element method (PFC-2D), rocks can be modeled as a combination of spherical particles at different scales, and the adjacent particles can be linked with the contact model. The interaction among particles can be linear, nonlinear, or viscous. Accordingly, PFC-2D can simulate various rock behavior patterns well, including elastoplastic deformation, failure, and the propagation of cracks. PFC-2D adopts the constitutive model describing the contact among particles to simulate the rock's constitutive characteristics. The constitutive models include the contact stiffness model, sliding model, and bonding mode. Scholars have also verified that the parallel bonding model could accurately simulate the mechanical behaviors of rock materials.^20–22 Figure 7 shows that rectangle parallel bonding regions exist among adjacent materials. When the maximum normal or tangential stress exceeds the corresponding maximum bonding strength, the parallel bonding among particles can be destroyed, accompanied by the initiation of cracks.

The internal normal (σ) and tangential (τ) stresses of the model can be derived as follows:

where F_iⁿ and F_i^s are the normal and shear forces acting on the parallel bonding zone surface, respectively, while A denotes the area of the parallel bonding zone.

This study adopted a parallel bonding model to simulate red sandstone behavior. The macro-mechanical properties of the rock model in PFC-2D are determined by some microparameters, including stiffness, contact modulus, and stiffness rate. The parameters should be calibrated based on mechanical test results on the rock²³ to determine the optimal microparameters and minimize the model error. Figure 8 compares the uniaxial compressive simulation results and the corresponding experimental data, and Table II lists the determined microparameters of the rock. The rock model with the parameter settings is closest to red sandstone in terms of mechanical properties. Figure 9 shows that both the test and simulation results under the excitation of ultrasonic vibration show similar failure patterns, thereby validating the accuracy of the established model.

This study established rock models of two different sizes (50 × 100 mm² and 400 × 200 mm²) for small and large rock samples, respectively. Walls with zero velocity were applied to the sample’s bottom boundary and its two sides to impose the boundary constraint. The velocity boundary was applied to the center of the sample top to simulate the ultrasonic vibration load.²⁴ The confining pressure was applied to both sides of the model. The vibration displacement of the loading surface under the excitation of ultrasonic vibration can be written as

The derivative of Eq. (2) gives the velocity boundary

where x and v denote the displacement and velocity of the excitation face, respectively, X is the vibration amplitude, f is the vibration frequency, and t is the excitation time.

Four simulation tests were performed on a small-size rock model to examine the effects of various parameters on rock damage and fracture under the excitation of ultrasonic vibration. The detailed test parameters in the test scheme are listed in Table III.

The orthogonal tests are used to analyze the effects of multiple factors. This study applied them to evaluating rock-breaking efficiency under various ultrasonic vibration parameters. Three indices (namely, the penetration depth of the exciter, rock fragmentation, and the total number of generated microcracks) were selected to evaluate the rock-breaking efficiency. Four factors that may affect rock-breaking efficiency include (A) vibration frequency, (B) vibration amplitude, (C) diameter of the circular loading surface, and (D) confining pressure. The specific parameters set for each factor are called levels.^25,26 Table IV lists the levels of various factors, and Table V describes the orthogonal test scheme. Sixteen sets of orthogonal tests, denoted as L₁₆(4²), were performed in total.

As shown in Fig. 10(a), the increased vibration amplitude aggravated the rock damage degree on the loading surface and increased the penetration depth. Meanwhile, the vertical propagation of macrocracks could be promoted by increasing rock fragmentation. As the vibration amplitude increased from 30 to 60 µm, the rock-breaking area increased from 411.2 to 808.5 mm², i.e., by 96.62%. Figure 10(b) shows that the increased vibration amplitude promoted both the initiation and propagation of microcracks. Under an external load, the energy absorbed by the rock could be transformed into strain energy. The energy was gradually dissipated, accompanied by the generation of microcracks and friction among internal particles. Accordingly, the energy dissipation process corresponded to rock damage and failure. As shown in Fig. 10(c), the dissipation energy increased with increased vibration amplitude. Under ultrasonic vibration, the particles in the rock were forced to vibrate. According to Eq. (4), the kinetic energy and stress in the particles increased with the vibration amplitude. Therefore, the bonds among particles were easily broken, accelerating the initiation and propagation of microcracks.

As shown in Fig. 11, the rock-breaking range increased with increasing vibration frequency. As the vibration frequency increased from 20 to 23 kHz, the rock-breaking range increased from 411.2 to 598.5 mm², i.e., by 32.81%. The increased vibration frequency also increased the force applied to the particles, accelerated the breakage of bonds, and promoted the development of microcracks. In addition, as the vibration frequency increased, the dislocation of rock particles became more frequent, and a greater amount of energy was dissipated in friction.

Figure 12 shows that as the loading surface size (diameter) increased to a specific value, inverted cone fragments formed below the surface. The fragmentation process became more intensive with the increased loading surface diameter. As the latter grew from 15 to 30 mm, the rock-breaking area increased from 411.2 to 951.5 mm², i.e., by 131.4%. The internal cracks were concentrated in the upper half of a small loading surface. As the loading surface expanded, the cracks extended to the whole rock body. This suggests that the increased loading surface can promote the rock damage and failure range, as well as increase the dissipation energy.

As shown in Fig. 13, the variation in confining pressure imposes no significant effect on the rock fragmentation degree but inhibits the generation of microcracks. Under increased confining pressure, the maximum extension depth of macrocracks decreased. The particles in the rock became compacted by the confining pressure, making the shear and tensile failure of bonds more difficult. In addition, the friction force among the particles increased, inhibiting their relative displacement and dissipation energy generation.

The above-mentioned results strongly indicate that increased vibration amplitude, frequency, and loading surface size accelerate rock damage failure and energy dissipation. In contrast, the increased confining pressure inhibited the initiation and propagation of cracks, reducing rock damage and failure rates.

Based on a large-size rock model, orthogonal tests were performed under the same vibration excitation time. The relations of the evaluation indices in the orthogonal test scheme, including the penetration depth, rock-breaking area, and the number of cracks, with four vibration parameters, were quantitatively analyzed with range analysis. Table VI lists the present 16 groups of simulation results.

Table VII presents the range analysis results of the penetration depth effect. Accordingly, the effects of vibration parameters and the confining pressure on the penetration depth were plotted, as shown in Fig. 14. The penetration depth increased linearly with both vibration frequency and amplitude. It showed slight variations in the loading surface’s size and the confining pressure. In particular, the vibration amplitude imposed the most significant effect on the penetration depth, with a range (R) of up to 16.508, followed by the vibration frequency, with a range of 13.503. In contrast, the loading surface size and the confining pressure imposed the most negligible effects, with R values of 2.99 and 1.001, respectively.

Table VIII presents the range analysis results of the rock-breaking area, and Fig. 15 shows the effects of various vibration parameters and the confining pressure on the rock-breaking area. The rock-breaking area increased steadily with the increased diameter of the loading surface and gradually decreased with the increased confining pressure. As the vibration frequency and amplitude increased, the rock-breaking area first decreased and then grew. Among the four vibration parameters, the vibration frequency imposed the most significant effect on the rock-breaking area, with an R-value of up to 1023.274. The remaining three parameters imposed similar effects. The confining pressure imposed a minimal impact on the rock-breaking area.

Table IX summarizes the range analysis results of the number of cracks; accordingly, the effects of the vibration parameters and the confining pressure on the number of cracks were plotted, as shown in Fig. 16. The total number of cracks in the rock increased with the vibration frequency, amplitude, and loading surface size, while it decreased with confining pressure. The loading surface size was the main factor controlling the number of cracks, with an R-value of 1591.25. Both vibration frequency and amplitude imposed similar effects, with their R-values being nearly twice lower than that of the loading surface size. The confining pressure had a minimal impact on the number of cracks, with its range being only 1/7 of the loading surface size.

Overall, under the excitation of ultrasonic vibration, the vibration amplitude determined the penetration depth of the exciter into the rock, the vibration frequency determined the rock-breaking volume, and the size of the loading surface determined the rock’s damage and failure range. Under the combined action of four parameters, the confining pressure imposed the slightest effect on the ultrasonic vibration rock-breaking efficiency.

The performed test and simulation results on the effects of various parameters on rock-breaking efficiency can provide theoretical guidance for the future application of ultrasonic vibration rock-breaking techniques to underground coal engineering.

In projects with great drilling distances (such as the boring of bolts and cables, the drilling of boreholes, and the formation of detection drilling), it is recommended to increase the vibration amplitude, appropriately increasing the vibration frequency and bit pressure, as well as the contact surface between the drilling tool and the rock. Meanwhile, the confining stress in the construction region should be released to enhance the drilling distance.

In projects with large rock fragments, such as the break-up and excavation of tunnels in hard rock masses, crushing of large gangues, and demolition of buildings, the static load and vibration frequency of the ultrasonic device should be increased, the vibration amplitude and loading surface on the rock should be appropriately increased, and the confining stress in the construction region should be released.

In projects involving the generation of numerous cracks in original rocks, such as the anti-reflection of coal seams, pre-fracturing of the roof, and ultrasonic fracturing of shale rocks, the loading area should be increased. The frequency and vibration amplitude of ultrasonic devices should be appropriately increased, and the confining stress in the construction region should be released to enhance the fracture development degree in the rock.

This study performed ultrasonic vibration excitation tests to examine the effect of static load on the rock-breaking efficiency of red sandstone samples. Using the PFC-2D software, single-factor simulation and orthogonal tests were conducted to qualitatively and quantitatively analyze the effects of vibration amplitude, frequency, loading surface size, and confining pressure on rock-breaking efficiency. The following main conclusions were drawn:

1. The increased static load can accelerate the rock damage and failure rate and expand the rock-breaking range. The maximum penetration depth and the maximum development depth of macrocracks varied with the static load in an exponential pattern. As the static load increased from 0.15 to 0.25 MPa, the rock-breaking time was shortened by six times. Simultaneously, the maximum penetration depth and the maximum development depth of macrocracks increased by 275% and 105.56%, respectively.

2. Rock particles were forced to vibrate under the excitation of ultrasonic vibration. The increased vibration amplitude led to increased rock particle acceleration; accordingly, particles were subjected to higher stress, and their bonds were more easily broken. The increase in vibration frequency accelerated the friction-induced movement of rock particles, thereby increasing the dissipation energy. The increased loading surface size `expanded the rock damage and failure range under the excitation of ultrasonic vibration. Particles were compacted under the confining pressure, so it became more challenging to generate relative displacement, thereby suppressing the initiation of cracks and reducing rock damage and fracture rates.

3. According to the orthogonal test results, the vibration amplitude was the main factor controlling the rock-breaking efficiency when using the penetration depth of the exciter into the rock as the evaluation index. The vibration frequency was defined as the crucial factor of rock-breaking efficiency when using the rock fragmentation volume as the evaluation index. Finally, the loading surface size was determined as the critical factor when using the total number of cracks as the evaluation index. The above-mentioned results provide theoretical guidance for promoting the application of ultrasonic vibration rock-breaking techniques to underground coal engineering.

This research was supported by the National Natural Science Foundation of China (Grant No. 51874282), the Six Talent Peaks Project in Jiangsu Province (Grant No. GDZB-052), and the Key Research and Development Projects of the China Pingmei Shenma Group. The authors are grateful for these supports.

The authors have no conflicts to disclose.

Zhanbiao Yang: Data curation (equal); Investigation (equal); Resources (equal). Xufeng Wang: Software (equal); Writing – review & editing (equal). Lei Zhang: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Resources (equal); Software (equal). Jiyao Wang: Investigation (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.