TheMechanical Properties of Granite under Ultrasonic Vibration

,e new technique of using ultrasonic vibration to break hard rock is still in the experimental stage, but it has significant potential for improving the efficiency of hard rock crushing. We have analyzed the mechanical properties of granite under ultrasonic vibration and the characteristics of the damage produced. ,is was achieved by using an ultraloading device to apply continuous and discontinuous ultrasonic vibrations, respectively, to 32mm diameter and 72mm high granite samples. An ultradynamic data acceptor combined with strain gauges was used tomonitor the strain of the granite in real time, and the elastic-plastic deformation behavior of the granite under ultrasonic vibration was observed. ,e results of this experiment indicate that the granite samples underwent elastic deformation, plastic deformation, and damage during this process. ,e samples first experienced compressive deformation with no obvious rupturing. As the vibration continued, the deformation finally became tensile, and significant fragmentation occurred. ,e mechanical properties of granite under ultrasonic vibration are analyzed in detail on the basis of these results, and the basis for selecting a vibration frequency is discussed.


Introduction
Due to the high strength of hard rock and its widespread distribution in deep strata, there is a common need for a means of rapidly breaking hard rocks for engineering projects such as tunneling and drilling [1][2][3].A technology called "resonance breaking" that utilizes ultrasonic vibration has been developed for this purpose.e NASA designed a high-axial force ultrasonic drilling sampler for planetary exploration and ice-drilling, consisting of piezoelectric transducers, free mass blocks, and a drill bit [4][5][6][7][8][9].Wiercigroch et al. [10,11] applied the ultrasonic vibration technique to improve the efficiency of hard rock drilling and conducted a variety of experiments to ascertain the effect of ultrasonic vibration on rock fragmentation.eir investigations showed that ultrahigh-frequency axial vibration can significantly enhance drilling rates compared to the traditional rotary-type method [12].Pavlovskaia et al. [13] concluded that a low-dimensional model provides good estimates for the optimal static force and the amplitude of the dynamic force and that this model can be used for the operational control of the drilling system, with the loading parameters being adjusted to achieve a resonant situation while drilling through different formations.Zhao [14] developed a simple nonlinear 2-DOFs (degrees of freedom) mass-spring model that can be used to analyze the process of dynamic cutting with normal ultrasonic vibration excitation.A compressive strength experiment was used to demonstrate that this technique can rapidly reduce the strength of hard granite rock, and CT scanning was used to examine the effect of static pressure on rock-breaking efficiency [15].e results indicated that a threshold of static pressure exists for this method, and samples will become damaged when the static pressure exceeds this threshold.However, the abovementioned investigations mainly focused on parameter selection for the ultrasonic vibration technology, and the mechanical properties of granite under ultrasonic vibration, which are of significance for understanding the rock mechanics of ultrasonic vibration breaking, have rarely been studied.
Many investigations have focused on the mechanical properties of rock under cyclic loading.A summary of relevant research on various rock types is provided in Table 1.Experimental results have clearly demonstrated that damage gradually accumulates in rocks undergoing cyclic loading [16,17].It has also been found that the mechanical properties of rock are significantly affected by the loading parameters.Of these, the most important are the loading rate, frequency, and stress amplitude [18,29].Rocks are more easily damaged at low frequencies and high amplitude than at high frequencies and low amplitude for a given energy input [19].e effect of loading frequency on the rock strength appears to be small compared to the stress magnitude at low frequencies [20,22,28,30].Additionally, theoretical work has been conducted on rock fatigue.Xie et al. [31] discussed the relationships between energy dissipation and strength and energy release and global failure during the deformation and failure of a rock mass.Li et al. [24] investigated the classification and fractal characteristics of coal rock fragments under uniaxial cyclic loading and found that as the loading rate increased, the specimens were crushed more thoroughly and the fragments became more uniform in length, width, thickness, and overall size.You et al. [25] concluded that the elastic energy index increases as damage increases.
Deformational behavior is another important theme in investigating the mechanical properties of rock under cyclic loading.For example, it has been found that strain data can reflect the process of crack development in cyclic tests and that crack closure accompanies compressive deformation [32].Liu et al. and Chen et al. [21,23] studied the types of deformation that occurred during the loading process and concluded that their rock samples showed near-elastic behavior during initial cyclic loading but began to exhibit elastic-plastic behavior with an increase in the number of cycles.Furthermore, they found that the residual stress became larger along with an increase in loading stress.Another study used a modified Burger model to describe the creep behavior of red sandstone subjected to cyclic loading [33], and on the basis of acoustic emission monitoring, another study showed that the progressive damage caused by cyclic loading can be divided into crack damage and plastic damage [26].Song et al. [27], meanwhile, showed that the S-N curves of rock samples were consistent with those observed in other brittle materials such as ceramics.
e abovementioned studies all focused on the mechanical properties of rock under conventional low-frequency cyclic loading.It has been found that the effect of this process on the mechanical properties of rock is related to the loading frequency, and many investigators have concluded that the response of rock materials under external harmonic excitation will change with loading frequency [34][35][36].
us, when ultrasonic vibration with a frequency in the same order of magnitude as the natural frequency of hard rock [37,38] is applied to rocks, the mechanical properties of the rock should differ from those under conventional low-frequency cyclic loading.
us, a comprehensive study of the mechanical properties of rock subjected to ultrasonic vibration is of great significance.
In this study, we analyzed the mechanical properties of granite, the characteristics of its deformation, the influence of vibration frequency, and the development of damage under ultrasonic vibration with a continuous and discontinuous loading path, constructing S-T (strain-time) curves.Due to the high frequency of ultrasonic vibration, there is a need to monitor the strain data dynamically.An advanced apparatus consisting of an ultradynamic data acceptor and strain gauges was therefore used.Our results will be conducive to a better understanding of fragmentation mechanisms under ultrasonic vibration and will provide theoretical guidance for the ultrasonic vibration technology.

Sample Preparation.
e rock samples used in the experiments were processed from fine granite, a common type of hard rock in strata.e mineralogical composition of the rock was determined by X-ray diffraction (XRD).A Rigaku D/Max 2500 Cu radiation powder diffractometer was used, with the scanning conditions set to 2θ angles of 10 °-90 °, a scan step size of 0.02 °, a scanning rate of 0.12 °/s in the continuous mode, and a beam intensity of 50 kV and 200 mA.e XRD result, shown in Figure 1, indicates that the main components of the rock are quartz, albite, orthoclase, and hydrobiotite, indicating that the rock material is highly anisotropic.e samples were cut into standard 2 Advances in Civil Engineering cylindrical blocks with a diameter of 36 mm and a height of 72 mm.In order to reduce the e ect of heterogeneity on the experimental results, the samples were tested using the knocking method to examine their natural frequencies [39].Samples with similar natural frequencies (26-27 kHz; Figure 2) were then selected for the subsequent experiments.
Table 2 shows the mechanical parameters of the granite samples.ese parameters were obtained through uniaxial compression tests, direct shear tests, and natural frequency tests.

Test Setup.
e test equipment, as shown in Figure 3(a), comprises an ultrasonic vibration device and a strain data acquisition device.e vibration apparatus is composed of an ultrasonic power source (1), an ultrasonic vibrator (2), and a static loading device (3).e ultrasonic vibrator can excite vibration at frequencies of 30 kHz, 35 kHz, and 40 kHz.
e strain data collection device was controlled using a computer (5), and an ultradynamic data acceptor (4) combined with four strain gauges placed on top of the sample (6) was used to collect strain data in real time.e loading method is shown in Figure 3(b).An ultrasonic dynamic load combined with a vertical static load was applied to the samples.
In the strain test, four strain gauges were placed on each sample to test the axial strain (A1 and A2) and the radial strain (R1 and R2). e height of A1 and R1 was Height 1 (H1) and the height of A2 and R2 was Height 2 (H2), where H1>H2.e speci c locations of the strain gauges can be seen in Figure 3(a).
In order to analyze the mechanical properties of the rock samples, we designed a continuous vibration strain experiment and a discontinuous vibration strain experiment.
e continuous test enabled the overall deformation law of the samples to be determined, while the discontinuous test allowed quantitative analysis of the elastic and plastic deformation.e two loading paths are shown in Figure 4, in which Δt is the time interval.Δt 0 in the continuous test, and Δt represents the time from the discontinuation of vibration to the stabilization of the strain data in the discontinuous test.
e detailed experimental arrangements are as follows: (1) For the continuous experiment, the granite samples were divided into three groups of ve samples.e three groups were subjected to applied static loading of 200 N with ultrasonic vibration frequencies of 30 kHz, 35 kHz, and 40 kHz, respectively.We  recorded the strain of the rock samples until the rock began to crack.(2) For the discontinuous experiment, we tested the axial and radial strain at H1 of 10 samples under a static loading of 200 N. e frequency found to have the best crushing e ect in the continuous tests was then selected as the discontinuous vibration parameter.During discontinuous vibration testing, the duration of each vibration ranged from 8 s to 30 s, after which the device was stopped until the monitoring system indicated that the strain curve had become stable.We repeated this process until fragmentation of the sample became evident.All experiments were conducted at room temperature.

Continuous Vibration Strain
Test. e development of rock damage mainly manifested as macroscopic deformation.
e magnitude of macroscopic deformation increases when cracks develop inside rock, and with a decrease in deformation, the cracks close [32].Figure 5 shows a representative example of the results obtained for axial, radial, and volumetric strain versus vibration time.e gure shows that strain initially decreased at a steadily decreasing rate (the yellow, green, and blue lines in Figure 5(a) indicate the strain curve slope).e slopes of the strain curves were close to zero (with small uctuations) at 120 seconds for the axial direction and 140 seconds for the radial direction, which means that the deformation barely changed in this period.And after this stable stage, the strain values increased as the vibration time increased.e strain versus vibration time curve is U-shaped, indicating that internal rock cracks mostly closed during the early period of vibration, and the compressive velocity of the sample gradually decreased.After a certain period of time, the strain tended to stabilize when the degree of crack closure became comparable to the degree of initiation and propagation of cracks.In the third stage, cracks mostly expanded as the rock dilated until destruction.However, the laws of strain in di erent directions and at di erent heights were not exactly the same.e results plotted in Figures 5(a)-5(c) show that the time taken for samples to compress to their limit along the axial direction was shorter than that in the radial direction.Furthermore, the stable phase was shorter along the axial direction than that in the radial direction.ese results indicate that cracks propagated more readily perpendicular to the loading direction of the ultrasonic vibration.e results in Figure 5(d) show that the absolute strain at H1 along both the axial and radial directions was larger than that is di erence was especially evident during the ascendant stage of strain when the rock cracked.e strain was positive at H1, while it was still negative at H2. e entire failure process of the sample under ultrasonic vibration is shown in Figure 6.Firstly, there is a small amount of damage at the edge.Next, these small damaged zones connect with each other, and the damaged area becomes larger.Finally, the failure plane develops from the edge to the center quickly, and fragments produced in this process y out of the sample (Figure 6(b)).e size distribution of the fragments produced in the tests is shown in Figure 6(c).ere were several large fragments combined with smaller fragments and some nes, which is an indication of fatigue failure [30].
To investigate the e ect of ultrasonic vibration frequency on breaking e ciency in more detail, we compared the axial strain at H1 of samples subjected to di erent vibration frequencies (Figure 7).e results show that the ultrasonic vibration frequency signi cantly in uenced the deformation process.e strain rate is here indicated by the slope of the strain curve, and the absolute value of the strain rate in both the descendant and ascendant stages decreased in the order 30 kHz, 35 kHz, and 40 kHz.During the strain reduction stage, the strain rate at 30 kHz frequency was 255% and 599% greater than that at the 35 kHz and 40 kHz frequencies, respectively.When in the ascendant stage, that at 30 kHz frequency was 623% and 680% greater than that at 35 kHz and 40 kHz, respectively.erefore, the time taken for the granite samples to break decreased in the order 40 kHz, 35 kHz, and 30 kHz. e vibration frequency selected for the discontinuous test was therefore 30 kHz.Advances in Civil Engineering

Discontinuous Vibration Strain Test.
e strain-time curve for the discontinuous vibration test is shown in Figure 8.In this experimental process, the sample began to crack after six intermittent vibrations.During the sixth vibration, the specimen expanded after it had been contracted for a period of time.Before the sixth vibration, the results indicated that the sample did not fully recover to its initial position after vibration.is illustrates that the deformation of samples under ultrasonic vibration can be decomposed into reversible and irreversible components.e distance between the stable strain line and the initial line on the curves represents the irreversible components, termed "residual strain."e results also indicated that, during the rst ve vibrations, the position of stable strain line was lower than the initial position after vibration had ceased.is result indicates that residual compressive strain was generated and that the sample su ered from residual compressive stress at the same time in both the radial and axial directions [40].
e reversible component was induced by the elasticity of the rock, while the irreversible component could be induced by plasticity and crack damage [41].e development of residual strain in the granite sample is shown in Figure 9.
ree stages of residual strain can be identi ed: (1) the uniform velocity phase, where residual compressive strain 6 Advances in Civil Engineering increases at a constant velocity; (2) the accelerated phase, where residual axial compressive deformation rapidly increases with increasing velocity; and (3) the reversed decrease phase, where residual axial compressive deformation decreases.In stages 1 and 2, the residual strain mostly resulted from plastic damage.In stage 3, crack damage had the largest e ect on the residual strain value because crack generation can result in the expansion of the sample, which can, in turn, decrease the residual compressive strain.

Mechanical Properties of Granite under Ultrasonic
Vibration.Since granite is a highly anisotropic material, it contains a large number of internal joints and microcracks.On the one hand, when the energy wave meets a crack surface during the transmission of ultrasonic vibration energy, the energy wave will re ect [42], as shown in Figure 10.e re ected energy will result in radial vibration, and the nonre ected energy will continue to propagate along the axial direction.On the other hand, the ultrasonic vibration will introduce residual compressive stress due to the inhomogeneous deformation caused by the high anisotropy of granite, and this is con rmed by the discontinuous ultrasonic vibration experiment results. is nding, the rst such observation for rock material subjected to ultrasonic vibration, is in good agreement with the results of ultrasonic vibration experiments performed by Ding et al. and Uhlmann on nonmetallic brittle material such as glass and ceramic materials [43,44].erefore, during the cyclic process, the external applied stress will superimpose the internal residual stress inside the specimen in both the axial and radial directions.
e stress distribution after superposition is shown in Figure 11.e generation of residual stress leads to a reduction in the stress ratio.
Since almost no new cracks are generated inside the rock in stage 1, the deformation of the rock at this time was mainly caused by the superimposed stress.Because of the reduced stress ratio, the degree of contraction during each cycle was larger than that of expansion, and the rock was squeezed in both the axial and radial directions.erefore, both the radial and axial strains decreased and cracks closed as a whole during this stage [32].As the vibration continued, new cracks were gradually generated, which led to an increase in expansion.
e strain rate then gradually decreased, and it entered stage 2 when strain became essentially unchanging.As the cracks continued to expand, the magnitude of the expansion deformation caused by crack  propagation became much larger than that of the contraction caused by superimposed stress.us, both the radial and axial strains increased in stage 3, and finally, the cracks interpenetrated and macroscopic damage occurred.
In the strain decrease stage, crack closure can change the internal structure of the rock [32,35], which in turn can affect the response of the rock to ultrasonic vibration.When rock is subjected to a continuous harmonic external excitation, a steady-state response is generated in the rock as follows [35]: where λ expresses the ratio of the harmonic force frequency over the natural frequency of the rock with λ � ω/ω n ; B d is the displacement amplitude of the rock (m); ζ is the damping ratio; ω is the external excitation frequency (Hz); ω n is the natural frequency of the rock (Hz); and A is the external loading amplitude.us, the displacement amplitude of rock will increase when the vibration frequency approaches its natural frequency.By using the following equation, we analyzed the relationship between the natural frequency of the rock and the total length of cracks [36]: where L is the length of the rock sample (m), S is the crosssectional area of the rock sample (m 2 ), L y is the length parameter of the cracks (m), m is the rock sample mass (kg), and a is the surface energy per unit area (J).When cracks in the sample close, the total length of the cracks decreases and the overall natural frequency of the sample increases.According to Eq. ( 1), the displacement amplitude of the rock will therefore increase as the natural frequency of the rock approaches the frequency of ultrasonic vibration, which can accelerate the damage process [20,22,30].We evaluate this finding by tracking the dynamic development of displacement amplitude based on the axial strain data in the continuous vibration test.Strain amplitude, which we define as the difference between the maximum and the minimum strain in each second (Figure 12(a)), can be used to reflect the displacement amplitude of the tested samples.A greater strain amplitude indicates a greater displacement amplitude, and vice versa.e evolution of strain amplitude in Figure 12(b) shows that, in the early period of vibration, the strain amplitude increased with continued vibration, indicating that the increase of the natural frequency caused by crack closure resulted in an increase in the displacement amplitude.When the rock had deformed to its compressive limit, the natural frequency also approached its maximum, and so did the displacement amplitude.e fatigue process will accelerate due to increased displacement [30,35].As the cracks subsequently expanded, the natural frequency decreased, and a decrease in the displacement amplitude occurred.

Effects of Vibration Frequency.
e results of our study show that the frequency of vibration had a significant influence on the mechanical properties of the granite samples.Advances in Civil Engineering When the vibration frequency is close to the natural frequency of the sample, resonance will cause a significant increase in the displacement amplitude of the sample [35]. is can rapidly increase the crack propagation rate [45].erefore, when we applied ultrasonic vibration at 30 kHz to a granite sample with a natural frequency of nearly 30 kHz, destruction occurred significantly more rapidly than at 35 kHz or 40 kHz.
According to the analysis above, the natural frequency of the sample first increases and then decreases during the vibration process.In order to enable high crushing efficiency, the frequency of applied ultrasonic vibration needs to be within the range of the changing natural frequency of the rock.

Conclusions
In this study, we investigated the mechanical properties of granite under ultrasonic vibration.
e following conclusions can be drawn from the experimental results: (1) e samples underwent elastic deformation, plastic deformation, and damage during ultrasonic vibration.e samples deformed with the same trend in both the axial and radial directions.Contraction occurred initially, then deformation stabilized for a period, and this was followed by expansion until failure.
(2) In the volumetric compaction phase, the energy reflected when meeting cracks inside the sample caused the samples to suffer from both ultrasonic vibration in the radial and axial directions and the residual compressive stress generated by this process.Crack closure under the action of the superimposed stress caused the sample to contract.Crack closure causes the natural frequency of rock to increase, in turn increasing the displacement amplitude, which can accelerate the fatigue process.With crack initiation and propagation, the rate of contraction decreased, and the rock entered a stage of volumetric expansion in which the rock damage speed increased due to the significant effect of stress concentration.(3) Vibration frequency had a significant influence on the mechanical properties of the granite samples.Since the natural frequency of rock first increases and then decreases during the process of applying vibration, it is necessary to enable high crushing efficiency to ensure that the frequency of the applied ultrasonic vibration is within the range of the changing natural frequency of the rock.
Further experimental work using methods such as the hole-drilling strain-gauge method and the ultrasonic nondestructive testing method, however, is required to validate the development of residual compressive stress under ultrasonic vibration quantitatively.Additionally, in order to observe the behavior of crack propagation, which is very hard to observe in physical experiments but is a very important factor for understanding the fragmentation mechanism with this technology, numerical simulation is necessary in the next study.Advances in Civil Engineering

Figure 5 :
Figure 5: Strain data in the continuous vibration strain test.(a) Axial strain at H1.(b) Radial and volumetric strain at H1. (c) Axial, radial, and volumetric strain at H2.(d) Axial and radial strain at H1 and H2.

Figure 6 :Figure 7 :
Figure 6: Fracture mode of the samples.(a) Destruction process of samples (the red line area represents the destruction area).(b) Injection radius.(c) Fragments size distribution (the numbers mean the average sizes of three types of fragments).

Figure 12 :
Figure 12: Change process of strain amplitude.(a) Detail of the strain data.(b) Development of strain amplitude and strain.

Table 1 :
Summary of work related to fatigue behavior on rock.

Table 2 :
Mechanical properties of the granite samples.