# Experimental Study on Failure Law and Mechanism of Red Sandstone under Ultrasonic Vibration Excitation

Authors: Jiyao Wang; Xufeng Wang; Xuyang Chen; Liang Chen; Zhanbiao Yang; Zechao Chang; Lei Zhang; Zhijun Niu
Journal: Geofluids
 (2022)

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## Abstract

Rock breakage is inevitable for creating openings in underground engineering operations. Ultrasonic vibration has been attracting extensive attention for such a practice considering its outstanding performance in rock breakage. In order to understand the fundamental failure mechanism of rocks subjected to ultrasonic vibrations, based on P-wave monitoring and the direct current electric method, we captured the evolution of the failure process of the red sandstone. In addition, we fundamentally analyse the failure mechanisms of the red sandstone using numerical simulation and microscopy scans. It was found that extensive fractures were initiated due to the ultrasonic vibration and the fractures propagated downwards forming a conical shape. The apparent resistivity became as high as 320000 Ω being 16 times the initial resistivity. The fracture propagated downwards as deep as 41 mm. The maximum damage parameter on the testing sample could be as high as 0.68, and it completely failed after 140 s of ultrasonic vibration duration. As a result of numerical simulation, it was found that the microfractures and pores in the testing sample were activated due to the stress wave resulting from the ultrasonic vibration leading to the fracture propagation and eventually complete failure. Through comparing the performance of uniaxial compressive loading and ultrasonic vibration techniques in rock damage, it was concluded the latter has a much higher capacity and competence in rock breakage.


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## Body

## 1. Introduction

The underground engineering operations have been surging in the past decades in both mining engineering and tunnelling engineering due to the decrease of mineral resources in shallow depth and available space on the surface [1, 2]. As such, the rock breakage has been significantly important and increasing the rock breakage efficiency as well as decreasing the associated cost has attracted significant attention from researchers [3]. The current common rock breakage methodologies include drilling and blasting, machinery, and hydraulic fracturing as well as thermal breakage [4–7]. It is noteworthy that these methods have common limitations of being high cost and lower rock breakage efficiency and as a result, adversely affect the rock breakage performance in the field.Rock is a heterogeneous material having extensive micropores and defects [8]. As such, if the rock is under a constant cyclic loading, the internal pores and defects would be activated leading to fracture propagation and eventually failure in the macro scale. To date, the failure mechanism of the rock under cyclic loading conditions has been extensively investigated. Guo et al. [9] has examined the evolution of the failure process of red sandstone under a cyclic loading up to 100 MPa and hence concluded that the hysteresis loop indicates the internal failure and a reduction in the hysteresis energy to carry the load. It was found as the hysteresis energy decreases during the cyclic loading testing, the load-carrying capacity of the rock would decrease as well. Taheri et al. [10] carried out the cyclic testing on the sandstone subjected to uniaxial compressive loading as well as triaxial loading condition. It was found that under a high confinement condition, a small number of loading cycles would initiate the rock failure followed by a complete failure after more loading cycles. Yan et al. [11] carried out dynamic cyclic testing on granite subjected to triaxial loading condition using the split-Hopkinson bar (SHPB) and examined the mechanical behaviour and pore size variation as well as the change in the hydraulic conductivity of the granite during the test using nuclear magnetic resonance (NMR). It was found that as the number of cycles increases, the pore size in the sample started to decrease followed by increasing. On the other hand, the rock strength tended to increase followed by decreasing whereas the hydraulic conductivity constantly increased.Nowadays, ultrasonic vibration has attracted extensive attention from rock mechanics researchers due to its excellent performance in rock breakage. The research mainly falls into a few categories including failure mechanism in the rock resulting from ultrasonic vibration and ultrasonic facilities modification and optimization for rock mechanics-related purposes. For instance, the materials of the ultrasonic facilities have been investigated [12, 13]. The driller of ultrasonic facilities has been studied as well [14, 15]. These research outcomes provided alternative methodologies for rock breakage. In addition, Neeson and Lucas [16] examined the evolution of the fractures and strength variation of the fully saturated porous rock subjected to ultrasonic vibration. It confirms the feasibility of ultrasonic vibration in reducing rock strength. Yin et al. [17] examined the strength of coal specimens under various static compressive loadings subjected to ultrasonic vibration. They also capture the evolution of the fracture propagation using a CT scan. As a result, it was found that the strength of the coal specimen tended to decrease as the static compressive strength applied to the specimen increased. Tang et al. [18] defined the fracture propagation of the coal specimen in three stages being the micropores formation, fracture propagation leading to form bigger pores, and eventually complete failure of the coal specimen. They successfully implemented their research into coal seam gas drainage practice. Zhao et al. [19, 20] visually observed the microfracture propagation of granite after 0, 2, and 4 mins damage by ultrasonic vibration using an electric microscope. It confirmed that the ultrasonic vibration enhanced the propagation of the micropores and defects in the rock, and the tensile failure of the microdefects was the main cause of the rock failure. Yang et al. [21, 22] examined the fracture propagation of the rock specimen under uniaxial compressive loading using the parallel network electrical instrument (WBD) and confirmed such a technique performs well in monitoring the evolution of the fracture propagation of small rock specimens.As opposed to the aforementioned studies, in this research, we examined the fracture propagation in the red sandstone due to ultrasonic vibration damage followed by further analysing the failure mechanism in the rock breakage. The scope of the paper is in Section2, where we introduced research methodologies and sample preparation as well as the testing facility; in Section 3, we presented our testing results along with data analysis; in Section 4, we investigated the failure mechanism of the red sandstone subject to ultrasonic vibration damage and in Section 5, we made a remarkable conclusion.


## 2. Experimental Design

### 2.1. Sample Preparation and Experiment Facility

The rock specimens were red sandstone obtained from the city of Xuzhou, Jiangsu Province. Two types of specimens were cored including the rectangle sample (50 × 50 × 100 mm) and cylindrical samples (50 mm in diameter and 100 mm in length). All the specimens were ground so each end is flat and smooth. In order to ensure the consistency of the specimens, the P-wave of each was monitored to identify the outlier samples having wave velocities less than the average value. The mechanical properties of the red sandstone are summarised in Table1.Table 1
Physical and mechanical parameters of red sandstone.
Elastic modulus (GPa)Poisson ratioCompressive strength (MPa)Extension strength (MPa)Internal friction angle (°)Cohesion (MPa)600.2554.26.1242.4418.21The core facilities in this research are the ultrasonic vibration component (see Figure1) and direct current electricity monitor (see Figure 2). The former consists of an ultrasonic generator to generate ultrasonic waves, a transducer to transfer electrical energy to mechanical energy, an amplitude transformer to enlarge the vibration amplitude as well as an air compressor to stabilize the pressure. This component has power as high as 1500 w, frequency 20 kHz, vibration amplitude 40 um, voltage up to 220 V, current up to 10 A, and up to 1 MPa loading pressure. The data acquisition was achieved by the WBD system developed by Huizhou Geological Safety Research Institute in Anhui province.Figure 1
Schematic of ultrasonic vibration inducer.Figure 2
Direct current electrical monitor.Rock normally fails in a few stages in sequence being elastic deformation, microfracture initiation, macrofracture formation, fracture propagation, and eventually complete failure. Such a failure mechanism is highly associated with the evolution of the internal fractures of the rock. It is noteworthy that the electrical resistivity would increase with the evolution of the fractures in the rock. The distribution of the electrical resistivity in the rock could be mapped out by the direct current electrical method, and thereafter, the apparent electrical resistivity in the rock can be visually illustrated with the aid of software such as Tecplot.As the P-wave velocity is sensitive to the microstructural variation, such a technique was adopted to detect the change in the micropores in the rock (see Figure3). During the test, the P-wave velocities at various stages were captured and hence correlated with the micropore size in the rock.Figure 3
Nonmetal ultrasonic monitoring device.


### 2.2. Electrical Detection Method and Electrode Arrangement

Electrical resistivity is a key geophysical parameter for rocks. It can be obtained by the direct current electrical method and hence used to indicate the internal failure or fractures in the rock. The principle is through supplying the current to the electrodes, the electrical resistivity can be determined by the voltage drop between the electrodes. The resistivity distribution provides an estimation of the fracture distribution as the electrical resistivity can be correlated with fractures in the rock. Nakamura and Kusumi [23] carried out extensive tests to determine the electrical resistivity of various rock specimens with different porosities and hence confirmed the electrical resistivity would increase with the size of the pores in the rock. Coli et al. [24] successfully captured the fractures in the excavation surface in underground operations based on their research in the correlation between the rock pore size and hydraulic conductivity as well as electrical resistivity. Niu et al. [25] further analysed the effect of the fracture propagation on the electrical resistivity of the rock based on the direct current electrical method and confirmed that the electrical resistivity would spike when the macro fractures were formed.The conventional electrodes were installed by drilling the holes on the sample. However, the red sandstone specimen was too small, and it was believed that the drilled holes would affect its performance. As such, the electrode stickers were attached onto the specimen surface. The glue was able to tolerate high temperatures and conduct electricity. The sticker was made of copper and had a dimension of 0.5 × 0.8 mm and a thickness of 0.05 mm.For a rectangular sample, eight electrodes were attached onto each of the four sides and connected to the electrical mainframe through wires (see Figure4). This arrangement was able to capture the real-time electrical resistivity distribution during the test.Figure 4
Distribution of electrodes. (a) Electrode distribution diagram (b) Physical picture of electrode distribution.
(a)(b)


### 2.3. Experiment Procedures

The ultrasonic vibrations were generated for six different periods of time being 40 s, 60 s, 80 s, 100 s, 120 s, and 140 s, respectively (see Table2). The electrical resistivity at different locations of the specimen was monitored straight after each vibration. Ten measurement points with 1 cm in between were arranged at each side of the specimen (see Figure 5). After each test, the P-wave velocities at three cross-sections of the rock specimen including the upper monitoring plane, middle monitoring plane, and lower monitoring plane were recorded.Table 2
Ultrasonic vibration generation experimental program.
Specimen numberTop load static pressure (MPa)Excitation time (s)10.024020.026030.028040.0210050.0212060.02140Figure 5
Measurement points distribution for the rectangular specimen.


## 2.1. Sample Preparation and Experiment Facility

The rock specimens were red sandstone obtained from the city of Xuzhou, Jiangsu Province. Two types of specimens were cored including the rectangle sample (50 × 50 × 100 mm) and cylindrical samples (50 mm in diameter and 100 mm in length). All the specimens were ground so each end is flat and smooth. In order to ensure the consistency of the specimens, the P-wave of each was monitored to identify the outlier samples having wave velocities less than the average value. The mechanical properties of the red sandstone are summarised in Table1.Table 1
Physical and mechanical parameters of red sandstone.
Elastic modulus (GPa)Poisson ratioCompressive strength (MPa)Extension strength (MPa)Internal friction angle (°)Cohesion (MPa)600.2554.26.1242.4418.21The core facilities in this research are the ultrasonic vibration component (see Figure1) and direct current electricity monitor (see Figure 2). The former consists of an ultrasonic generator to generate ultrasonic waves, a transducer to transfer electrical energy to mechanical energy, an amplitude transformer to enlarge the vibration amplitude as well as an air compressor to stabilize the pressure. This component has power as high as 1500 w, frequency 20 kHz, vibration amplitude 40 um, voltage up to 220 V, current up to 10 A, and up to 1 MPa loading pressure. The data acquisition was achieved by the WBD system developed by Huizhou Geological Safety Research Institute in Anhui province.Figure 1
Schematic of ultrasonic vibration inducer.Figure 2
Direct current electrical monitor.Rock normally fails in a few stages in sequence being elastic deformation, microfracture initiation, macrofracture formation, fracture propagation, and eventually complete failure. Such a failure mechanism is highly associated with the evolution of the internal fractures of the rock. It is noteworthy that the electrical resistivity would increase with the evolution of the fractures in the rock. The distribution of the electrical resistivity in the rock could be mapped out by the direct current electrical method, and thereafter, the apparent electrical resistivity in the rock can be visually illustrated with the aid of software such as Tecplot.As the P-wave velocity is sensitive to the microstructural variation, such a technique was adopted to detect the change in the micropores in the rock (see Figure3). During the test, the P-wave velocities at various stages were captured and hence correlated with the micropore size in the rock.Figure 3
Nonmetal ultrasonic monitoring device.


## 2.2. Electrical Detection Method and Electrode Arrangement

Electrical resistivity is a key geophysical parameter for rocks. It can be obtained by the direct current electrical method and hence used to indicate the internal failure or fractures in the rock. The principle is through supplying the current to the electrodes, the electrical resistivity can be determined by the voltage drop between the electrodes. The resistivity distribution provides an estimation of the fracture distribution as the electrical resistivity can be correlated with fractures in the rock. Nakamura and Kusumi [23] carried out extensive tests to determine the electrical resistivity of various rock specimens with different porosities and hence confirmed the electrical resistivity would increase with the size of the pores in the rock. Coli et al. [24] successfully captured the fractures in the excavation surface in underground operations based on their research in the correlation between the rock pore size and hydraulic conductivity as well as electrical resistivity. Niu et al. [25] further analysed the effect of the fracture propagation on the electrical resistivity of the rock based on the direct current electrical method and confirmed that the electrical resistivity would spike when the macro fractures were formed.The conventional electrodes were installed by drilling the holes on the sample. However, the red sandstone specimen was too small, and it was believed that the drilled holes would affect its performance. As such, the electrode stickers were attached onto the specimen surface. The glue was able to tolerate high temperatures and conduct electricity. The sticker was made of copper and had a dimension of 0.5 × 0.8 mm and a thickness of 0.05 mm.For a rectangular sample, eight electrodes were attached onto each of the four sides and connected to the electrical mainframe through wires (see Figure4). This arrangement was able to capture the real-time electrical resistivity distribution during the test.Figure 4
Distribution of electrodes. (a) Electrode distribution diagram (b) Physical picture of electrode distribution.
(a)(b)


## 2.3. Experiment Procedures

The ultrasonic vibrations were generated for six different periods of time being 40 s, 60 s, 80 s, 100 s, 120 s, and 140 s, respectively (see Table2). The electrical resistivity at different locations of the specimen was monitored straight after each vibration. Ten measurement points with 1 cm in between were arranged at each side of the specimen (see Figure 5). After each test, the P-wave velocities at three cross-sections of the rock specimen including the upper monitoring plane, middle monitoring plane, and lower monitoring plane were recorded.Table 2
Ultrasonic vibration generation experimental program.
Specimen numberTop load static pressure (MPa)Excitation time (s)10.024020.026030.028040.0210050.0212060.02140Figure 5
Measurement points distribution for the rectangular specimen.


## 3. Experimental Results and Data Analysis

### 3.1. Ultrasonic Vibration Effect on Rock Compressive Strength

The fractures in the cylindrical specimen propagated during the ultrasonic vibration leading to the complete failure of the rock (see Figure6). Figure 6(a) shows the severe crack at the top section of the rock specimen whereas Figure 6(b) shows the bulky crush after the test. Both can be seen as failures. After each ultrasonic vibration, the cylindrical samples were tested under uniaxial compressive loading to determine their uniaxial compressive strength (UCS). The influence of each ultrasonic vibration on the UCS of the rock specimen is illustrated in Figure 7.Figure 6
Failure observation of rock specimen after ultrasonic vibration. (a) Upper crushing of specimen (b) Large fragments separated from the body of the specimen.
(a)(b)Figure 7
Effect of ultrasonic vibration on the UCS of the rock specimen.As seen from Figure7, the damage in the rock due to the ultrasonic vibration became visually clear after the vibration has been being generated for 40 s. As the ultrasonic vibration being generated longer, the area of the damage on the surface of the rock specimen increased and so did the length and the width of the fractures in the rock. As a result, the UCS of the rock specimen decreased as evidenced by Figure 7 where the UCS decreased from 54.2 MPa to 40 MPa equivalent to approximately 26% reduction.


### 3.2. Fracture Propagation Induced by Ultrasonic Vibration

In addition to the tests on cylindrical samples, more tests have been carried out on rectangular samples to capture the fracture propagation induced by ultrasonic vibration. The testing conditions for rectangular samples were exactly the same as those for cylindrical samples. As a result, it was found that the damage area on the top of the sample as well as the fracture length at the side of the sample increased as the ultrasonic vibration was generated for a longer period of time (see Figures8 and 9).Figure 8
Illustration of fracture propagation. (a) 40 s. (b) 60 s. (c) 80 s. (d) 100 s. (e) 120 s. (f) 140 s.Figure 9
The change of different failure parameters with time.Overall, the damage diameter on the top of the sample increased from 19 mm when ultrasonic vibrating for 40 s to 38 mm when ultrasonic vibrating for 140 s. It is noteworthy that the increase rate in the damage diameter was more significant from 19 mm at 40 s vibration duration to 35 mm at 100 s vibration duration. By contrast, the increase rate became slower thereafter leading to an increase from 35 mm to 38 mm. The damage depth increased from 2 mm at 40 s vibration duration to 28 mm at 140 s vibration duration. The fracture length at the sample side increased from 5 mm at 40 s vibration duration to 10 mm at 80 s vibration duration at a slower rate followed by a spike increase to 41 mm at 140 s vibration duration.It has been observed that the rock failure induced by ultrasonic vibration is a progressive failure starting with the initial crack at the area of the rock closer to the vibration generator. Thereafter, the fractures at the top surface of the specimen formed followed by propagating downwards. Over the course of fracture propagation, the bulk at the top section of the sample fell off along with crushed fine materials until the complete failure of the rock specimen (see Figure10). As opposed to conventional uniaxial compressive tests and triaxial tests, ultrasonic vibration could lead to a rock failure to a higher extent.Figure 10
Illustration of progressive failure in rock during the test. (a) Broken starting. (b) In the broken. (c) Completely broken.
(a)(b)(c)


### 3.3. Electrical Resistivity Distribution in Rectangular Specimen during the Test

The direct current electrical method was used to capture the electrical resistivity at different locations of the rock samples at different time durations subjected to ultrasonic vibration. The electrical resistivity distribution in the rock sample after different ultrasonic vibration durations is illustrated in Figure11. At the 40 s vibration duration, the top surface of the rock sample exhibited an electrical resistivity as high as 80000 Ω whereas the other portions of the sample showed a lower resistivity. As the ultrasonic vibration being generated longer, the electrical resistivity at the top surface of the rock sample increased and it decreased gradually as moving downwards. When the sample was under the longest ultrasonic vibration for 140 s, the electrical resistivity at the top surface of the rock specimen was up to 320000 Ω being equivalent to 16 times of that before inducing the ultrasonic vibration.Figure 11
Electrical resistivity distribution in the rock specimen at various ultrasonic vibration durations. (a) 40 s. (b) 60 s. (c) 80 s. (d) 100 s. (e) 120 s. (f) 140 s.It is noteworthy that the fractures due to the ultrasonic vibration tend to concentrate more as opposed to that due to the conventional testing. In order to investigate the fracture propagation induced by the ultrasonic vibration, the electrical resistivity distribution along the longitudinal direction was mapped out based on the measurements at points 1 and 2 at the top, points 4 and 5 in the middle, and points 8 and 9 at the bottom (see Figure12). In addition, the electrical resistivity along the lateral direction was mapped out based on the measurements at points 11, 12, 1, 14, and 15 at the top section as well as points 16, 17, 4, 19, and 20 in the middle (see Figure 13).Figure 12
Electrical resistivity distributions along the longitudinal direction.Figure 13
Electrical resistivity distributions along the lateral direction. (a) At the top section of the rock specimen. (b) In the middle of the rock specimen.
(a)(b)As Figure12 shows, the electrical resistivity at points 1 and 2 increased as the ultrasonic vibration was generated longer indicating the damage at the top section of the rock became more extensive. By contrast, the electrical resistivity at points 4 and 5 remained constantly if ultrasonic vibration was generated for less than 100 s indicating that the energy generated by the ultrasonic vibration would be absorbed by the top section of the rock specimen first. Thereafter, the electrical resistivity increased from 5000 Ω to 12500 Ω indicating the top section has failed and the middle section started absorbing energy induced by ultrasonic vibration.As the fractures propagated only down to the middle section of the rock specimen as demonstrated by Figure11, we decided to analyse the electrical resistivity distribution along the lateral direction based on the measurements at points 11, 12, 1, 14, and 15 at the top (see Figure 13(a)) as well as 16, 17, 4, 19, and 20 in the middle (see Figure 13(b)). It could be seen the centre part of the rock specimen has the highest electrical resistivity whereas as moving towards the sides, the electrical resistivity gradually decreased. The peak value of the electrical resistivity could be up to 320000 Ω at the top and 230000 Ω in the middle of the rock specimen. This indicated that the majority of fractures occurred in the centre of the specimen highlighting the good control of the ultrasonic vibration direction and excellent energy concentration generated by the vibration. Such an advantage would no doubt enhance the rock breakage.


### 3.4. P-Wave Velocities Analysis Results

In order to identify the damage at different locations of the rock specimen due to the ultrasonic vibration, three cross-sections at the top, middle, and bottom of the specimen were selected for measuring the P-wave velocities. Table3 shows the P-wave velocities at different locations after ultrasonic vibration for various periods of time.Table 3
P-wave velocities after ultrasonic vibration for various periods of time.
Monitoring locationInitial wave velocity40 s60 s80 s100 s120 s140 sSection A4875432341213521315628102741Section B4863479146534355402037663564Section C4871486948664860484248364833Average4889496849984756453143783646P-wave velocity is sensitive to any minor variation of microstructures in the rock such that it could be used to reflect the fracture distribution in the rock according to(1)Dm=1−VpiVp02,where Dm is the damage parameter as a result of ultrasonic vibration, Vpi is the P-wave velocity after ith ultrasonic vibration in m/s, and Vp0 is the P-wave velocity before the ultrasonic vibration in m/s. The P-wave velocities and damage parameters at different locations of the rock specimen after various vibration durations are shown in Figure 14.Figure 14
P-wave velocities and damage parameters at different locations of the rock specimen after various ultrasonic vibration durations. (a) Section A. (b) Section B. (c) Section C.
(a)(b)(c)It could be seen that the damage became visually apparent at cross-section A after ultrasonic vibration for 40 s. As the duration of ultrasonic vibration increased from 40 s to 140 s, the P-wave velocity decreased from 4625 m/s to 2741 m/s. In the meantime, the damage parameter increased from 0.09 to 0.68. In addition, as per cross-section B, the P-wave velocity decreased at a low rate from 4799 m/s after 40 s vibration to 4625 m/s after 60 s vibration whereas the damage parameter increased from 0.02 to 0.08. Thereafter, the P-wave velocity further decreased to 3546 m/s after 140 s vibration at a higher rate whereas the damage parameter increased to 0.46. By contrast, the P-wave velocity remained stable at the cross-section C regarding the duration of the ultrasonic vibration. This could be attributed to the intact rock at cross-section C where the fractures did not propagate to.All the observations and testing results reinforced that the ultrasonic vibration technique can be well controlled in terms of the vibration direction and rock damage area. It has distinguished advantages over other rock breakage techniques by having more energy concentration on the damage area in the rock and better direction orientation.


## 3.1. Ultrasonic Vibration Effect on Rock Compressive Strength

The fractures in the cylindrical specimen propagated during the ultrasonic vibration leading to the complete failure of the rock (see Figure6). Figure 6(a) shows the severe crack at the top section of the rock specimen whereas Figure 6(b) shows the bulky crush after the test. Both can be seen as failures. After each ultrasonic vibration, the cylindrical samples were tested under uniaxial compressive loading to determine their uniaxial compressive strength (UCS). The influence of each ultrasonic vibration on the UCS of the rock specimen is illustrated in Figure 7.Figure 6
Failure observation of rock specimen after ultrasonic vibration. (a) Upper crushing of specimen (b) Large fragments separated from the body of the specimen.
(a)(b)Figure 7
Effect of ultrasonic vibration on the UCS of the rock specimen.As seen from Figure7, the damage in the rock due to the ultrasonic vibration became visually clear after the vibration has been being generated for 40 s. As the ultrasonic vibration being generated longer, the area of the damage on the surface of the rock specimen increased and so did the length and the width of the fractures in the rock. As a result, the UCS of the rock specimen decreased as evidenced by Figure 7 where the UCS decreased from 54.2 MPa to 40 MPa equivalent to approximately 26% reduction.


## 3.2. Fracture Propagation Induced by Ultrasonic Vibration

In addition to the tests on cylindrical samples, more tests have been carried out on rectangular samples to capture the fracture propagation induced by ultrasonic vibration. The testing conditions for rectangular samples were exactly the same as those for cylindrical samples. As a result, it was found that the damage area on the top of the sample as well as the fracture length at the side of the sample increased as the ultrasonic vibration was generated for a longer period of time (see Figures8 and 9).Figure 8
Illustration of fracture propagation. (a) 40 s. (b) 60 s. (c) 80 s. (d) 100 s. (e) 120 s. (f) 140 s.Figure 9
The change of different failure parameters with time.Overall, the damage diameter on the top of the sample increased from 19 mm when ultrasonic vibrating for 40 s to 38 mm when ultrasonic vibrating for 140 s. It is noteworthy that the increase rate in the damage diameter was more significant from 19 mm at 40 s vibration duration to 35 mm at 100 s vibration duration. By contrast, the increase rate became slower thereafter leading to an increase from 35 mm to 38 mm. The damage depth increased from 2 mm at 40 s vibration duration to 28 mm at 140 s vibration duration. The fracture length at the sample side increased from 5 mm at 40 s vibration duration to 10 mm at 80 s vibration duration at a slower rate followed by a spike increase to 41 mm at 140 s vibration duration.It has been observed that the rock failure induced by ultrasonic vibration is a progressive failure starting with the initial crack at the area of the rock closer to the vibration generator. Thereafter, the fractures at the top surface of the specimen formed followed by propagating downwards. Over the course of fracture propagation, the bulk at the top section of the sample fell off along with crushed fine materials until the complete failure of the rock specimen (see Figure10). As opposed to conventional uniaxial compressive tests and triaxial tests, ultrasonic vibration could lead to a rock failure to a higher extent.Figure 10
Illustration of progressive failure in rock during the test. (a) Broken starting. (b) In the broken. (c) Completely broken.
(a)(b)(c)


## 3.3. Electrical Resistivity Distribution in Rectangular Specimen during the Test

The direct current electrical method was used to capture the electrical resistivity at different locations of the rock samples at different time durations subjected to ultrasonic vibration. The electrical resistivity distribution in the rock sample after different ultrasonic vibration durations is illustrated in Figure11. At the 40 s vibration duration, the top surface of the rock sample exhibited an electrical resistivity as high as 80000 Ω whereas the other portions of the sample showed a lower resistivity. As the ultrasonic vibration being generated longer, the electrical resistivity at the top surface of the rock sample increased and it decreased gradually as moving downwards. When the sample was under the longest ultrasonic vibration for 140 s, the electrical resistivity at the top surface of the rock specimen was up to 320000 Ω being equivalent to 16 times of that before inducing the ultrasonic vibration.Figure 11
Electrical resistivity distribution in the rock specimen at various ultrasonic vibration durations. (a) 40 s. (b) 60 s. (c) 80 s. (d) 100 s. (e) 120 s. (f) 140 s.It is noteworthy that the fractures due to the ultrasonic vibration tend to concentrate more as opposed to that due to the conventional testing. In order to investigate the fracture propagation induced by the ultrasonic vibration, the electrical resistivity distribution along the longitudinal direction was mapped out based on the measurements at points 1 and 2 at the top, points 4 and 5 in the middle, and points 8 and 9 at the bottom (see Figure12). In addition, the electrical resistivity along the lateral direction was mapped out based on the measurements at points 11, 12, 1, 14, and 15 at the top section as well as points 16, 17, 4, 19, and 20 in the middle (see Figure 13).Figure 12
Electrical resistivity distributions along the longitudinal direction.Figure 13
Electrical resistivity distributions along the lateral direction. (a) At the top section of the rock specimen. (b) In the middle of the rock specimen.
(a)(b)As Figure12 shows, the electrical resistivity at points 1 and 2 increased as the ultrasonic vibration was generated longer indicating the damage at the top section of the rock became more extensive. By contrast, the electrical resistivity at points 4 and 5 remained constantly if ultrasonic vibration was generated for less than 100 s indicating that the energy generated by the ultrasonic vibration would be absorbed by the top section of the rock specimen first. Thereafter, the electrical resistivity increased from 5000 Ω to 12500 Ω indicating the top section has failed and the middle section started absorbing energy induced by ultrasonic vibration.As the fractures propagated only down to the middle section of the rock specimen as demonstrated by Figure11, we decided to analyse the electrical resistivity distribution along the lateral direction based on the measurements at points 11, 12, 1, 14, and 15 at the top (see Figure 13(a)) as well as 16, 17, 4, 19, and 20 in the middle (see Figure 13(b)). It could be seen the centre part of the rock specimen has the highest electrical resistivity whereas as moving towards the sides, the electrical resistivity gradually decreased. The peak value of the electrical resistivity could be up to 320000 Ω at the top and 230000 Ω in the middle of the rock specimen. This indicated that the majority of fractures occurred in the centre of the specimen highlighting the good control of the ultrasonic vibration direction and excellent energy concentration generated by the vibration. Such an advantage would no doubt enhance the rock breakage.


## 3.4. P-Wave Velocities Analysis Results

In order to identify the damage at different locations of the rock specimen due to the ultrasonic vibration, three cross-sections at the top, middle, and bottom of the specimen were selected for measuring the P-wave velocities. Table3 shows the P-wave velocities at different locations after ultrasonic vibration for various periods of time.Table 3
P-wave velocities after ultrasonic vibration for various periods of time.
Monitoring locationInitial wave velocity40 s60 s80 s100 s120 s140 sSection A4875432341213521315628102741Section B4863479146534355402037663564Section C4871486948664860484248364833Average4889496849984756453143783646P-wave velocity is sensitive to any minor variation of microstructures in the rock such that it could be used to reflect the fracture distribution in the rock according to(1)Dm=1−VpiVp02,where Dm is the damage parameter as a result of ultrasonic vibration, Vpi is the P-wave velocity after ith ultrasonic vibration in m/s, and Vp0 is the P-wave velocity before the ultrasonic vibration in m/s. The P-wave velocities and damage parameters at different locations of the rock specimen after various vibration durations are shown in Figure 14.Figure 14
P-wave velocities and damage parameters at different locations of the rock specimen after various ultrasonic vibration durations. (a) Section A. (b) Section B. (c) Section C.
(a)(b)(c)It could be seen that the damage became visually apparent at cross-section A after ultrasonic vibration for 40 s. As the duration of ultrasonic vibration increased from 40 s to 140 s, the P-wave velocity decreased from 4625 m/s to 2741 m/s. In the meantime, the damage parameter increased from 0.09 to 0.68. In addition, as per cross-section B, the P-wave velocity decreased at a low rate from 4799 m/s after 40 s vibration to 4625 m/s after 60 s vibration whereas the damage parameter increased from 0.02 to 0.08. Thereafter, the P-wave velocity further decreased to 3546 m/s after 140 s vibration at a higher rate whereas the damage parameter increased to 0.46. By contrast, the P-wave velocity remained stable at the cross-section C regarding the duration of the ultrasonic vibration. This could be attributed to the intact rock at cross-section C where the fractures did not propagate to.All the observations and testing results reinforced that the ultrasonic vibration technique can be well controlled in terms of the vibration direction and rock damage area. It has distinguished advantages over other rock breakage techniques by having more energy concentration on the damage area in the rock and better direction orientation.


## 4. Discussion

Due to the current study of ultrasonic vibration excitation, broken rock is still in its infancy, so this article from the perspective of the abovementioned test results of ultrasonic vibration excitation, the failure mechanism of the rock are discussed for the failure mechanism in the process of rock specimen broken for further exploration, with the method of numerical simulation to simulate the process of specimen damage analysis.A numerical simulation was conducted using PFC 2D to further analyse the failure mechanism associated with rock breakage induced by the ultrasonic vibration. The size of the model is consistent with the cylindrical rock specimen tested, 50 mm in diameter and 100 mm in length (see Figure15). The ultrasonic vibration was simulated by the wall module following the sine form:(2)μ=Asin2πft,where A is the vibration amplitude being 40 um in this study and f is the vibration frequency being 2000 in this study.Figure 15
Schematic illustration of the numerical model.In order to ensure the accuracy of the numerical simulation test, the microscopic parameters should be calibrated properly first. After selecting the relevant microscopic parameters, the numerical simulation was carried out to obtain the values of each parameter, and the corresponding macro mechanical parameters obtained from laboratory tests were compared and analysed. Through continuous debugging, until the simulated calculation value is close to the real value obtained in the room, a set of reasonable microscopic parameters are finally selected as shown in Table4.Table 4
Microscopic parameter values.
Microscopic parameterMicroscopic parameter valuesMinimum particle radius (mm)0.15Maximum particle radius (mm)0.3Density (kg/m3)2700Particle normal/tangential stiffness ratio1Particle friction coefficient0.45Parallel bond modulus (GPa)1.7Normal strength of parallel bond (MPa)31Tangential strength of parallel bond (MPa)39Figure16 shows that the uniaxial compressive strength measured in the complete sample chamber is 67.8 MPa, while the uniaxial compressive strength calculated by numerical simulation is 68.4 MPa, which is less than 1%. Since there is no compaction stage in numerical simulation, the strain generated by numerical simulation is higher than that of the laboratory test. The elastic modulus is the secant modulus of the stress-strain curve. The elastic modulus obtained by numerical simulation is 3.44 GPa, and the elastic modulus obtained by experiment is 3.42 GPa, with only 0.6 difference between them. Therefore, the selection of model parameters is reasonable.Figure 16
Comparison between numerical simulation and experimental stress-strain curves.The fracture propagation at various ultrasonic vibration durations was simulated (see Figure17). The cracks due to shear and tension were highlighted in blue and red in Figure 17 which shows the fracture propagation at five different points of time (a, b, c, d, and e). Figure 17(a) shows the initiation of the fracture starting from the left side followed by moving towards the right as illustrated in Figure 17(b). The cracks were mainly associated with tension at these two stages. Figure 17(c) shows the fracture propagation in the conical shape where the failure at the top is mainly associated with shear crack whereas that at the bottom is a combination of shear and tension. These three stages (a, b, and c) reflect the progressive failures as illustrated in Figure 8. Thereafter, the fractures further propagated downwards and towards the rock surface (see Figure 17(d)) until the complete failure had bulks falling off (see Figure 17(e)).Figure 17
Progressive fracture propagation simulated in PFC 2D. (a) Typical time A. (b) Typical time B. (c) Typical time C. (d) Typical time D.
(a)(b)(c)(d)In order to further verify the development law of cracks in the process of ultrasonic vibration excitation in numerical simulation, the red sandstone samples were scanned by using an electron microscope before ultrasonic vibration excitation. At the end of the ultrasonic vibration excitation test, rock samples were extracted from the fracture area and fracture development area of the specimen for the SEM test. SEM results before ultrasonic vibration excitation are shown in Figure18, while SEM results after ultrasonic vibration excitation are shown in Figure 19.Figure 18
Electrical microscopy scan before the test.Figure 19
Electrical microscopy scan of the sample after 140 s ultrasonic vibration duration. (a) Fracture place. (b) Crack zone.
(a)(b)As shown in Figure18, red sandstone have evenly distributed grains and very few internal micro defects. The grain surface is smooth and surrounded by cement. The only defects are the pores and minor cracks at the interface between grains and cement. After the test with 140 s ultrasonic vibration duration, the failure interface is smooth indicating a shear failure. In a conventional rock breakage by static loading condition, as the loading rate is slow, the fracture would initiate from the internal defects in the rock and propagate through an optimum pathway with the least resistance. By contrast, the high vibration velocity and frequency of the ultrasonic generator could result in an extremely fast stress wave propagation through the rock sample, even faster than the crack propagation from the internal defects. As such, the rock fails in shear only before the massive crack propagating from internal defect as demonstrated in Figure 19(a). On the other hand, the crack interface exhibits cracks in grain and step-wise pattern (see Figure 19(b)). Cracks in grain are mainly associated with tensile failure whereas the step crack is associated with shear failure. Such an observation is consistent with the numerical simulation which shows a combination of the shear and tensile failures induced by ultrasonic vibration after the test. In addition, extensive crushed materials were observed after the test indicating a shear failure at the failure interface.


## 5. Conclusions

The failure mechanisms associated with ultrasonic vibration-induced damage on rock have been comprehensively investigated using laboratory testing and numerical simulation methodologies. The distinguished advantages of the ultrasonic vibration technique over the conventional rock breakage methodology and the uniaxial compressive loading, in particular, were also highlighted. We hence made the following remarkable conclusions:(1)
As a result of an ultrasonic vibration for up to 140 s, the UCS of red sandstone decreased by 26%. The fracture was as long as 41 mm whereas the depth of the damage was around 28 mm.(2)
As a result of direct current electrical monitoring on the red sandstone specimen, the electrical resistivity increased from 8000 Ω before the test to 320000 Ω at the failure. In addition, the observation showed that the energy generated by ultrasonic vibration is mainly concentrated at the centre of the rock specimen.(3)
As a result of P-wave velocities monitoring, the damage parameter could be as high as 0.68 demonstrating its excellent capability for rock breakage.(4)
As a result of electrical microscopy scan and numerical simulation of the damage on the rock induced by ultrasonic vibration, it is confirmed that the rock failure is associated with a combination of tensile and shear resulting from the compressive stress waves frequently generated by the ultrasonic vibration generator.



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