# Experimental Study on Energy Dissipation of Saturated Mudstone in Coal Mine under Impact Loading

Authors: Liangjie Guo; Yongyu Wang
Journal: Geofluids
 (2022)

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## Abstract

The influence of blasting energy on blasting fragmentation and damage of reserved rock is important for safety and schedule of drill-blasting construction in coal mine. This study is aimed at investigating the dynamic mechanical properties of mudstone in coal mine using the energy characterization method, and their quantitative relation formula was also developed. The impact compression experiments of mudstone in Huainan mining area were conducted to study the saturated mudstone dynamic mechanism, crack properties, and energy dissipation law using the diameter 50 mm split Hopkinson pressure bar (SHPB). The results show that under the back-and-forth reflection of the stress wave, the saturated mudstone specimens are characterized by circumferential failure and axial splitting damage, which appear in the rock grain interface. By energy analysis, the energy dissipation per volume (EDV), energy dissipation per mass (EDM), and absorption impedance energy ratio (AIER) are used to represent the energy dissipation characteristic of mudstone. And the AIER is the best index. Additionally, there is the quadratic function relationship between three indexes and average strain ratio, showing the dependence of the strain ratio.


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## Body

## 1. Introduction

Mudstone is widely distributed in coal measure strata, which is characterized by loose, poor cementation and low strength. Hence, mudstone is extremely sensitive to stress, moisture, temperature, and subsurface water [1, 2]. The mechanical property and inner structure of mudstone vary with the change of stress condition [3–5]. Many researchers studied the physical and mechanical properties and failure laws of mudstone in coal mine under complex natural environment conditions. The strength of mudstone is less than 30 MPa, reviewing the existing literature researches. And its strength would be lower when faced with water, temperature, weathering, and so on [6, 7]. Bhattarai et al. investigated the effect of chemical and physical weathering on the shear strength of the mudstone [8]. The results showed that the shear strength of fully weathered mudstone is 10 times larger than that of weak weathered mudstone. Huang et al. carried out a series of uniaxial compression experiments and creep experiments of mudstone specimens under different water contents and found that the rock strength and elastic modulus decreased rapidly with the increment of water content, and a nonlinear creep constitutive equation was established based on the experimental data [9]. Both Zhang et al. and Lu et al. studied the softening effect of mechanical properties of mudstone under high temperatures [10, 11]. High temperatures would cause thermal expansion of mudstone, and the expansion will increase with temperature increasing.Due to the effects of impact loading, such as blasting and mechanical vibration in coal mine, the disturbance range of surrounding rock mass in roadway increases, yet the bearing capacity of rock mass decreases. Hence, the roof fall and rock bottom drum are easily happened [12–15]. The dynamic behavior of rock under impact loading is an important issue for coal mining [16, 17]. Some typical complete dynamic stress-strain curves for marble and granite using SHPB technique are given by Shan et al. [18], together with an interpretative discussion on the shapes and meanings of the curves. Chen et al. tested the dynamic mechanical behavior of granite [19]. The results showed that impact dynamic strength increases as the precompression stress increases and can reach its maximum when the precompression stress is about 50% of the static tension strength. Liu et al. studied the mechanic properties of amphibolites, sericite-quartz schist, and sandstone under impact loading and analyzed the dynamic compressive strength, failure modes, and energy dissipation variation with the strain rate and the strain rate hardening effect from the perspective of sandstone microstructure [20]. Mardoukhi et al. used optical microscopy and profilometry to analyze the drop rate of tension strength and damage area of rock under impact loading using SHPB tests [21]. The dynamic mechanics of granitic specimens under different hydrostatic pressures were studied by Du et al., and the results showed that the dynamic strength of rock specimens increased with increasing the strain rate, while the rate sensitivity of rock strength decreased as the hydrostatic pressure increased [22]. The thermal effect on the dynamic properties of rock is another significant issue for deep coal mining. Fan et al. investigated the effects of high temperature on the dynamic behavior of granite using SEM and SHPB tests, and the results showed that both the dynamic strength and energy absorption capacity decreased as temperature increased [23].Many researchers studied the failure morphology of rock specimens under impact loadings. And Chinese scientists have made tremendous achievements. Li et al. studied the impact failure characteristics of rock subjected to one-dimensional coupled static and dynamic loads [24]. Rock specimens will break with a shear failure model subjected to one-dimensional coupled static and dynamic loads, while the failure mode will be splitting faulting for conventional impact testing. Zhao et al. considered that the impact failure of rock consists of tensile strain failure, axial splitting tensile failure, and crushing failure [25]. Li et al. performed the numerical study on the failure of sandstone, limestone, and dolomite under impact loading [26]. The failure modes of rock are integrity, cleavage, and smashing.Although many studies on mechanical properties of rock under impact loadings have been conducted [27–40], little attention was paid to the dynamic behavior of mudstone in coal mine. In consequence, this study is aimed at investigating the dynamic mechanical properties of mudstone in coal mine using the energy characterization method, and their quantitative relation formula was also developed. In the present study, a series of compression experiments of mudstone under different impact loadings from Huainan mining area, China, was conducted to study the mudstone dynamic behaviors, crack properties, and energy dissipation law using the diameter 50 mm SHPB test device. The relationships of crack and material composition of mudstone were determined. From the perspective of energy absorption, the deformation, failure, and energy dissipation of mudstone were described. The study provides good theoretical and technical supports for coal-rock roadway blasting excavation construction.


## 2. Theoretical Basis of SHPB Tests

In the conventional SHPB technique, the mudstone specimen is located in between the incident bar and the transmitted bar. The SHPB device is shown in Figure1. When the striker bar hits the incident bar, a rectangular stress pulse is generated and travels along the incident bar until it strikes the specimen. Parts of the incident stress pulse reflect from the bar/specimen interface because of the material impedance mismatch. And part of it transmits through the specimen. The transmitted pulse emitted from the specimen travels along the transmitted bar until it strikes the end of the bar. The SHPB device is from Anhui University of Science and Technology. The length of the striker, incident bar, and transmitted bar is 0.60 m, 2.40 m, and 1.20 m, respectively. All the material of the bar is alloy steel. And the density of the bar is 7.8 g/cm3, Young’s modulus is 210 GPa, and longitudinal wave velocity is 5.19 km/s, respectively.Figure 1
Structural constituents of SHPB device.Under the failure of rock subjected to impact loading, rock constantly exchanges energy with the exotic environment. It is an evolutionary process that the microcracks vary from disorder to order and finally develop into macrocracks. The process from microdamage to macrofracture is the process of energy dissipation [41]. Hence, the failure mechanism can be easily revealed by energy analysis. In SHPB tests, both the stress and strain can be obtained in terms of the recorded strains of the incident and transmitted bars. During the impact loading, the incident energy WIt, transmitted energy WRt, and reflected energy WTt of specimens are as follows [12, 22, 32]:
(1)WIt=AEC0∫0tεI2tdt,(2)WRt=AEC0∫0tεR2tdt,(3)WTt=AEC0∫0tεT2tdt,where A is the section area of the bar, E is Young’s modulus of the bar, and C0 is the wave velocity of the bar. εIt, εRt, and εTt are the strain of the incident wave, reflected wave, and transmitted wave at time t, respectively.By omitting the wasted energy induced by the friction force between the specimen and incident bar, transmitted bar during the impact loadings, the absorbed energy of specimenWSt is
(4)WSt=WIt−WRt+WTt.


## 3. Specimen Preparation and Physics

### 3.1. Preparation of Specimens

Located in the central of Anhui province, China, middle and lower reaches of Yangtze River (see in Figure2), the Panyi mine is faced with the danger of high in situ stress, water pressure, and temperature in rock roadway construction. This mining area was in use in December 2016. The roadway floor heave and side extrusion deformation were found in 2017. The mudstone blocks, used to be in experiments, originated from the 800 m deep 5# coal seam mining area as shown in the geological section in Figure 3. The coal mine area consists of mudstone, sandstone, and coal formations dipping about 40° to the south in the area of interest. There are some faults passing through the mudstone-sand layers, easily leading to rock fall. The mudstone forms in the development period of continental strong tensional faulting and experienced main squeezing and luffing tectonic and hydrothermal alteration activity.Figure 2
Specimen location: Panyi mining area, Huainan, China.Figure 3
Geological section along 5# coal seam mining area. The obtained rock specimen is located within mudstone that dips approximately 40 deg south.The cylindrical specimens are obtained by drilling, cutting, and grinding in the laboratory. In order to meet the assumption of one-dimensional stress wave propagation theory of SHPB and reduce the friction and axial inertia effect of the specimen, the length-diameter ratio of the prepared specimens is 0.5. Hence, the diameter of the specimen is 50 mm; the length of the specimen is 25 mm. No parallelism is within 0.05 mm on both ends of the specimen, and the roughness is within 0.02 mm. Those mudstone specimens in coal mine are shown in Figure4.Figure 4
Mudstone specimen: diameter 50 mm and length 25 mm.Before testing, the process of saturating specimens with liquid was conducted using the vacuum saturation device (ZYB-IA, see Figure5), by following the below procedure. Distilled water was used as a saturated liquid to avoid the potential influence of chemical factors.
(1)
Put the dry mudstone specimen in a basket in the vacuum saturation device(2)
Vacuum the specimen storehouse until no air bubbles were generated in the liquid storage tank(3)
Switch on the specific valve; the distilled water in the liquid storage tank was sucked into the specimen storehouse(4)
The mudstone specimen was immersed in the distilled water (i.e., vacuum water-saturated environment) for 7 days, and the saturation pressure was set as 1.0 MPa(5)
Take out the mudstone specimen for the next step of testingFigure 5
Vacuum saturation device (ZYB-IA).


### 3.2. Physics and Mechanical Properties of Mudstone Specimen

The chemical composition of mudstone has much effect on the macromechanical properties of mudstone specimens. The chemical composition of mudstone in coal mine was determined using X-ray fluorescence (XRF) and X-ray Diffraction (XRD) by grinding the mudstone specimen after drying. The results of XRF and XRD are plotted in Table1 and Figure 6. It is shown that a total of 8 components are identified in mudstone. The main products are silicon dioxide (SiO2), aluminum oxide (Al2O3), and iron trioxide (Fe2O3), reaching 56.6%, 20.38%, and 12.32%, respectively. And sodium oxide (Na2O) is the least of the ingredients. In terms of mineral composition, kaolinite is one of the largest minerals in mudstone. Hence, the strength of mudstone is low, compared with other rocks. The static mechanical properties of mudstone were also tested, which results are shown in Table 2. The compressive strength and tensile strength of mudstone specimens are 28.96 MPa and 2.16 MPa, respectively. Hence, the strength of mudstone is lower than that of other rocks from coal mine.Table 1
The chemical composition of mudstone in coal mine.
Chemical componentNa2OMgOAl2O3SiO2K2OTiO2Fe2O3CaOPercent (%)1.2001.94320.38356.6163.9891.41912.3280.964Figure 6
The XRD spectra of mudstone.Table 2
Static mechanical properties of mudstone.
Density (g/cm3)Longitudinal wave velocity (m/s)Compressive strength (MPa)Tensile strength (MPa)Poisson ratio2.57217628.962.160.23


## 3.1. Preparation of Specimens

Located in the central of Anhui province, China, middle and lower reaches of Yangtze River (see in Figure2), the Panyi mine is faced with the danger of high in situ stress, water pressure, and temperature in rock roadway construction. This mining area was in use in December 2016. The roadway floor heave and side extrusion deformation were found in 2017. The mudstone blocks, used to be in experiments, originated from the 800 m deep 5# coal seam mining area as shown in the geological section in Figure 3. The coal mine area consists of mudstone, sandstone, and coal formations dipping about 40° to the south in the area of interest. There are some faults passing through the mudstone-sand layers, easily leading to rock fall. The mudstone forms in the development period of continental strong tensional faulting and experienced main squeezing and luffing tectonic and hydrothermal alteration activity.Figure 2
Specimen location: Panyi mining area, Huainan, China.Figure 3
Geological section along 5# coal seam mining area. The obtained rock specimen is located within mudstone that dips approximately 40 deg south.The cylindrical specimens are obtained by drilling, cutting, and grinding in the laboratory. In order to meet the assumption of one-dimensional stress wave propagation theory of SHPB and reduce the friction and axial inertia effect of the specimen, the length-diameter ratio of the prepared specimens is 0.5. Hence, the diameter of the specimen is 50 mm; the length of the specimen is 25 mm. No parallelism is within 0.05 mm on both ends of the specimen, and the roughness is within 0.02 mm. Those mudstone specimens in coal mine are shown in Figure4.Figure 4
Mudstone specimen: diameter 50 mm and length 25 mm.Before testing, the process of saturating specimens with liquid was conducted using the vacuum saturation device (ZYB-IA, see Figure5), by following the below procedure. Distilled water was used as a saturated liquid to avoid the potential influence of chemical factors.
(1)
Put the dry mudstone specimen in a basket in the vacuum saturation device(2)
Vacuum the specimen storehouse until no air bubbles were generated in the liquid storage tank(3)
Switch on the specific valve; the distilled water in the liquid storage tank was sucked into the specimen storehouse(4)
The mudstone specimen was immersed in the distilled water (i.e., vacuum water-saturated environment) for 7 days, and the saturation pressure was set as 1.0 MPa(5)
Take out the mudstone specimen for the next step of testingFigure 5
Vacuum saturation device (ZYB-IA).


## 3.2. Physics and Mechanical Properties of Mudstone Specimen

The chemical composition of mudstone has much effect on the macromechanical properties of mudstone specimens. The chemical composition of mudstone in coal mine was determined using X-ray fluorescence (XRF) and X-ray Diffraction (XRD) by grinding the mudstone specimen after drying. The results of XRF and XRD are plotted in Table1 and Figure 6. It is shown that a total of 8 components are identified in mudstone. The main products are silicon dioxide (SiO2), aluminum oxide (Al2O3), and iron trioxide (Fe2O3), reaching 56.6%, 20.38%, and 12.32%, respectively. And sodium oxide (Na2O) is the least of the ingredients. In terms of mineral composition, kaolinite is one of the largest minerals in mudstone. Hence, the strength of mudstone is low, compared with other rocks. The static mechanical properties of mudstone were also tested, which results are shown in Table 2. The compressive strength and tensile strength of mudstone specimens are 28.96 MPa and 2.16 MPa, respectively. Hence, the strength of mudstone is lower than that of other rocks from coal mine.Table 1
The chemical composition of mudstone in coal mine.
Chemical componentNa2OMgOAl2O3SiO2K2OTiO2Fe2O3CaOPercent (%)1.2001.94320.38356.6163.9891.41912.3280.964Figure 6
The XRD spectra of mudstone.Table 2
Static mechanical properties of mudstone.
Density (g/cm3)Longitudinal wave velocity (m/s)Compressive strength (MPa)Tensile strength (MPa)Poisson ratio2.57217628.962.160.23


## 4. The Procedure of Tests

Three kinds of drive pressure were applied to saturated mudstone specimens in the SHPB tests. The impact pressure is 0.25 MPa, 0.30 MPa, and 0.40 MPa, respectively, used in the SHPB tests. An approximate uniform deformation of the rock specimen is a prerequisite of the valid dynamic uniaxial compression tests. Before the tests, the dynamic stresses on both ends of the specimen should be roughly identical. This can be checked by comparing the stress histories on both ends of the specimen during the dynamic tests. Figure7 illustrates the dynamic stress balance on both ends of the specimen for the typical test. It is clear that in this test, the uniformity of the dynamic stress across the specimen has been achieved, and thus, the axial inertial effect has been reduced to a negligible level, verifying that the SHPB test conforms to the assumption of one-dimensional stress wave. With the dynamic stress balance, the stress-strain curves of rocks can be obtained under different drive pressures in the SHPB tests. After dynamic stress balance tests, a total of nine mudstone specimens were examined in the SHPB tests.Figure 7
Strain balance check for a typical dynamic SHPB test with pulse shaping. In: incident wave; Re: reflected wave; Tr: transmitted wave.


## 5. Results of SHPB Tests

### 5.1. Failure Mode of SHPB Tests

Figure8 shows the failure models of saturated mudstone under different impact loadings. It is shown that as the impact pressure increases, both the length and aperture of cracks in the mudstone specimen increase. A main circular crack appears in the mudstone specimen when impact pressure is 0.25 MPa. The crack passes throughout the whole specimen, and the length and aperture further increase. There are other cracks along the axial of specimens, which length is small. The specimen is broken into large blocks, due to the circular and axial cracks. When the impact pressure reaches 0.30 MPa, the number of axial cracks increases and some cracks extend to circular cracks of specimens, which is shown in Figure 8(b). At the same time, many split cracks are found in the test, and the size of these split cracks is large. Under the 0.40 MPa impact pressure, the cracks along with the axial of the specimen further extend and finally pass throughout the whole specimen. And the aperture of circular and axial cracks increases. The specimen is broken into lots of smaller blocks.Figure 8
Crack morphology of mudstone under different impact pressures.
(a)
Impactpressure=0.25 MPa(b)
Impactpressure=0.30 MPa(c)
Impactpressure=0.40 MPa


### 5.2. Dynamic Stress-Strain Curve

The stress-strain curves of mudstone specimens under different impact loadings are shown in Figure9. The dynamic stress-strain curve can be divided into four stages: (I) elastic stage, (II) crack expansion stage, (III) plastic deformation stage, and (IV) failure stage, seen in Figure 10. In the elastic stage, stress increases linearly with strain increasing. When reaching elastic limit stress, the microcrack will generate and expand. The plastic deformation stage will appear under the larger strain. In addition, the dynamic strength increases slowly in this stage. After yield stress, the stress dramatically decreases with an increase of strain. The specimen is finally destroyed. The failure model can be seen in Figure 8. Unlike the general relationships of stress and strain, there is no existence of the initial crack closure stage. The main reason is the fact that the high strain ratio leads the internal microcracks not to be closed in time and directly enter the elastic stage. It can be also inferred in Figure 9 that as the impact loading increases, the dynamic strength of the mudstone specimen increases.Figure 9
Dynamic stress-strain curves of mudstone specimens under different impact loadings.
(a)
Impactpressure=0.25 MPa(b)
Impactpressure=0.30 MPa(c)
Impactpressure=0.40 MPaFigure 10
The typical stress-strain curve of mudstone under impact loading.


### 5.3. Time-History Curve of Energy under Impact Loading

According to Equations (1), (2), (3), and (4), the incident energy, absorbed energy, transmitted energy, and reflected energy at any time can be obtained. The results are shown in Figure 11. It is illustrated that all the energy increases with an increase in time. The incident energy grows fastest. In addition, the intensity of incident energy is largest, the transmitted energy is second, and the reflected energy is smallest. The incident energy, absorbed energy, transmitted energy, and reflected energy at the final time are 103 J, 44.3 J, 42.2 J, and 16.5 J, respectively.Figure 11
The time-history curve of energy under impact loading.Combined with the crack morphology of the mudstone specimen shown in Figure8, the energy absorption process of the mudstone specimen can be divided into three stages from the perspective of absorbed energy.
(1)
First Stage. The absorbed energy increases during 0 to 50 μs. The mudstone specimen is at the elastic compressive deformation condition. The absorbed energy exists in the form of elastic energy.(2)
Second Stage. This stage begins at 50 to 200 μs. The absorbed energy of the specimen is smaller than reflected energy in the earlier stage and then is larger than reflected energy after 80 μs. The main reason can be summarized as follows. The incident end surface of the specimen would generate reflected tensile stress and transfer reflected energy under incident stress waves, due to a mismatch between the wave impedance of the specimen and the bar. In this state, the absorbed energy is smaller than reflected energy. However, the contact surface will be smooth and the reflected energy will decrease under the incident bar continuously impacting. The circular crack will generate under the tensile stress wave. Subsequently, under the effect of high incident stress, the original microcracks inside the mudstone specimen extend, and a large number of new microcracks are generated at the same time, and the absorption energy continues to increase slowly.(3)
Third Stage. After 200 μs, the primary cracks in the mudstone specimen rapidly expand and new cracks will generate and pass through the specimen. And then, the axial cracks will be produced. Because there is no energy supplement, eventually, the energy tends to have a stable energy value.


### 5.4. The Relationships of Incident Energy and Transmitted Energy and Reflected Energy

The final incident energy, absorbed energy, transmitted energy, and reflected energy time can be obtained using Equations (1), (2), (3), and (4). The relationships of all the energy are shown in Table 3 and Figure 12.Table 3
Results of energy dissipation of mudstone under different impact loadings.
NumberDrive pressure (MPa)ScaleImpedance (105 g/(cm2 s))Incident energy (J)Transmitted energy (J)Reflected energy (J)Absorbed energy (J)Energy dissipation density (J·cm-3)Average strain ratio (s-1)Dynamic compressive strength (MPa)Peak strainDiameter (mm)Length (mm)10.2549.8326.194.9154.9428.147.6419.160.3754557.500.009920.2549.9526.115.5952.5326.1912.9313.440.2624756.650.011130.2550.0524.085.7650.5323.177.7719.590.4144252.500.011740.349.6425.564.4060.3730.019.8820.480.4145355.320.013850.350.0525.304.5568.1936.707.9623.530.4736262.300.010360.349.8826.765.1661.8033.77.1021.000.4046062.130.009870.450.0426.065.49103.1542.4317.6443.090.8417164.340.01580.449.9726.654.2996.3538.5714.5043.240.8286667.690.01690.449.7425.785.30105.5140.2016.5948.720.9737063.570.0212Figure 12
The relationships between incident energy and transmitted energy, reflected energy, and absorbed energy.
(a)(b)(c)It is indicated from Figure12(a) that when the incident energy is smaller, the transmission energy increases with the increase of the incident energy. When the incident energy is larger, the transmission energy increment decreases with the increase of the incident energy. For the lower incidence energy, the mudstone specimen is in the elastic stage. With the increase of the incident energy, the mudstone is in the plastic stage, the inner primary microcrack growth and the new microcrack are produced, and the transmission of the transmission wave is weakened.As shown in Figure12(b), when the incident energy is small, the reflected energy increases slowly with the increase of the incident energy. When the incident energy exceeds 70 J, the reflected energy increases faster; the transmission energy tends to be stable. It is known from Figure 12(c) that the absorbed energy of the specimen increases linearly with the increase of the incident energy, and the absorbed energy is less than 0.5 times the incident energy. It is indicated that more than half of the energy of the impact incident can be dissipated in the form of an elastic wave of the bars.


### 5.5. The Relationships of Absorbed Energy, Transmitted Energy, and Reflected Energy between Peak Strains

The energy transmission is related to the deformation of mudstone specimens. Hence, the relationships of absorbed energy, transmitted energy, and reflected energy between peak strains are plotted in Figure13. It is shown that as the peak strain increases, the absorbed energy, transmitted energy, and reflected energy increase. However, the increases are different among the absorbed energy, transmitted energy, and reflected energy, and there is some volatility during the increases. And the largest growth in energy is absorbed energy. The reason is that the deformation increments of mudstone specimens need more energy.Figure 13
The relationship between energy and peak strain of mudstone specimens.


### 5.6. EDV, EDM, and AIER

Three energy dissipation indexes were introduced to represent the energy absorption characteristics of mudstone specimens. One is absorbed energy per volume (EDV)wd, which is defined as follows:
(5)wd=WsVs,where Vs is the volume of rock specimens. Considering the effect of mass, the second index is defined as absorbed energy per mass (EDM) md. The formula is
(6)md=WsMs,where Ms is the volume of rock specimens. The impedance of mudstone specimens is closely related to the energy transfer efficiency. Hence, introducing the impedance, the third index is defined as
(7)Zw=WsρCs,where Zw is absorption impedance energy ratio (AIER).The relationships between three indexes and incident energy are plotted in Figure14. Also plotted in Figure 14 are the best-fitted curves for the data using the linear function, implying that the linear relationship between the three indexes and incident energy fits the flow data very well for most of the data points. Comparing with the fitting coefficient (R2) of three indexes (wd,md,Zw), the best fitting is the relationship of AIER and incident energy, and this fitting coefficient is 0.936. It is indicated that AIER Zw, which takes into account the wave impedance property, can more effectively reflect the energy absorption of mudstone specimens:
(8)wd=0.011WI−0.247R2=0.848,md=0.004WI−0.104R2=0.836,Zw=0.114WI−0.267R2=0.936.Figure 14
The relationship between energy indexes and incident energy.


### 5.7. The Effect of Energy Dissipation on Strain Ratio

The relationships between EDV, EDM, and AIER and average strain ratioε are plotted in Figure 15. The quadratic function can be used to describe the relationships between three indexes and average strain ratio. When the strain rate is low, the absorbed energy causes mudstone with many internal defects. When the strain rate increases, the increase of the absorbed energy of the specimen will cause the new microcracks to generate in the mudstone specimens. When the strain rate is high, the original microcracks in the mudstone expand and pass through the mudstone specimens. And the specimen is crushed and broken finally:
(9)wd=0.0041ε̇2−0.134ε̇+3.65R2=0.855,md=0.0005ε̇2−0.055ε̇+1.49R2=0.827,Zd=0.0008ε̇2−0.069ε̇+1.85R2=0.678.Figure 15
The relationship between energy indexes and average strain rate.


## 5.1. Failure Mode of SHPB Tests

Figure8 shows the failure models of saturated mudstone under different impact loadings. It is shown that as the impact pressure increases, both the length and aperture of cracks in the mudstone specimen increase. A main circular crack appears in the mudstone specimen when impact pressure is 0.25 MPa. The crack passes throughout the whole specimen, and the length and aperture further increase. There are other cracks along the axial of specimens, which length is small. The specimen is broken into large blocks, due to the circular and axial cracks. When the impact pressure reaches 0.30 MPa, the number of axial cracks increases and some cracks extend to circular cracks of specimens, which is shown in Figure 8(b). At the same time, many split cracks are found in the test, and the size of these split cracks is large. Under the 0.40 MPa impact pressure, the cracks along with the axial of the specimen further extend and finally pass throughout the whole specimen. And the aperture of circular and axial cracks increases. The specimen is broken into lots of smaller blocks.Figure 8
Crack morphology of mudstone under different impact pressures.
(a)
Impactpressure=0.25 MPa(b)
Impactpressure=0.30 MPa(c)
Impactpressure=0.40 MPa


## 5.2. Dynamic Stress-Strain Curve

The stress-strain curves of mudstone specimens under different impact loadings are shown in Figure9. The dynamic stress-strain curve can be divided into four stages: (I) elastic stage, (II) crack expansion stage, (III) plastic deformation stage, and (IV) failure stage, seen in Figure 10. In the elastic stage, stress increases linearly with strain increasing. When reaching elastic limit stress, the microcrack will generate and expand. The plastic deformation stage will appear under the larger strain. In addition, the dynamic strength increases slowly in this stage. After yield stress, the stress dramatically decreases with an increase of strain. The specimen is finally destroyed. The failure model can be seen in Figure 8. Unlike the general relationships of stress and strain, there is no existence of the initial crack closure stage. The main reason is the fact that the high strain ratio leads the internal microcracks not to be closed in time and directly enter the elastic stage. It can be also inferred in Figure 9 that as the impact loading increases, the dynamic strength of the mudstone specimen increases.Figure 9
Dynamic stress-strain curves of mudstone specimens under different impact loadings.
(a)
Impactpressure=0.25 MPa(b)
Impactpressure=0.30 MPa(c)
Impactpressure=0.40 MPaFigure 10
The typical stress-strain curve of mudstone under impact loading.


## 5.3. Time-History Curve of Energy under Impact Loading

According to Equations (1), (2), (3), and (4), the incident energy, absorbed energy, transmitted energy, and reflected energy at any time can be obtained. The results are shown in Figure 11. It is illustrated that all the energy increases with an increase in time. The incident energy grows fastest. In addition, the intensity of incident energy is largest, the transmitted energy is second, and the reflected energy is smallest. The incident energy, absorbed energy, transmitted energy, and reflected energy at the final time are 103 J, 44.3 J, 42.2 J, and 16.5 J, respectively.Figure 11
The time-history curve of energy under impact loading.Combined with the crack morphology of the mudstone specimen shown in Figure8, the energy absorption process of the mudstone specimen can be divided into three stages from the perspective of absorbed energy.
(1)
First Stage. The absorbed energy increases during 0 to 50 μs. The mudstone specimen is at the elastic compressive deformation condition. The absorbed energy exists in the form of elastic energy.(2)
Second Stage. This stage begins at 50 to 200 μs. The absorbed energy of the specimen is smaller than reflected energy in the earlier stage and then is larger than reflected energy after 80 μs. The main reason can be summarized as follows. The incident end surface of the specimen would generate reflected tensile stress and transfer reflected energy under incident stress waves, due to a mismatch between the wave impedance of the specimen and the bar. In this state, the absorbed energy is smaller than reflected energy. However, the contact surface will be smooth and the reflected energy will decrease under the incident bar continuously impacting. The circular crack will generate under the tensile stress wave. Subsequently, under the effect of high incident stress, the original microcracks inside the mudstone specimen extend, and a large number of new microcracks are generated at the same time, and the absorption energy continues to increase slowly.(3)
Third Stage. After 200 μs, the primary cracks in the mudstone specimen rapidly expand and new cracks will generate and pass through the specimen. And then, the axial cracks will be produced. Because there is no energy supplement, eventually, the energy tends to have a stable energy value.


## 5.4. The Relationships of Incident Energy and Transmitted Energy and Reflected Energy

The final incident energy, absorbed energy, transmitted energy, and reflected energy time can be obtained using Equations (1), (2), (3), and (4). The relationships of all the energy are shown in Table 3 and Figure 12.Table 3
Results of energy dissipation of mudstone under different impact loadings.
NumberDrive pressure (MPa)ScaleImpedance (105 g/(cm2 s))Incident energy (J)Transmitted energy (J)Reflected energy (J)Absorbed energy (J)Energy dissipation density (J·cm-3)Average strain ratio (s-1)Dynamic compressive strength (MPa)Peak strainDiameter (mm)Length (mm)10.2549.8326.194.9154.9428.147.6419.160.3754557.500.009920.2549.9526.115.5952.5326.1912.9313.440.2624756.650.011130.2550.0524.085.7650.5323.177.7719.590.4144252.500.011740.349.6425.564.4060.3730.019.8820.480.4145355.320.013850.350.0525.304.5568.1936.707.9623.530.4736262.300.010360.349.8826.765.1661.8033.77.1021.000.4046062.130.009870.450.0426.065.49103.1542.4317.6443.090.8417164.340.01580.449.9726.654.2996.3538.5714.5043.240.8286667.690.01690.449.7425.785.30105.5140.2016.5948.720.9737063.570.0212Figure 12
The relationships between incident energy and transmitted energy, reflected energy, and absorbed energy.
(a)(b)(c)It is indicated from Figure12(a) that when the incident energy is smaller, the transmission energy increases with the increase of the incident energy. When the incident energy is larger, the transmission energy increment decreases with the increase of the incident energy. For the lower incidence energy, the mudstone specimen is in the elastic stage. With the increase of the incident energy, the mudstone is in the plastic stage, the inner primary microcrack growth and the new microcrack are produced, and the transmission of the transmission wave is weakened.As shown in Figure12(b), when the incident energy is small, the reflected energy increases slowly with the increase of the incident energy. When the incident energy exceeds 70 J, the reflected energy increases faster; the transmission energy tends to be stable. It is known from Figure 12(c) that the absorbed energy of the specimen increases linearly with the increase of the incident energy, and the absorbed energy is less than 0.5 times the incident energy. It is indicated that more than half of the energy of the impact incident can be dissipated in the form of an elastic wave of the bars.


## 5.5. The Relationships of Absorbed Energy, Transmitted Energy, and Reflected Energy between Peak Strains

The energy transmission is related to the deformation of mudstone specimens. Hence, the relationships of absorbed energy, transmitted energy, and reflected energy between peak strains are plotted in Figure13. It is shown that as the peak strain increases, the absorbed energy, transmitted energy, and reflected energy increase. However, the increases are different among the absorbed energy, transmitted energy, and reflected energy, and there is some volatility during the increases. And the largest growth in energy is absorbed energy. The reason is that the deformation increments of mudstone specimens need more energy.Figure 13
The relationship between energy and peak strain of mudstone specimens.


## 5.6. EDV, EDM, and AIER

Three energy dissipation indexes were introduced to represent the energy absorption characteristics of mudstone specimens. One is absorbed energy per volume (EDV)wd, which is defined as follows:
(5)wd=WsVs,where Vs is the volume of rock specimens. Considering the effect of mass, the second index is defined as absorbed energy per mass (EDM) md. The formula is
(6)md=WsMs,where Ms is the volume of rock specimens. The impedance of mudstone specimens is closely related to the energy transfer efficiency. Hence, introducing the impedance, the third index is defined as
(7)Zw=WsρCs,where Zw is absorption impedance energy ratio (AIER).The relationships between three indexes and incident energy are plotted in Figure14. Also plotted in Figure 14 are the best-fitted curves for the data using the linear function, implying that the linear relationship between the three indexes and incident energy fits the flow data very well for most of the data points. Comparing with the fitting coefficient (R2) of three indexes (wd,md,Zw), the best fitting is the relationship of AIER and incident energy, and this fitting coefficient is 0.936. It is indicated that AIER Zw, which takes into account the wave impedance property, can more effectively reflect the energy absorption of mudstone specimens:
(8)wd=0.011WI−0.247R2=0.848,md=0.004WI−0.104R2=0.836,Zw=0.114WI−0.267R2=0.936.Figure 14
The relationship between energy indexes and incident energy.


## 5.7. The Effect of Energy Dissipation on Strain Ratio

The relationships between EDV, EDM, and AIER and average strain ratioε are plotted in Figure 15. The quadratic function can be used to describe the relationships between three indexes and average strain ratio. When the strain rate is low, the absorbed energy causes mudstone with many internal defects. When the strain rate increases, the increase of the absorbed energy of the specimen will cause the new microcracks to generate in the mudstone specimens. When the strain rate is high, the original microcracks in the mudstone expand and pass through the mudstone specimens. And the specimen is crushed and broken finally:
(9)wd=0.0041ε̇2−0.134ε̇+3.65R2=0.855,md=0.0005ε̇2−0.055ε̇+1.49R2=0.827,Zd=0.0008ε̇2−0.069ε̇+1.85R2=0.678.Figure 15
The relationship between energy indexes and average strain rate.


## 6. Discussion

In order to understand the fact that chemical components and microstructures lead to the macrocrack phenomenon of saturated mudstone specimens under impact loading, the crack morphology was observed using the BIST digital microscope. Two axial and two circular crack surfaces of the typical broken mudstone specimen were selected to examine and numbered A, B, C, and D. Obvious roughness characteristics are easily observed in two kinds of crack surfaces, shown in Figure16. But the roughness of the circular surface is greater than that of the axial surface. The main reason is that the axial crack surface (A and C) is caused by shear slip and wearing, and the stress wave tension results in the circular crack surface (B and D) under impact loadings. In addition, from Table 1, SiO2 is one of the main components in mudstone, followed by Al2O3 and Fe2O3. Their grain distribution is shown in Figure 8(b). And it is concluded that both the axial and circular cracks mainly occur in the grain interface, because it is a weak area in rock.Figure 16
The crack characteristic of mudstone under impact loading: (a) axial splitting and axial tension crack locations numbered as A, B, C, and D, respectively; (b) crack micrograph under electron digital microscope (×1000).
(a)(b)Combining the one-dimensional stress wave propagation theory and physics component of mudstone, the reason for the generation of circular and axial cracks in specimens under impact loadings is as follows. Mudstone is characterized by viscoplasticity, softening, and low structural strength. The microstructure of mudstone will change when suffering from impact loading. The microparticle of mudstone is redistributed along with forced direction from the free condition. In the SHPB test, the incident stress reflects and transmits to tensile stress when the stress transmits to the contact surface between transmitted bar and specimen. The tensile stress causes the circular crack due to the low tensile strength of the mudstone in the coal mine specimen. Meanwhile, under the continuous action of the incident compression stress wave, the specimen is subjected to axial splitting failure.Drill-blasting is the main way for roadway tunneling in coal mine. Generally, the cylindrical charge is used for blasting holes, and the surrounding rock is in a one-dimensional compression situation. In addition, the effect of blasting energy on blasting fragmentation and damage of reserved rock is important for drill-blasting, especially for mudstone with low strength. Hence, the energy dissipation law and failure mechanism of mudstone under impact loading provide strong support for mining blasting safety.


## 7. Conclusions

In this paper, the dynamic mechanical properties of mudstone in coal mine are investigated using the energy characterization method, and their quantitative relation formula is also developed. Therefore, a series of compression experiments of mudstone under different impact loadings are conducted to study the mudstone dynamic behaviors, crack properties, and energy dissipation law using the diameter 50 mm SHPB test device. The above analyses support the following conclusions:(1)
The axial splitting failure and circular tensile failure are observed in mudstone specimens during the test. It is because the tensile stress would be generated and easily cause circular tensile failure for low strength rock due to the reflection and transmission effect of the transmitted bar. Additionally, continuous compressive stress leads to axial splitting failure(2)
It is shown from the crack micromorphology that the failure surface appears in the mudstone grain interface, and the roughness of the tensile failure surface is greater than that of the splitting surface(3)
The absorbed energy, transmitted energy, and reflected energy of mudstone increase with the increase of incident energy, showing linear, logarithmic, and quadratic functions, respectively(4)
Comparing the three energy dissipation indexes (EDV, EDM, and AIER) with incident energy, the AIER is more a reflection of the energy dissipation of mudstone. The quadratic function relationship between three energy dissipation indexes and average strain rate of mudstone specimen shows a strong dependence of strain rate



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