Experimental Study of Dynamic Mechanical Properties of Water-Saturated Coal Samples under Three-Dimensional Coupled Static–Dynamic Loadings

: It is very important to study the inﬂuence of water content on the mechanical properties of coal rock to prevent rock burst and roadway instability under dynamic disturbance. In this study, the split Hopkinson pressure bar (SHPB) test system was applied to conduct three-dimensional dynamic and static impact tests on natural and water-saturated coal samples at different strain rates to determine the dynamic mechanical properties of a series of water-bearing coal samples. Based on the new data, we discuss the strength, deformation, crushing energy dissipation, and fractal characteristics of natural and saturated coal rocks. We speciﬁcally focus on the different effects of hydraulic pressure on crack propagation under static and dynamic loads. Our results document a well-deﬁned linear relationship between the peak stress and the strain rate of coal in the natural state and the water-saturated state. Once the impact rate reaches a certain value, a double peak phenomenon is observed, and the curve shows a certain leap. The critical impact velocity of the curve leap is ca. 9.485~10.025 m/s. At the same strain rate, the average peak stress in the water-saturated state is ca. 2.684% higher than that in the natural state. The secant modulus of the two states generally increases with the rise in strain rate, but the scatter of the results is large. The average secant modulus of the water-saturated coal sample increases by 2.309% compared with the natural state. The energy consumption density and absorbed energy of saturated and natural coal samples rise with the increase in strain rate, and both show a well-deﬁned power–function relationship. However, under the same condition, the absorbed energy and absorbed energy density of water-saturated coal samples are higher than that of natural coal samples. The fractal dimension of water-saturated coal rises with the increase in strain rate and energy consumption density, showing a strong linear and quadratic relationship, respectively. Under dynamic loading, the cohesive force, jointly generated by free water and the Stefan effect, hinder the expansion of coal and rock fractures, thus improving the compressive strength of coal and rock. The study provides a reliable theoretical basis for preventing rock burst and providing roadway support.


Introduction
With the depletion of near-surface resources, the mining of underground resources has successively extended into the deep worldwide [1].The mechanical properties of deep coal and rock are not only affected by the internal fractures [2], but also by the external environment as the main factor affecting the mechanical properties [3].Due to the complex external environment such as the increase of in situ stress, the intensification of water gushing, and a strong impact, many deep coal and rock faces are subjected to the coupling effect of a water-dynamic-static combination (see Figure 1), which greatly changes the mechanical properties of coal and rock, resulting in the occurrence of rock burst, roadway instability, and other disruptive disasters [4][5][6].Therefore, it is of great significance to study the influence of water content on the dynamic mechanical properties of coal and rock to prevent rock burst and roadway instability under dynamic disturbance.In general, coal and rock often combine with water to produce chemical and physical interactions, resulting in changes in the mechanical properties of coal and rock [7][8][9].Specifically, under static load, water has a softening effect on the mechanical properties of coal and rock [10][11][12][13].The reason is that under the condition of static load, the strength of coal and rock is reduced due to the similar "wedging" effect and "rainbow suction" effect produced by free water in coal and rock fissures [14,15].Given may previous studies, it has become a recognized fact that water has a weakening effect on the compressive strength of rocks under static load, especially in rocks with a lot of clay [16][17][18].
However, blasting, roof fractures, earthquakes, and other impact loads are often encountered in practical projects.In order to study the influence of dynamic load on the dynamic mechanics of coal and rock, experts in China and abroad have performed a large amount of research.The research shows that the influence of the dynamic load on the mechanical properties of coal and rock is very different from that of the static load [19,20].With the increase in strain rate, the weakening effect of water on the strength of coal and rock gradually weakens, and even at a critical strain rate, water can enhance the dynamic mechanical properties of coal and rock, which has been documented by Cai et al. [21] and Ross et al. [22].The reason for this phenomenon is that the cohesive force generated and the Stefan effect by free water together hinder the expansion of coal and rock fissures, thus enhancing the strength of coal and rock [23,24].Wang K et al. [25] studied the dynamic mechanics, failure mode, and energy dissipation characteristics of coal and rock samples under the water-dynamic-static coupling, based on the improved Hopkinson pressure bar experimental equipment.The results showed that the fracture water pressure enhanced the compressive strength of coal samples under combined dynamic-static loading.Wang Wen et al. [26] used the improved Hopkinson pressure bar test system to conduct a true triaxial dynamic and static combination experiment on cube water-bearing coal samples.The results showed that the compressive strength of water-saturated coal samples in the X-axis direction (impact direction) was lower than that of natural coal samples, and the compressive strength in the Y-axis and Z-axis directions was higher than that of natural coal samples.Yuan Pu et al. [27] compared the uniaxial impact strength of natural, naturally saturated, and compulsively saturated sandstone in three states.Among them, compulsively saturated dynamic strength is the largest, followed by natural saturated dynamic strength, and finally the natural dynamic strength.However, some researchers have come to the opposite conclusion.They believe that water has little influence on the dynamic strength of coal and rock under dynamic load, and the reason is that the content of clay minerals in coal and rock is low [28][29][30].
The review documents that a certain weakening effect on the strength of coal and rock under static load through the addition of water has been recognized in several previous studies.However, the influence of launching water on the strength of coal and rock under dynamic load is controversial, and uniaxial compression has been mostly used in this aspect, whereas many deep coal and rock occurrences are better represented by a combination of three-dimensional dynamic and static conditions.Therefore, in this study we used the SHPB test system to conduct three-dimensional dynamic and static combined impact tests on coal and rock samples in a natural state and a saturated state under different strain rates.The strength, deformation, crushing energy consumption, and fractal characteristics of coal and rocks under different water-bearing conditions are analyzed, and the impact of different water pressure in the cracks of water-bearing coal samples under static and dynamic loads is discussed based on the principle of wing crack propagation.It provides a reliable theoretical basis for preventing rock burst, roadway instability, and other disruptive disasters.

Coal Sample Processing and Determination of Basic Physical Parameters
We selected coal samples from the Fu Xiang Mine, Guizhou province (China) for the experiment.They were sampled at a depth of about 300 m and are mainly coking coal.This experiment used the core machine to take the coal from the vertical stratification direction.The specimens were Φ50 mm × 30 mm cylinders with a non-parallelism of less than 0.05 mm and a surface evenness of less than 0.02 mm.The processed coal samples are shown in Figure 2, and the basic physical parameters of the coal samples are summarized in Table 1.

Test Equipment and Scheme
The combined dynamic and static impact test was conducted in the laboratory of dynamic load failure parameter test of coal and rock, School of Emergency Management and Safety Engineering, China University of Mining and Technology (Beijing, China).Based on the one-dimensional loading system, the confining pressure and axial pressure were added to the three-dimensional coupled static-dynamic combined loading test system.The test equipment is shown in Figure 3, and the three-dimensional mechanical forces of the coal sample under dynamic load under static load are illustrated in Figure 4.The coal samples were subdivided into two groups, namely, the saturated state and the natural state, and numbered accordingly as S 1 -S 5 and N 1 -N 5 .The natural water absorption method was used to soak the coal samples naturally for four days, and the saturated coal samples are shown in Figure 5.The confining pressure and axial pressure were both set at 10 MP in the test because the impact velocity and strain rate showed a linear relationship (Figure 6).Consequently, the loading of coal samples with different strain rates could be realized by changing the impact velocity.The impact velocities of the natural coal samples are 6.285 m/s, 7.639 m/s, 9.485 m/s, 10.888 m/s, and 11.568 m/s, respectively, and the impact velocities of the saturated coal samples are 6.688 m/s, 7.954 m/s, 10.025 m/s, 11.449 m/s, and 11.606 m/s.

Strength Characteristics
The dynamic mechanical parameters of the water-bearing coal samples can be calculated through tests, as shown in Table 2.
We obtained the stress-strain diagrams of coal samples in the saturated and natural states (Figures 7 and 8) by processing the experimental data in Table 2.The diagrams show that the variation trend of the stress-strain curves is basically the same in the saturated and natural states.At the initial stage, due to confining pressure and axial pressure in the 3D impact test, coal and rock specimens were compacted when the impact force was applied.Therefore, under the three-dimensional dynamic-static combined load, coal and rock specimens do not exist in the compaction stage and directly enter the elastic deformation stage, unlike the results of the uniaxial impact test.Subsequently, the coal samples enter the plastic deformation stage, during which the pre-existing cracks expand and new cracks continuously increase.As the strain continuously increases, the stress attains the peak value, termed the dynamic compressive strength.Because coal and rock are porous materials, the samples are not immediately destroyed at this time but still retain a certain bearing capacity.After unloading, the cracks continue to expand until pattern failure.Remarkably, the initial rising stage of the coal sample appears non-linear in the two states; when the impact velocity is small but becomes successively linear with the rise in the impact velocity.A double-peak phenomenon is developed in both states once the impact rate attains a certain value and the curve shows a certain leap forward; the reason for this phenomenon may be related to the role of carbon in crystal microfracture, which is consistent with the analysis results of Shan Renliang et al. [31][32][33].The stress reaches the maximum value of the first stress peak (compressive strength).Subsequently, the stress decreases with the increase in strain, and the coal rock specimen enters the yield stage.During a further increase in strain, the stress increases again and attains the second peak maximum value.Figures 7 and 8 show that the critical impact velocity of coal samples in the natural state and saturated state; the curve leaping is about 9.485~10.025m/s.
With the increase in impact velocity, the peak stresses of the natural coal sample are 49.776MPa, 53.426 MPa, 73.437 MPa, 81.697 MPa, and 82.160 MPa, respectively, and the average peak stress is 68.099MPa.The peak stresses of the saturated coal samples are 51.728MPa, 58.556 MPa, 73.922 MPa, 78.323 MPa, and 87.358 MPa, respectively, and the average peak stress is 69.977MPa.The dynamic triaxial compressive strength of the saturated coal rock is ca.2.684% higher than that of the natural state.Figure 9 illustrates that the peak stress of both states increases with the rise in the strain rate, representing an obvious linear relationship.

The Deformation Characteristics
The deformation characteristics of rocks can be expressed by calculating the elastic modulus, deformation modulus, secant modulus, and Poisson's ratio [34].Although the elastic modulus is unequivocally defined and is the most widely used attribute in expressing rock deformation, its value depends on strongly subjective factors [35].Therefore, we applied the secant modulus in the present study to define the deformation characteristics of coal samples.The date of secant modulus and the strain rate were fitted in Figure 10.It can be seen from the Figure 10 that the secant modulus and strain rate of coal samples in natural state have a large discrete relationship.On the contrary, the secant modulus and strain rate of coal samples in saturated state have a good linear relationship, indicating that the secant modulus of saturated coal samples is more sensitive to the strain rate effect.

Energy Dissipation Analysis
In the application to practical engineering, the coal rock crushing absorption energy can be used to describe the problem of coal rock failure [36].The absorption energy W d of coal and rock samples can be calculated by the following equation [37]: with W d , W i , W r , and W t as the absorbed energy, incident energy, reflected energy, and transmitted energy, respectively.The above parameters can be obtained by the following equation [38]: with E 0 as the elastic modulus of the incident and transmitted bar, C 0 as the stress wave propagation velocity in the bar, A 0 as the cross-sectional area of the incident and transmitted bar, and ε i , ε r , and ε t as the incident strain, reflected strain and transmitted strain at a certain time, respectively.The calculation of the energy parameter is summarized in Table 3.During the three-dimensional dynamic and static combined test, the experimental equipment and coal rock sample are regarded as a system.In this system, the sample and equipment conform to the law of the conservation of energy, precluding heat transfer with the outside world during the experiment.The impact energy provided by the external load (incident energy) will be converted into reflected energy, specimen absorption energy, and transmission energy.Table 3 and Figure 11 show that reflected energy, absorbed energy of specimen, and transmitted energy increase linearly with the increase in incident energy.Absorbed energy accounts for the largest proportion of incident energy (53.134%), followed by reflected energy (37.211%) and transmitted energy (9.655%).From the analysis of the energy characteristics, the incident energy is mainly used for breaking coal and rock samples.Figure 12 documents that the absorption energy of coal and rock samples under different water content states increases as a power function with the increase in strain rate.The fitting function is y = 3.914x 0.550 .According to the relationship between absorbed energy and strain rate, when the impact load is too large, the more absorbed energy there is, the more easily broken coal rock is.Under the same strain rate, the energy absorbed by coal and rock specimens in a saturated state is higher than that in a natural state.With the continuous increase in absorbed energy in coal and rock specimens, deformation hysteresis occurs, thus greatly improving the dynamic strength of coal and rock specimens.Because the strength characteristics of coal samples have a strong size effect, which leads to different absorption energy of coal and rock per unit volume, the absorption energy of the specimen can be expressed by the absorption energy of the sample per unit volume in the SHPB test [39].According to previous studies, the energy consumption of coal and rock crushing can be directly replaced by the absorption energy, which will not have a significant influence on the conclusions.The energy consumption per unit volume of sample is calculated by the equation: with V as the specimen volume, and W v as the energy consumption per unit volume of the specimen.
Figures 13-15 show the relationship between energy dissipation density and incident energy, strain rate, and peak intensity, respectively.Figure 13 shows that the energy consumption density in the two water-bearing states increases linearly with the rise in incident energy.The correlation is well-defined.Moreover, the energy consumption density of the saturated coal sample exceeds that of the coal and rock samples in the natural state for the same incident energy.Figure 14 shows a strong power-function relationship between the energy consumption density and the strain rate in the two states, which is related to the increase in strain rate.The original cracks of the coal and rock samples expand, and new cracks grow; therefore, the energy absorbed by the specimen and also the energy dissipation density of the specimen increase.Figure 15 documents that the energy required by coal sample destruction in the saturated state exceeds the required energy in the natural state, indicating that water saturation has a reinforcing effect on coal sample strength.

Failure Mode and Fractal of Coal Sample 4.1. Coal Rock Failure Mode
Figures 16 and 17 show the failure modes of coal and rock under different strain rates in the natural state and water-bearing state.The figures document that with an increase in strain rate, the size of the broken particles of different water-bearing coal samples decreases and the number of fragments increases.Figures 16a and 17a indicate that stress concentration occurs on the two end faces of the coal samples at a low strain rate, resulting in a minor part of the coal samples on both end faces falling off, causing tensile and shear mixed failure.A gradual increase in strain rate causes serious breaking of the coal and rock specimens Figures 16b-e

Fractal Characteristics of Coal Fragmentation
The fragmentation distribution can be used to evaluate the crushing effect of coal and rock (Wang Qisheng et al., 2009) [40].In previous studies, statistical functions of fragmentation distribution were widely used in the Rosin-Rammler (R-R) distribution and Gate-Gaudin-Schuhmann (G-G-S) distribution [41,42].We used the G-G-S distribution function to calculate the fractal dimension of the coal sample breakage, according to the published equation [43]: where D is the fractal dimension and α is the slope in the logarithmic coordinate system composed of lg (m r /m) and lgr: where m r is the mass of fragments with particle size less than r, r is the diameter of the round hole coal screen respectively, and m is the total mass of sample fragments.According to the crushing characteristics of coke coal samples after the three-dimensional dynamic and static group impact test, the diameter of the round hole coal screen is 30 mm, 20 mm, 10 mm, 3 mm, 2 mm and 1 mm, respectively.The coal samples were screened after the saturation test, and the results are summarized in Table 4. From the data in Table 4, we drew the fractal dimensional-strain rate curve and the fractal dimensional-energy density curve (Figures 18 and 19). Figure 18 documents a strong linear relationship between the fractal dimension of water-saturated coal rock specimens and the strain rate.With the increase in strain rate, the fractal dimension increases, and the degree of breakage of coal samples rises.Figure 19 shows that the fractal dimension increases with the rise in energy consumption density.A well-defined quadratic function describes the relationship between the two parameters, with the fitting function y = −0.075x 2 + 0.356x + 1.820; hence, the higher the crushing degree is, the more energy is required.

Discussion on Dynamic Failure Mechanism of Water-Bearing Coal
Our study shows that the failure of coal and rock is caused by the rapid expansion of airfoil crack sample [44].However, the promotion of crack propagation is not only related to the strain rate and physical properties of coal and rock, but also to water saturation.During static loading, the crack propagation speed of the sample is slow.Under the influence of surface tension, the free water of the crack has enough time to attain the crack tip, and the free water of the tip will produce splitting tension on the crack.The pore water pressure is similar to the chipping effect of "chipping" body, which produces extrusion stress P SW on the wing crack and a free water "siphoning" effect on the wing crack tip, thus promoting the development or expansion of the crack [45].Figure 20a shows the effect of fracture water pressure under static load.Under dynamic loading, the crack expands faster than the free water, and therefore the free water in the crack cannot reach the crack tip in a short time.Surface tension P dw is active on the surface of the free water, which is equivalent to the tensile force acting on the crack surface, which hinders the crack expansion as shown in Figure 20b.
Under dynamic loading, the surface tension of free water produces the bonding force F 1 .In addition, the Stefan effect of free water in the crack surface will induce resistance F 2 that impedes the relative separation of the two crack surfaces [46].F 1 and F 2 jointly hinder the diffusion of fractures, thus improving the strength of water-bearing coal rock.F 1 and F 2 can be calculated by the equations: where γ is the surface energy; ψ is the wetting angle, δ is the radius of the water meniscus; r is the radius of the two parallel circular plates filled with incompressible viscous liquid in the middle; η is the liquid viscosity; − ν is the relative speed at which the two circular plates separate; h is the distance between the two circular plates, and V is the volume of free water.
According to Equations ( 6) and ( 7), the stress P dW that hinders crack propagation can be obtained through the equation: Based on the above theoretical analysis of the dynamic failure mechanism of waterbearing sandstone, the water-bearing state of coal rock will change the original stress field where the coal rock is located.Due to the extrusion stress generated by free water at the crack tip, the coal and rock cracks expand under static load, which leads to the reduction in strength and facilitates breaking under the same conditions.On the contrary, free water produces cohesive force and the Stefan effect under dynamic loading, which impedes fracture diffusion and increases the dynamic strength of coal and rock.This also explains the phenomenon that the strength of coke coal samples in the saturated state exceeds the strength in natural state.

Conclusions
In order to prevent water-bearing coal rock from rock burst and roadway instability under dynamic disturbance, we conducted three-dimensional dynamic-static combined impact tests on coal samples under different strain rates in a natural state and saturated state using the improved SHPB test system to study the dynamic mechanical properties of a series of water-bearing coal samples under three-dimensional dynamic-static combined loadings.We obtained the dynamic mechanical properties of coal samples under two states and discuss the different effects of hydraulic pressure in cracks of water-bearing coal samples under static and dynamic loads by using the principle of wing crack propagation.The following conclusions were drawn from our investigation: (1) There is a good linear relationship between the peak stress of coal and the strain rate in both the natural state and the saturated state.In both states, the crack development goes through three stages: elastic deformation stage, plastic deformation stage, and unloading stage.When the impact rate reaches a certain value, there is a double peak phenomenon, and the curve shows a certain leap.The critical impact velocity of curve jump is about 9.485~10.025m/s.Under the same strain rate, the peak stress in the saturated state is ca.2.684% higher than that in natural state.(2) The secant modulus of the two states increases linearly with the rise in strain rate.
The secant modulus and strain rate of coal samples in the natural state have a large discrete relationship.On the contrary, the secant modulus and strain rate of coal samples in a saturated state have a good linear relationship, indicating that the secant modulus of saturated coal samples is more sensitive to the strain rate effect Under the same strain rate, the secant modulus of the saturated coal sample is 2.309% higher than that of the natural state.(3) The absorption energy and energy consumption density of saturated and natural coal samples increase with the rise in the strain rate, and they show a well-defined power-function relationship.According to the relationship between absorbed energy and strain rate, when the impact load is too large, the more absorbed energy there is, the more easily broken coal rock is.Under the same strain rate, the energy absorbed by coal and rock specimens in the saturated state is higher than that in the natural state.With the continuous increase in absorbed energy in coal and rock specimens, deformation hysteresis occurs, thus greatly improving the dynamic strength of coal and rock specimens.(4) The fractal dimension of saturated coal increases with the rise in the strain rate and energy consumption density, showing a strong linear and quadratic relationship, respectively.The cohesive force generated by free water and the Stefan effect jointly hinder the expansion of coal and rock fractures under dynamic loading, thus reinforcing the compressive strength of coal and rock.

Figure 1 .
Figure 1.Underground occurrence conditions and diagram of coal rock.

Figure 4 .
Figure 4. Three-dimensional dynamic and static combination force diagram of coal sample (P c is the confining pressure load; P d is the dynamic load, and P s is the static load).

Figure 6 .
Figure 6.Relationship between strain rate and impact velocity.

Figure 7 .
Figure 7. Stress-strain diagram of coal sample under natural condition.

Figure 8 .
Figure 8. Stress-strain diagram of coal sample at saturation state.

Figure 9 .
Figure 9. Peak stress-strain rate diagram of coal sample.
From the concrete numerical analysis, the values of the secant modulus of the coal samples in natural state are 9459.530MPa, 10,096.349MPa, 11,525.246MPa, 53,721.647MPa, and 32,387.804MPa, respectively, and the average secant modulus is 23,438.115MPa.The values of the secant modulus of the saturated coal samples are 13,514.515MPa, 9025.420MPa, 34,935.049MPa, 30,045.407MPa, and 32,439.570MPa, respectively, and the average secant modulus is 23,911.993MPa.The value of the secant modulus of the saturated coal samples is 2.309% higher than that of the natural state.

Figure 10 .
Figure 10.Relationship between elastic modulus and strain rate.

Figure 11 .
Figure 11.Incident energy in relation to other energies.

Figure 12 .
Figure 12.Relationship between absorption energy and strain rate.

Figure 13 .
Figure 13.The relation between energy consumption density and incident energy.

Figure 14 .
Figure 14.Relationship between energy consumption density and strain rate.

Figure 15 .
Figure 15.Relationship between peak stress and energy consumption density.
Figures 16 and 17  show the failure modes of coal and rock under different strain rates in the natural state and water-bearing state.The figures document that with an increase in strain rate, the size of the broken particles of different water-bearing coal samples decreases and the number of fragments increases.Figures16a and 17aindicate that stress concentration occurs on the two end faces of the coal samples at a low strain rate, resulting in a minor part of the coal samples on both end faces falling off, causing tensile and shear mixed failure.A gradual increase in strain rate causes serious breaking of the coal and rock specimens Figures16b-eand 17b-e, mainly by shear failure.Comparing Figures 16 and 17 documents that the damage degree of natural coal rock exceeds that of coal under a saturated state at the same strain rate.

Figure 18 .
Figure 18.Relationship between fractal dimension of saturated coal sample and strain rate.

Figure 19 .
Figure 19.Relationship between fractal dimension of saturated coal sample and energy consumption density.

Figure 20 .
Figure 20.Force of free water on crack surface under dynamic and static loading.(a) Force of free water on crack under static load and (b) force of free water on crack under dynamic load.

Table 1 .
Basic physical parameters of coal samples.

Table 2 .
Dynamic mechanical parameters of coal samples.

Table 3 .
Energy parameters of coal sample.

Table 4 .
Fractal dimension analysis of coal sample crushing.