Simulation and Experimental Study on the Discontinuous Dynamic Impact on Unidirectional Confined Coal-Rock Damage

/e deformation and the damage characteristics of coal and rock under different restraint static load and different impact velocity were studied with the FEM software LS-DYNA. Based on this, the influence of impact load on the damage of coal rock under onedimensional constraint condition was studied by using the self-developed constrained pendulum impact dynamic loading test device and ultrasonic testing device. /e results show that the deformation of coal and rock increases with the increase of impact velocity and decreases firstly and then remains constant with the increase of constraint static load; when the constraint static load exceeds the compression strength, the displacement increases rapidly and the coal collapses at a strike; the damage quantity of coal and rock has a cumulative effect, and the damage quantity increases with the increase of impact number; when the constraint static load is identical, the increase of impulse contributes to microcrack propagation, and the damage quantity of coal and rock accelerates with the increase of single impact impulse; when the impulse is identical, the constraint static load restrains the microcrack propagation, and the damage quantity of coal and rock decelerates with the increase of constraint static load; the complete damage quantity range of coal and rock is 0.65∼0.75. In order to fully destroy the coal and rock, if the single horizontal impulse is greater, the number of shocks needed is less; if the constrained static load is greater, the more impact times are needed.


Introduction
As an important engineering material, the rock is often in a complex combined stress environment.
e instability of rock materials under the action of external loads threatens the safe production of rock engineering.
e pillars in mining bear the weight of overlying strata and may be subjected to blasting, mechanical, and other dynamic loads.
e related engineering problems can be simplified to study the effect of dynamic impact on rock damage under unidirectional restraint.e rock is damaged by external loads, and its nature is the result of the microcrack structural evolution inside the rock.at is to say, the macrodamage of the rock caused by dynamic impact under unilateral constraints is the overall reflection of the internal microcrack structural evolution [1].
Many scholars have studied the dynamics damage of rock: Shan et al. proved the feasibility of testing the dynamic total stress-strain curve of rock using the SHPB device [2].Weng et al. conducted one-dimensional, two-dimensional, and three-dimensional dynamic and static combined loading tests on rocks based on the modified SHPB test system and studied the rock deformation and strength characteristics, energy transmission laws and failure mode, etc. [3][4][5][6].Fakhimi et al. used SHPB to evaluate the strength characteristics of sandstone under uniaxial compressive loading.
e results suggest that rock strength increases under dynamic loading [7]; Jin et al. studied and analyzed the failure mode and mechanism as well as definition method of damage variable of sandstone under the combined action of static load and cyclic impact [8].Zhu et al. simulated the deformation and failure process of rock under combined static and dynamic loading by the Rock Failure Process Analysis for Dynamics [9]; Zhao et al. conducted the drop-weight test on the briquettes and analyzed the development and evolution laws of internal microstructure and new surface cracks under the action of di erent impact loads [10]; Yavuz et al. found that dynamic compressive strength of rocks increases with increase in loading rate and/ or increase in rock property values except porosity [11].Lindholm et al. and Kinoshita et al. described the dynamic mechanical behavior of rock by the over stress model [12,13].
e traditional research method of rock dynamic mechanics is to apply the cyclic impact load, and to conduct the statistics of dissipative energy di usion laws and the crack propagation of rock, for giving the dynamic mechanical properties of rock.However, the damage law of coal and rock under dynamic and static combination state is still rare.In order to fully understand the dynamic characteristics of coal and rock and to evaluate the stability of rock engineering more accurately, it is necessary to study the mechanical response of coal and rock mass under the joint action of static and dynamic loads.
In this paper, the damage model of coal and rock was established by numerical analysis software ANSYS, and the in uence of impact velocity and restrained static load on the deformation of coal and rock mass was analyzed.en, based on ultrasonic wave speed as an indicator, the evolution law of coal and rock damage under combined action of static and dynamic loads was studied from a mesoscale, and the inuence of constraint static load, impact load, and impact number on the coal-rock damage was analyzed.e unilateral constraint dynamic impact model is shown in Figure 1.
It can be seen from Figure 1 that there are two kinds of unilateral constraint dynamic impact models: the static load P s and the impact load P d are in the same direction and the static load P s and the impact load P d are perpendicular to each other.In this paper, a one-way constraint dynamic impact model with static load and impact load perpendicular to each other is adopted (see Figure 1(b)).

Numerical Simulation Research on Dynamic and Static Combination
e numerical simulation research in this paper mainly considers the in uence of impact velocity and constraint static load on the evolution of coal-rock damage, expects to nd out the failure laws of coal and rock under the above external conditions, analyzes the in uence degree of the magnitude of impact velocity and constraint static load on the damage of coal and rock, analyzes the failure mode of coal and rock from the theoretical point of view, tries to get its universal laws, and provides the theoretical guidance for e cient mining of coal and improving the impact resistance of pillars.

Modeling and Parameter Settings.
In this paper, the model is classi ed by impulse and constrained static load.In order to study the damage evolution of impulse magnitude on coal and rock, the simulation process applied the same constraint static load to the coal-rock model, conducted a comparative analysis by changing the impulse magnitude, applied the same-sized constraint static load P d to the square coal-rock models (a) to (f ), and gradually increased the impulses from (a) to (f ).When studying the damage evolution of constraint static load on coal and rock, the simulation process applied the same impulse to the coal-rock model, conducted a comparative analysis by changing the magnitude of constraint static load, applied the same-sized impulse P s to the square coal-rock models (a) to (f ), and gradually increased the constraint static loads from (a) to (f ).Considering the actual conditions of the coal-rock deposits, a steel plate was placed at the bottom of the sample.e bottom of the steel plate was xed.
e square coal-rock model is a cube with a side length of 70 mm.
e model was divided into 35 * 35 * 35 42875 units.is simulation test used a cylinder with a diameter of 60 mm and a height of 40 mm to perform the impact, and the impact loading model is shown in Figure 2.
e loading gradient of con ned static stress was 0-5 Mpa. e impulse was converted into the loading velocity of the cylinder according to the laboratory test, and its loading velocity was 2.08-5.48m/s respectively.A total of 12 models were simulated, and the contact time was assumed to be 0.01 s. e loading mechanical parameters of each model are shown in Table 1.e physical and mechanical parameters used in the calculation were based on briquette coal.e mechanical parameters used in the calculation are shown in Table 2. Based on the Holmquist-Johnson-Cook constitutive model of LS-DYNA nite element analysis software, the coal-rock impact test simulation is realized [14,15].e HJC constitutive model is shown in Figure 3.

Calculation Results and Analysis.
In order to facilitate the description and analysis of the model results, a schematic diagram of the loading of coal-rock model was drawn, the surface where the impulse is applied is de ned as the impact surface, the two side surfaces where the constraint static load is applied are the constraint static surfaces, and the surface without any load is the free surface.According to the force range of the impact surface, it can be divided into bearing   Shock and Vibration surface area, crossed area, and nonbearing surface area, as shown in Figure 4.
According to the constraint static load and impulse loading conditions, the coal-rock model was numerically simulated to obtain the displacement of the dynamic and static combined loading model.Take the model of impact load (No.(b) as an example), as shown in Figure 5.
As can be seen from Figure 5(c), the z-direction displacement value of the surface of coal under impact has regional characteristics.
e displacement in the bearing surface area is the largest, the crossed area is the second, and the nonbearing surface area is the smallest.e displacement direction of the bearing surface area and the crossed area is the same as the impact direction, while the displacement direction of the nonbearing surface area is opposite to the impact direction.After the impact, the rock mass in the nonimpact area will be subjected to the swelling and extrusion e ect of the rock mass in the impact area, resulting in the reverse displacement of the nonimpact area.Due to the weak expansion and extrusion e ect, the surface displacement of the nonimpact area is very small.
As can be seen from Figures 5(a) and 5(b), the transverse deformation of coal and rock is caused by impact.e Ydisplacement is less than the X-displacement due to the constraint static load in the y-direction.

In uence of Impulse Magnitude on Damage of Coal-Rock Model.
e simulation conditions are as follows: the constraint static load is 2 MPa and the initial velocity given to the cylinder is 2.08 m/s-5.48m/s.e simulated results of e ective strain and impact velocity of the coal-rock model are obtained by loading the coal-rock model according to the above conditions, as shown in Figure 6.With the increase of  Shock and Vibration impact velocity, the e ective strain of coal after impact increases gradually and the damage degree of coal increases gradually.When the impact velocity is 2.08 m/s or 2.94 m/s, there is no obvious damage on the surface of the coal sample.

4
Shock and Vibration of the impact surface at di erent impact velocities, as shown in Figure 7.
It can be seen from Figure 7 that when the impact velocity is 2.08 m/s or 2.94 m/s, there is no obvious deformation in the bearing surface area.With the increase of the initial velocity given to the cylinder, the displacement of the bearing surface area gradually increases, and the rate of increase gradually increases.ere is a positive correlation between the displacement and the impact velocity of the bearing surface area. is is because the greater the impact velocity is, the greater the impact energy given to the coalrock model is, and the greater the damage produced is, appearing macroscopically as the increase of displacement.As the initial velocity increases, the displacement of the crossed area of the coal-rock model gradually increases.e displacement in the crossed area has a positive correlation with the impact velocity.From the analysis on the nonbearing surface area, the displacement of the coal-rock model in this area is close to zero, so the displacement of the nonbearing surface area has no obvious correlation with the impact velocity.erefore, the variation trend of displacement of the bearing surface area is consistent with the variation trend of displacement of the crossed area.e displacement of the two regions increases with the increase of loading speed.When the impact velocity is relatively small, there is no clear dividing line between the displacements of the bearing surface area and the crossed area.When the impact velocity reaches 3.60 m/s, the displacements of the two regions have a dividing line, and the displacement in the crossed area is larger than that in the bearing surface area. is is due to the shear stress in the crossed area, which is more likely to cause damage and failure.

In uence of Constraint Static Load on Impact Damage of Coal-Rock Model.
e simulation conditions are as   follows: the impact velocity given to the cylinder was 3.60 m/ s and the static loading imposed on the surface was 0-5 MPa respectively.
e effective strain cloud profile along the constraint direction after impact was obtained, as shown in Figure 8.When q � 0 MPa, the crossed area is damaged and destroyed after a single impact, showing the sample failure.Compression deformation occurs in the impact zone and a small number of sample failures occur in the sample.When q � 1-4 MPa, the sample is subjected to constraint static load, and no sample failure occurs after a single impact.e kinetic energy is mainly converted into strain energy.With the increase of constrain static load, the effective strain value increases gradually after impact, and the maximum strain value concentrates in the middle of the sample.When q � 5 MPa, obvious damage and failures occur in the sample after impact, the failure area of the sample is connected, and the sample loses the ability to resist the reimpact.
rough data analysis, the relationship curve between displacement and constraint static load of the bearing surface area and the crossed area under the action of the same impact velocity can be obtained, as shown in Figure 9.
From the analysis on the displacement of the bearing surface area, it can be seen that when the constraint static load is 0 MPa, the bearing surface area shows obvious deformation.e surface displacement decreases after static load is applied.e displacement of the crossed area decreases faster than that of the bearing surface area.When the constraint static load is 1 MPa to 4 MPa, the displacement of the bearing surface area and crossed area mainly unchanged with the increase of the constraint static load, and both displacement values are near to zero.When the constraint static load is 5 MPa, the maximum compression strength of the coal and rock is exceeded, and the coal and rock collapse.
e surface displacement of coal sample increases rapidly.e displacement value of the crossed area increases faster than that of the bearing surface area.Totally, the displacements of the bearing surface area and the crossed area are affected by the action of the constraint static load.Within the range of 0-4 MPa of constraint static load, the displacement decreases firstly and then remains constant with the increase of constraint static load.When the constraint static load is 5 MPa, the collapse will suddenly occur.
ere is a threshold value for the rock studied by previous scholars, and when a certain threshold value is exceeded, a collapse at a stroke will occur.
e above phenomenon shows that when the constraint static load is within the uniaxial compression strength of the coal-rock model, the improvement of the constraint static load can effectively enhance the impact resistance of the coal-rock model.When the constraint static load reaches or exceeds the uniaxial compression strength of the coal-rock model, the coal-rock model will suddenly collapse.

Coal-Rock Damage Simulation under Cyclic Impact.
e numerical simulation software LS-DYNA is used to simulate the cyclic impact of coal and rock.In the numerical simulation, the impact velocity was 3.6 m/s.Before each cyclic impact, the coal and rock maintained the property after the last impact, and the velocity remained constant during the cyclic impact process.e simulation results of cyclic impact effective strain are shown in Figure 10.With the increase of the number of cyclic impact, the damage amount of the sample increases gradually.Macroscopic damage occurred in the sample after 5 cycles, and the sample lost the ability to resist damage.After the first impact, no failure was found in each unit of the sample, and the sample remained intact.After the second impact, element failure occurred at the boundary around the sample.After the third impact, the number of unit failures around the sample increased.e damage of the sample was further increased.After the fourth impact, two obvious cracks formed in the middle of the sample, and the internal damage of the sample occurred.e failure range of the element around the sample increased and penetrated through the impact surface, and the number of element failures increased.After the fifth impact, the crack on the impact surface continued to expand, and the number of unit failures continued to increase and expand to the interior.Finally, the sample was pulled off from the middle, losing the ability to resist the second impact.
e relationship between the effective strain of the sample and the impact numbers in the cyclic impact process is shown in Figure 11.As can be seen from Figure 11, the effective strain of the sample increases with the increase of impact number.e effective strain has the characteristics of stage, including deceleration growth stage and acceleration growth stage.e relationship between effective strain and impact times is a cubic function, and the correlation coefficient is 0.962.

Statistical Description of Coal-Rock Damage
Quantity.e macroscopic catastrophe of rock material originates from its mesodamage evolution.
e damage quantity of rock materials can reflect the degree of rock failure when rock materials are subjected to load action.Under the action of certain loads, the internal defects of the rock will gradually evolve into microcracks and forming macroscopic catastrophes, resulting in the changes of the rock's elastic modulus, ultrasonic wave velocity, and other parameters.
e microscopic damage characteristics of rock materials are mainly represented by acousto-optic electromagnetic signals, which can reflect the evolution process of internal damage of rock materials [16].At present, the research methods of rock material damage characteristics include the following categories: the statistics of rock damage quantity based on ultrasonic detection technology; the rock damage research based on nuclear magnetic resonance technology [17,18]; rock damage positioning research based on acoustic emission [19][20][21]; evolution study of rock temperature field based on infrared thermal imaging technology [22,23]; simulation of rock damage under impact load based on ANSYS/LS-DYNA or other numerical software [24,25]; and research on digital speckle techniques for rock failure and research on constitutive model of rock failure under impact loads [26,27].
It is di cult to observe and calculate rock damage directly under existing technology, so it is necessary to de ne the damage quantity.e current methods for de ning the damage quantity mainly include the following: the damage scalar de ned by microcrack area, the damage tensor de ned by microcrack con guration, and the damage variable de ned by the change of elastic modulus [28,29].It is di cult to intuitively describe and measure the microcrack area or microcrack con guration, but the damage variable de ned by the change of elastic modulus can be used to de ne the damage variable of the rock through the ultrasonic wave velocity.Rock materials will have di erent degrees of damage after being subjected to impact loads.e damage process will be accompanied by varying degrees of acoustic characteristics and ultrasonic propagation parameters.e relationship between ultrasonic wave velocity and damage variables of rock materials will be established to calculate the quantity change factor of internal structure at the time of impact for rock materials and then used to indirectly make statistics for the damage variables of rock materials.
In order to study the in uence of dynamic impact on coal-rock damage under unilateral constraint conditions, the initial wave velocity of coal rock is V 0 , and the wave velocity is V n after the coal rock is subjected to external loading, and then the damage quantity of coal and rock is [11] 3.2.Test Equipment.Figure 12 shows a test device based on a constraint pendulum impact dynamic loading.e device consists of a frame, a pendulum, a dial, and a constraint loading mechanism.e constrained loading auxiliary device can be used to carry out one-dimensional static loading of coal and rock in di erent sizes.e pendulum can be used to produce impact loads of di erent sizes on the coal and rock by adjusting the angle of the pendulum.As shown in

Shock and Vibration
Figure 12, the pendulum is a cylinder and is connected with the bearing via a pendulum rod.When calculating the impact energy of the pendulum on the coal sample, the equivalent mass of the pendulum and the pendulum rod must be considered (the pendulum rod has greater in uence on the equivalent mass, while other components of the equipment have less in uence) [30].e actual measurement shows that the e ective length of the pendulum rod L 0.73 m; the mass of the pendulum rod m 2 0.457 kg; the pendulum mass m 1 1.303 kg; and the pendulum diameter d 0.06 m.
Pendulum rod inertia: Equivalent mass: e impact load given to rock materials is the result of the action of damage force and time, and the impulse is a physical quantity describing the time cumulative e ect of the force on the object.erefore, it is more representative to represent the impact energy by As the current testing method cannot accurately measure the impact time of the pendulum on the coal sample, according to the relationship between impulse I and momentum, we may know When the initial velocity v 1 is zero, the direction is ignored; then, we can obtain (5) According to the principle of conservation of energy, According to formulas (4) and ( 5), the impulse I can be obtained: e values are substituted in where h: pendulum height.Ultrasonic detection uses HC-U81 concrete ultrasonic detector, the sampling period is 0.05 μs∼2.0 μs, the soundtime measurement accuracy is 0.05 μs, the amplitude measurement range is 0-170 dB, the test system parameters are shown in Table 3, and Vaseline is used as a coupling agent between sensor and coal sample.

Sample Preparation.
Due to the development of joint cracks in natural coal and di culty to process, the variation laws of briquette and raw coal have fairly good consistency, and briquette is easy to process; the briquette prepared successfully has minor di erence, so the majority of scholars usually adopt the briquette with mechanical properties to raw coal as test object [31].In this test, the briquette is used as the research object, and the briquette is prepared into a cube with a side length of 70 mm through a briquette production device, as shown in Figure 13.

Test Program.
is test adopts a self-made constraint pendulum impact dynamic loading test device, applies the initial static axial load to the coal sample by a constraint loading mechanism, and uses the pendulum on the device as a power source to apply the impact load on the coal sample.
e test was divided into 5 groups with 5 coal samples in each group.According to the uniaxial compression strength of coal samples, it was divided into ve initial constraint static loads of 0 MPa, 1.127 MPa, 2.254 MPa, 3.38 MPa, and 4.506 MPa. e ve initial restraint static loads correspond to 0, 0.2, 0.4, 0.6, and 0.8 times of uniaxial compressive strength, respectively.Each group of coal sample was subjected to one gradient of initial static load, and ve coal samples within each group were again subjected to cyclic impact loads until the coal samples failed eventually.e fall height of the pendulum was 22 cm∼110 cm, having a total of ve levels; ve coal samples within each group were, respectively, subjected to one level of impact load, each of which corresponds to the size of the unit impulse, as shown in Table 4. Before and after each impact loading, the wave velocity of coal sample was measured and recorded.

Evolution Laws of Dynamic and Static Loads
and Coal-Rock Damage

Evolution Relationship between the Magnitude of Impulse and the Coal-Rock Damage.
e microcracks inside the coal and rock expand under the action of external loads and cause macroscopic catastrophes.e degree of coal-rock damage is negatively correlated with the ultrasonic wave velocity.Taking the rst group of 0 MPa unilateral constraint static load as an example for analysis, ve levels of ultrasonic wave velocity are measured through ultrasonic testing device, Shock and Vibration using equation ( 9) to obtain the coal-rock damage quantity D n .en, the curve of tting relationship between D n and the impact number with di erent levels can be obtained, as shown in Figure 14.

Cumulative E ect of Coal-Rock Damage Quantity.
It can be seen from Figure 14 that the tting curve of coalrock damage under ve levels of impulse loadings gradually increases with the increase of the number of cyclic impacts, and the cumulative damage quantity D n of coal and rock increases with the increase of the number of cyclic impacts.e constraint static load and loading methods of ve levels of impulse loading tests are the same.erefore, the reason of the change in the coal-rock damage quantity is the number of cyclic impacts and the magnitude of impulse.e coal-rock damage quantity under ve levels of impulse loading increases with the increase of the number of cyclic impacts, and the growth rate is related to the magnitude of impulse. is is because each impulse impact loading is an e ective impact on coal and rock, and the internal microcracks of coal and rock have the propagation under the action of external loads, and the tensile stress at the tip of the microcracks inside the coal and rock begins to expand, forms crack clusters, produces crack penetrations, and eventually leads to macroscopic failure.e process of the microcrack propagation is continuous under cyclic impact loading conditions, and the microscopic cracks nally expand to form macroscopic crack failure.From the point of view of ultrasonic wave velocity, the wave velocity is continuously reduced, so the coal-rock damage quantity continues to increase.

Variation Trend of Coal-Rock Damage.
It can be seen from Figure 14 that the upward trend of the tting curve of the coal-rock damage quantity under ve levels of impulse loads is approximately proportional to the linear growth.
e constraint static loads and loading methods of ve levels of impulse loading tests are the same.erefore, the reason of di erent failure trends in coal-rock damage is the di erent magnitude of impulse.When the impact load and the static    Shock and Vibration load are constant, the number and extent degree of microcracks determine the subsequent propagation process of the microcracks inside the coal and rock because the quantity of microcracks inside the coal and rock is significantly reduced after multiple cyclic impacts.e new crack clusters and the penetrating cracks are more difficult to form, making the failure velocity of coal and rock not increase or even decrease.However, due to the continuous propagation of the microcracks, the original crack clusters continue to expand into the penetrating cracks under the action of cyclic impact.e microcracks form new crack clusters, thereby increasing the degree of coal-rock damage.e number and complexity of microcracks in coal and rock increase linearly with the increase of impact times, and the porosity of coal and rock increases linearly with the increase of impact times.As a result, the damage of coal and rock increases linearly with the increase of impact times.When the size of static load is the same, under the of cyclic impact, each impact causes the coal and rock subjected to a greater impact load to be damaged more quickly.Macroscopically, the fitting curve of coal-rock damage quantity increases with the increase of the impulse.

Differentiation Effect of Different Levels of Impulse
Loading on the Coal-Rock Damage Quantity.From the longitudinal analysis of the coal-rock damage quantity under different levels of impulse in Figure 14, the coal-rock damage quantity under different levels of impulse loading has a differentiation effect at the first impact, and the greater the loading of the impulse, the greater the damage of the coal and rock. is is because when the first impulse loading is carried out, the microcracks within the large-impulse-loaded coal rock have a greater degree of microcracks propagation and the degree of the coal-rock damage is large, and the coalrock microcrack propagation process is continuous, so that the damage degree of large-impulse-loaded coal rock is getting larger and larger and the degree of differentiation of coal and rock is also getting larger and larger.When the third impact occurs, the coal and rock with the largest impulse loading has eventual failure.At this time, the degree of differentiation of the coal and rock loaded with different levels of impulse loading reaches its maximum value.

Coal-Rock Eventual Failure Zone under Different Levels of Impulse
Loading.It can be seen from Figure 14 that the cumulative quantity of coal-rock damage increases with the increase of the impact number; while the ultimate failure degree of coal and rock with different levels of impulse loading is close, the damage quantity range of coal and rock with five levels of impulse loading is about 0.65∼0.75.It can be considered that this zone is a coal-rock eventual failure zone under 0 MPa constraint static load.If the degree of coal-rock damage wants to reach the eventual failure zone, the larger the impulse loading is, the less time it takes for impact loading, and this is because the larger impulse loading makes the faster propagation speed of microcracks within the coal and rock, causing the failure rate of coal and rock faster.

Influence of Cumulative Impulses on Coal-Rock Damage Quantity.
e cumulative impulse is the mutual accumulation of multiple impulses, namely, the secondary cumulative impulse is the accumulation of the first two impulses.e external reason of coal-rock damage caused by coal-rock microcracks propagation is the cumulative effect of impulses.e curve of fitting relationship between the coal-rock damage quantity D n and the cumulative impulse can be obtained, as shown in Figure 15.
All the five levels of impulse loading tests are constant type impulse cyclic impact tests.e constraint conditions are all unconstrained.erefore, the difference condition of this test is the magnitude of the single impact impulse.It can be seen from Figure 15 that if the cumulative impulses are the same, the failure velocity of coal and rock is faster when the single impact impulse is larger.Taking the cumulative impulse of 3500 N•s•m −2 as an example, when the cumulative impulse is 3500 N•s•m −2 , the fifth level of impulse loading of coal and rock completes the eventual damage and failure, while the damage quantity of other lower single impulse decreases in turn and the degree of damage and failure is smaller.If all the five levels of impulse loaded of coal and rock complete the eventual damage and failure, the coal and rock with a lower single impact impulse require more cumulative impulses, which can be applied in engineering to carry out cyclic impact by applying larger single impulse, thus having more efficient rock breaking.

Evolution Relationship of Constraint Static Load and
Coal-Rock Damage.Coal and rock are damaged under external loads.Constrained static loading is one of the factors causing coal-rock failure.
is test made a comparison study by applying five groups of different constraint static loads to coal and rock and analyzed the damage and failure laws of coal and rock.e difference in the loading conditions between each group of coal and rock tests was the magnitude of the constraint static load.Substituting the ultrasonic wave velocities of the five groups in the test into equation ( 9) can obtain the coal-rock damage quantity under different constraint static loads.rough data analysis, the relationship between the coal-rock damage quantity D n under different constraint static loads and the impact number can be obtained, as shown in Figure 16.

Relationship between the Coal-Rock Damage Quantity and the Impact Number.
From Figure 16, it can be seen that under the conditions of unconstraint static loading, the impact number is 3 to 10 when the coal and rock is completely destroyed; under the conditions of 1.127 MPa constraint static loading, the impact number is 6 to 10 when the coal and rock is completely destroyed; under the conditions of 3.38 MPa constraint static loading, the impact number is 5 to 14 when the coal and rock is completely destroyed; under the conditions of 3.943 MPa constraint static loading, the impact number is 4 to 14 when the coal and rock is completely destroyed; under the conditions of 4.506 MPa constraint static loading, the impact number is 4 to 13 when the coal and rock is completely destroyed.From the statistics of the impact Shock and Vibration number, under 0 to 1.127 MPa constraint static load, the impact number required is relatively small when the coal and rock is completely destroyed.Under 3.38 to 4.506 MPa constraint static load, the impact number required is relatively large when the coal and rock is fully damaged.It is assumed that 0 to 1.127 MPa is the low-constraint static-load bearing   Shock and Vibration pressure zone of coal and rock; 3.38 MPa to 4.506 MPa is the high-constraint static-load bearing pressure zone of coal and rock, namely, 0 to 20% of the uniaxial compression strength of coal and rock is the low-constraint static-load bearing pressure zone, and 40% to 80% of the uniaxial compression strength of coal and rock is the high-constraint static-load bearing pressure zone.From the above statistics, it can be seen that the impact number required for the coal and rock failure in the low-constraint static-load bearing pressure zone is smaller, and the impact number required for coal and rock failure in the high-constraint static-load bearing pressure zone is greater.It is possible to achieve the purpose of efficient mining in engineering through the pressure relief of coal and rock in advance.
When the coal and rock are loaded with the same impulse, the constraint static load suppresses the failure and propagation process of the microcracks of the coal and rock, making the microcrack propagation difficult.In macroscopic terms, it is shown that the greater the static load imposed on the coal and rock, the more times of cyclic impact the coal and rock is required when it is fully destroyed.

Failure Trend of Coal-Rock Damage under Different
Constraint Static Loads.From Figure 16, it can be seen that the fitting curve of coal-rock damage for each level of impulse under different constraint static loads tends to approach the x-axis as the constraint static load increases, and the slope of the fitting curve of the coal-rock damage for each level of impulse generally becomes smaller and smaller as the constraint static load increases, which indicates that the increase of constraint static load suppresses the microcrack propagation of coal and rock and slows down the damage process of coal and rock.

Crack Propagation Law of Coal Surface under Dynamic and Static Load.
e impact loading mechanism of this test is cylinder.After the surface of cube coal is impacted, the force surface is the contact surface between coal and cylindrical pendulum.In the test, the boundary of the stressed surface of coal shows crack expansion in different degrees.
When the coal is impacted, the shear stress area is formed by the intersection of the stressed surface area and the nonstressed surface area.e existence of shear stress makes the crossed area easy to form cracks. e degree of fracture expansion on the surface of coal and rock can reflect the degree of damage of coal [10].e images of crack propagation on impact surface of coal and rock under constraint static load were obtained by means of HD digital camera.Figure 17 shows the crack condition of coal impact surface after four cyclic impacts.rough Photoshop, cracks on the surface of coal and rock were processed, and the sketch drawing of cracks on the surface was obtained.
As can be seen from Figure 17, when the constraint static load is low (Figure 17(a) and 17(b)), a large number of cracks appear in both the crossed area and the stressed surface area, and vertical penetrating cracks appear in the stressed surface area.When the constraint static load is low, the effect of static load on crack propagation is weak.e rigid pad block supporting the specimen is adjacent to the impact surface of the specimen.erefore, it is easy for the specimen to form vertical penetrating cracks under impact.When the constraint static load is high (Figure 17(c)-17(e)), there are few cracks in the crossed area of coal and rock and no macroscopic cracks in the stressed surface area. is is because the high-constraint static load inhibits the expansion of microcracks in coal and rock, resulting in fewer macroscopic cracks on the surface of coal and rock.

Conclusions
e main conclusions of this paper are as follows: (1) e damage quantity of coal and rock has a cumulative effect, which increases with the increase of Shock and Vibration the impact number; the ultimate damage degree of coal and rock loaded with different levels of impulse under the same constraint static load is close, namely, the eventual failure D n of coal and rock is approximately 0.65∼0.75.(2) e deformation displacement of coal-rock model increases with the increase of single impact velocity, and the damage quantity of coal and rock increases with the increase of single impulse, which means that increasing single impulse contributes to the microcrack propagation.In engineering, it is possible to perform a cyclic impact by applying a larger single impact impulse so as to efficiently break rock and conserve energy.(3) e damage quantity of coal and rock decreases with the increase of the constraint static load, indicating that the constraint static load suppresses the microcrack propagation.In engineering, it is possible to enhance the impact resistance of rock engineering by increasing the constraint static load and to achieve the purpose of high-efficiency mining through pressure relief.(4) e coal-rock model shows that when the constraint static load reaches or exceeds the uniaxial compression strength of the coal-rock model, the coalrock model will suffer the collapse at a stroke.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.
When the impact velocity is 3.60 m/s or 4.15 m/s, the phenomenon of slag failure occurs around the coal sample.When the impact velocity is 4.64 m/s, obvious damage occurs in the impact crossed area, and partial damage occurs in the nonbearing surface area.When the impact velocity is 5.48 m/s, obvious damage occurs in the crossed area and around the sample surfaces, and the sample loses the ability to resist the impact.eresultant displacements of the bearing surface area and the crossed area are extracted to obtain the displacement D = 0 (undamaged)

Figure 7 :
Figure 7: Displacement of impact surface at di erent impact velocities.

Figure 14 :
Figure 14: Relationship between damage quantity and number of impulse cyclic impact of di erent levels.

Figure 15 :
Figure 15: Relationship between damage quantity at di erent levels of impulse and cumulative impulse.

Table 1 :
Model loading mechanics parameters.

Table 2 :
Mechanical parameters used in the calculation.

Table 4 :
Relationship between impulse per unit area and pendulum height.