The 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 one-dimensional constraint condition was studied by using the self-developed constrained pendulum impact dynamic loading test device and ultrasonic testing device. The 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.
As an important engineering material, the rock is often in a complex combined stress environment. The instability of rock materials under the action of external loads threatens the safe production of rock engineering. The pillars in mining bear the weight of overlying strata and may be subjected to blasting, mechanical, and other dynamic loads. The related engineering problems can be simplified to study the effect of dynamic impact on rock damage under unidirectional restraint. The rock is damaged by external loads, and its nature is the result of the microcrack structural evolution inside the rock. That 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 [
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 [
The traditional research method of rock dynamic mechanics is to apply the cyclic impact load, and to conduct the statistics of dissipative energy diffusion 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 influence of impact velocity and restrained static load on the deformation of coal and rock mass was analyzed. Then, 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 influence of constraint static load, impact load, and impact number on the coal-rock damage was analyzed. The unilateral constraint dynamic impact model is shown in Figure
Unilateral constraint dynamic impact model.
It can be seen from Figure
The numerical simulation research in this paper mainly considers the influence of impact velocity and constraint static load on the evolution of coal-rock damage, expects to find out the failure laws of coal and rock under the above external conditions, analyzes the influence 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 efficient mining of coal and improving the impact resistance of pillars.
In this paper, the model is classified 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
The square coal-rock model is a cube with a side length of 70 mm. The model was divided into 35 ∗ 35 ∗ 35 = 42875 units. This 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
Schematic diagram of simulated impact loading.
Model loading mechanics parameters.
Model | No. | Constraint static load MPa | Impact velocity m/s |
---|---|---|---|
Impulse model | a | 2 | 2.08 |
b | 2 | 2.94 | |
c | 2 | 3.60 | |
d | 2 | 4.15 | |
e | 2 | 4.64 | |
f | 2 | 5.48 | |
|
|||
Constraint static load model | a | 0 | 2.08 |
b | 1 | 2.08 | |
c | 2 | 2.08 | |
d | 3 | 2.08 | |
e | 4 | 2.08 | |
f | 5 | 2.08 |
Mechanical parameters used in the calculation.
Density kg/m³ | Elastic modulus GPa | Compressive strength MPa | Poisson’s ratio | Damage factor |
Damage factor |
---|---|---|---|---|---|
1428 | 0.81 | 5.6 | 0.3 | 0.04 | 1 |
Holmquist–Johnson–Cook constitutive model.
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 defined 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 surface area, crossed area, and nonbearing surface area, as shown in Figure
Conventions of each surface of coal-rock model.
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
Displacement of dynamic and static combined loading model. (a)
As can be seen from Figure
As can be seen from Figures
The 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–5.48 m/s. The simulated results of effective 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
Relationship between effective strain and impact velocity of coal rock. (a)
The resultant displacements of the bearing surface area and the crossed area are extracted to obtain the displacement of the impact surface at different impact velocities, as shown in Figure
Displacement of impact surface at different impact velocities.
It can be seen from Figure
The 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. The effective strain cloud profile along the constraint direction after impact was obtained, as shown in Figure
Relationship between effective strain and constraint static load of impact of coal rock. (a)
Through 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
Displacement of impact surface under different loads.
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. The surface displacement decreases after static load is applied. The 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. The surface displacement of coal sample increases rapidly. The 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.
There 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. The 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.
The 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. The simulation results of cyclic impact effective strain are shown in Figure
Effective strain of sample under cyclic impact. (a) No. 1. (b) No. 2. (c) No. 3. (d) No. 4. (e) No. 5.
The relationship between the effective strain of the sample and the impact numbers in the cyclic impact process is shown in Figure
Relationship between effective strain and impact number.
The macroscopic catastrophe of rock material originates from its mesodamage evolution. The 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. The 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 [
It is difficult to observe and calculate rock damage directly under existing technology, so it is necessary to define the damage quantity. The current methods for defining the damage quantity mainly include the following: the damage scalar defined by microcrack area, the damage tensor defined by microcrack configuration, and the damage variable defined by the change of elastic modulus [
In order to study the influence of dynamic impact on coal-rock damage under unilateral constraint conditions, the initial wave velocity of coal rock is
Figure
Test situation.
Pendulum rod inertia:
Equivalent mass:
The 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 effect of the force on the object. Therefore, it is more representative to represent the impact energy by impulse. As the current testing method cannot accurately measure the impact time of the pendulum on the coal sample, according to the relationship between impulse
When the initial velocity
According to the principle of conservation of energy,
According to formulas (
Then, the impulse
The values are substituted in
Ultrasonic detection uses HC-U81 concrete ultrasonic detector, the sampling period is 0.05
Setting of system parameters of ultrasonic devices.
Sampling period/ |
Emission voltage/V | Measuring point spacing/mm | Testing surface | Testing method |
---|---|---|---|---|
0.5 | 500 | 70 | Surface | Relative measuring method |
Due to the development of joint cracks in natural coal and difficulty 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 difference, so the majority of scholars usually adopt the briquette with similar mechanical properties to raw coal as test object [
Test Coal Sample. (a) Size of briquette. (b) Briquette samples.
This 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. The 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 five initial constraint static loads of 0 MPa, 1.127 MPa, 2.254 MPa, 3.38 MPa, and 4.506 MPa. The five 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 five coal samples within each group were again subjected to cyclic impact loads until the coal samples failed eventually. The fall height of the pendulum was 22 cm∼110 cm, having a total of five levels; five 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
Relationship between impulse per unit area and pendulum height.
Height |
Impulse per unit area |
---|---|
0.22 | 535 |
0.44 | 756 |
0.66 | 926 |
0.88 | 1069 |
1.1 | 1195 |
The microcracks inside the coal and rock expand under the action of external loads and cause macroscopic catastrophes. The degree of coal-rock damage is negatively correlated with the ultrasonic wave velocity. Taking the first group of 0 MPa unilateral constraint static load as an example for analysis, five levels of ultrasonic wave velocity are measured through ultrasonic testing device, using equation (
Relationship between damage quantity and number of impulse cyclic impact of different levels.
It can be seen from Figure
It can be seen from Figure
From the longitudinal analysis of the coal-rock damage quantity under different levels of impulse in Figure
It can be seen from Figure
The cumulative impulse is the mutual accumulation of multiple impulses, namely, the secondary cumulative impulse is the accumulation of the first two impulses. The external reason of coal-rock damage caused by coal-rock microcracks propagation is the cumulative effect of impulses. The curve of fitting relationship between the coal-rock damage quantity
Relationship between damage quantity at different levels of impulse and cumulative impulse.
All the five levels of impulse loading tests are constant type impulse cyclic impact tests. The constraint conditions are all unconstrained. Therefore, the difference condition of this test is the magnitude of the single impact impulse. It can be seen from Figure
Coal and rock are damaged under external loads. Constrained static loading is one of the factors causing coal-rock failure. This 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. The 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 (
Relationship between damage quantity and impact number under different constraint static loads. (a)
From Figure
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.
From Figure
The 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. The existence of shear stress makes the crossed area easy to form cracks.
The degree of fracture expansion on the surface of coal and rock can reflect the degree of damage of coal [
Crack propagation on coal surface. (a)
As can be seen from Figure
The main conclusions of this paper are as follows: The damage quantity of coal and rock has a cumulative effect, which increases with the increase of 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 The 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. The 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. The coal-rock model shows that when the constraint static load reaches or exceeds the uniaxial compression strength of the coal-rock model, the coal-rock model will suffer the collapse at a stroke.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
The authors gratefully acknowledge the support of the Open Fund of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University) (grant no. PLN1304), the National Key R&D Program of China (2018YFC1504800), the National Natural Science Foundation of China (grant no. 51474220), and the National Key R&D Program of China (grant no. 2018YFC0808403).