In order to investigate the high loading rate effect on the behaviour and mechanical properties of coal-rock combined body, the dynamic compressive tests were conducted by using the Split-Hopkinson Pressure Bar (SHPB) device under the loading rate range from 2.7×105 MPa/s to 4.0×105 MPa/s. The stress-strain curves, dynamic peak stress and strain, elastic modulus, and energy distribution law of coal-rock combined body under different loading rates were analyzed and discussed. The results show that the dynamic stress-strain curves of coal-rock combined body have a double-peak feature under high loading rate range, which can be divided into the initial bearing stage, the bearing decline stage, the bearing enhance stage, and the unstable stage. The first peak stress of the coal-rock combined body is independent of the loading rate, while the dynamic compressive strength (the second peak stress) and dynamic peak strain (the second peak strain) have a strong loading rate effect and will generally increase linearly with the loading rate. The first and second elastic moduli of coal-rock combined body are not sensitive to the loading rate. With the increase of the loading rate, the incident energy and reflective energy of coal-rock combined body increase rapidly, while the change of transmitted energy is very small. The absorption energy ratio of the coal-rock combined body shows a good linear law with the incident energy under different loading rates.
In deep mining of coal mine, rock burst or coal burst is often encountered and is becoming more and more serious with the increase of depth, which seriously threatens the safety of mine production [
Referring to literature [
Specimen photograph of coal-rock combined body.
In the investigation of the dynamic characteristics of rock or coal materials under high loading rate [
Experimental system sketch of SHPB apparatus.
Incident wave, reflective wave, and transmitted waves recorded during the impact test.
Before the tests, the basic geometric and physical parameters of coal-rock combined body were measured (Table
Testing results of coal-rock combined body.
No. | | | | | Impact pressure |
---|---|---|---|---|---|
A1 | 48.0 | 51.2 | 1886.2 | 2.1 | 0.5 |
A2 | 48.1 | 50.9 | 1909.0 | 1.8 | 0.5 |
A3 | 48.0 | 52.4 | 1862.2 | 2.4 | 0.6 |
A4 | 48.0 | 51.3 | 1852.9 | 2.0 | 0.6 |
A6 | 48.0 | 52.2 | 1871.4 | 2.1 | 0.7 |
A7 | 48.1 | 52.4 | 1901.1 | 1.9 | 0.7 |
During the SHPB tests, stress equilibrium at both ends of the specimen is the necessary condition to ensure the accuracy of the test results. Figure
Stress equilibrium check for the dynamic compression tests of coal-rock combined body.
According to the principle of one-dimensional stress wave propagation during SHPB test, the stress-strain curves of coal-rock combined body can be obtained. The results of the loading rate, stain rate, peak stress, elastic modulus, and energy consumption parameters are also calculated (Table
Test results of dynamic compressive tests of coal-rock combined body.
No. | | | | | | | | | | |
---|---|---|---|---|---|---|---|---|---|---|
A1 | 2.71×105 | 65.90 | 11.06 | 28.23 | 7.5 | 2.2 | 55.67 | 37.54 | 2.89 | 15.23 |
A2 | 2.74×105 | 70.25 | 9.51 | 34.43 | 8.2 | 2.3 | 52.02 | 34.83 | 6.75 | 10.44 |
A3 | 2.98×105 | 65.90 | 9.36 | 37.23 | 6.8 | 2.7 | 60.49 | 40.02 | 3.87 | 16.58 |
A4 | 3.36×105 | 77.07 | 9.43 | 41.32 | 8.5 | 2.6 | 79.81 | 56.91 | 6.22 | 16.67 |
A6 | 3.41×105 | 80.14 | 10.63 | 43.36 | 7.5 | 2.8 | 88.15 | 58.93 | 5.85 | 23.35 |
A7 | 4.01×105 | 92.12 | 10.20 | 44.49 | 8.0 | 2.8 | 107.42 | 74.38 | 6.00 | 27.03 |
In dynamic tests, both loading rate and strain rate are usually used as the rate effect parameters. However, the corresponding relation between the two parameters was rarely investigated. The previous studies show that there is a linear function relationship between the logarithm of loading rate and the logarithm of strain rate under low loading rate range [
Relationship between the logarithm of loading rate and the logarithm of strain rate.
The failure modes of the coal-rock combined body specimen at different loading rate are shown in Figure
Failure modes of coal-rock combined body specimen.
A1: 2.71×105 MPa/s
A2: 2.74×105 MPa/s
A3: 2.98×105 MPa/s
A4: 3.36×105 MPa/s
A6: 3.41×105 MPa/s
A7: 4.01×105 MPa/s
The stress-strain curves of coal-rock combined body specimens under high loading rate are shown in Figures
Stress-strain curves of coal-rock combined body specimens.
Impact pressure of 0.5 MPa
Impact pressure of 0.6 MPa
Impact pressure of 0.7 MPa
Stress-strain curves of coal-rock combined bodies under different loading rates.
The reason why there are two peak stresses in the stress-strain curve of combined specimen is closely related to the propagation of stress waves in coal body and rock body. During the loading process, the stress wave was first introduced into the sandstone from the incident bar. Owing to fast wave velocity and higher strength of sandstone, the sandstone sample remains stable at the initial stage of loading. When the stress wave is approximately transmitted to the rock-coal body interface, a local failure occurs in the coal sample because of its low velocity and weaker strength. Thus, the first peak stress was formed in the early stage of loading. However, with the transmission of stress wave, the coal sample still possesses certain bearing capacity that enables it to be compacted together with the rock sample and continues to bear the dynamic load until the rock sample also breaks up, then forming the second peak stress.
To more systematically investigate the strength and deformation characteristics of coal-rock combined body under different high loading rates, the maximum stress (the second peak stress) was defined as the dynamic compressive strength of coal-rock combined body and the corresponding strain (the second peak strain) is the dynamic peak strain. As shown in Figure
The relationship between dynamic compressive strength, dynamic peak strain, and loading rate.
Dynamic compressive strength
Dynamic peak strain
The stress values of the first peak in the stress-strain curves of all specimens were also measured. As shown in Figure
The relationship between the first peak stress and loading rate.
Due to the double-peak characteristic in stress-strain curves, the elastic modulus of coal-rock combined body cannot be calculated with the conventional method. The first and second elastic moduli
Comparison of two elastic moduli under different loading rates.
According to the one-dimensional stress wave propagation theory in SHPB test, the incident energy
Variation in incidence energy, reflective energy, transmitted energy, and loading rate.
In the analysis of energy consumption law, the absorption energy can directly reflect the energy consumption of coal-rock combined body specimen and is given by
Further, the unit volume absorption energy
As shown in Figure
Unit volume absorption energy under different loading rates.
By using SHPB testing system, the dynamic compression tests of coal-rock combined body were carried out under different high loading rates. Before the test, the stress equilibrium at both ends of coal-rock combined body specimen has been checked, and the results show that the specimens can achieve stress equilibrium during the impact process. 3 kinds of air pressure were set for impact, and the stress-strain curves under 6 loading rates were obtained. The characteristics of failure mode, strength and deformation, and energy distribution law of coal-rock combined body specimens were analyzed. The main conclusions are as follows.
(1) The stress-strain curves of the coal-rock combined body can be divided into four stages: the initial bearing stage, the bearing decline stage, the bearing enhance stage, and the unstable stage.
(2) The stress-strain curves of coal-rock combined body have double-peak feature under high loading rate. The second peak stress is defined as the dynamic compressive strength of coal-rock combined body specimen and will increase with the increase of the loading rate. The first peak stress has no loading rate effect. Both the first and second elastic moduli of coal-rock combined body are independent of the loading rate.
(3) With the increase of the loading rate, the incident energy and reflective energy of coal-rock combined body will increase linearly, while the transmitted energy has little change. Both the unit volume absorption energy and breaking degree of coal-rock combined body specimen will increase obviously when the loading rate increases.
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.
This research was financially supported by the Research Project of State Key Laboratory of Coal Resources and Safe Mining, CUMT (13KF06).