Vibration response of the interfaces in multi-layer combined coal and rock mass under impact load

doi:10.21203/rs.3.rs-1959260/v1

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Vibration response of the interfaces in multi-layer combined coal and rock mass under impact load

https://doi.org/10.21203/rs.3.rs-1959260/v1

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The stress wave generated by impact or dynamic load would have significant reflection and transmission at the rock-coal or rock-rock interfaces in the process of propagation, resulting in dynamic effects such as dynamic tensile, stress superposition and mutation. These dynamic effects would lead to obvious vibration at the interfaces which is a key factor leading to dynamic damage and failure of coal and rock mass. In the process of underground engineering excavation, the dynamic damage of a series of layered rock masses is the important factor causing geological disasters. Based on the two-dimensional similar material simulation experiment, the coal and rock mass combined by five layers of fine sandstone, medium sandstone, coal, coarse sandstone and mudstone is taken as the research object, single and multi-point excitation (synchronous / step-by-step) were used to test the time-history vibration curves of rock-coal and rock-rock interfaces under impact load. It was concluded that the change of extreme value of vibration amplitude presented two stages: first increase and then attenuation. Most of them needed 2.25 cycles to reach the peak value, and the dynamic attenuation of amplitude conformed to the law of exponential. Based on Fast Fourier transform (FFT), the spectrum structures of amplitude-frequency of interfaces vibration were studied, and the two predominant frequencies were 48.9Hz~53.7Hz and 92.4Hz respectively. Based on Hilbert-Huang transform and energy equation, 5~7 vibration modes (IMF) were obtained respectively by decomposing the time-history curves. The three modes IMF1、IMF2、IMF3 contained high energy and were effective vibration modes. IMF2 accounted for the highest proportion and was the main vibration mode whose predominant frequencies were concentrated in 45.6Hz~50.2Hz. Therefore, IMF2 played a decisive role in the whole vibration process and had an important impact on the dynamic response, damage and failure of coal and rock mass. In real condition, the actual predominant frequencies could be converted according to the size and mechanical properties of coal and rock mass, and the vibration response characteristics of the interfaces between coal and rock mass under impact load were preliminarily revealed.

The sedimentary process and the arrangement of mineral particles during the formation of coal measure rock mass make it have obvious bedding structure and show layered structure macroscopically [1–3]. This layered rock mass widely exists in mining, construction, transportation and water conservancy projects [4–6], which is prone to vibration, damage and even failure under the action of external dynamic disturbances, such as blasting, roof and floor breaking, rock instability and so on [7–8]. For example, the roof strata of working face in mine, especially in the early stage of mining, is subjected to the loading/unloading action of dynamic disturbance, and the appearance of mineral-pressure is violent, which would lead to obvious mine earthquake and even roof collapse. Therefore, in the process of underground engineering excavation, the dynamic damage of a series of layered rock masses is the key factor causing geological disasters.

At present, scholars at home and abroad mainly studied the static mechanical properties of single, two-layer or three-layer combined coal and rock mass [9–12], while the research on dynamic response, the vibration characteristics and dynamic damage of coal and rock mass, especially multi-layer combined coal and rock mass, are still in the stage of experimental exploration. The stress wave generated by impact or dynamic load would have significant reflection and transmission at the rock-coal or rock-rock interfaces in the process of propagation, resulting in dynamic effects such as dynamic tensile, stress superposition and mutation. These dynamic effects would lead to obvious vibration at the interfaces which is a key factor leading to dynamic damage and failure of coal and rock mass [13–16].

Based on the two-dimensional similar material simulation experiment, the coal and rock mass combined by five layers of fine sandstone, medium sandstone, coal, coarse sandstone and mudstone was taken as the research object, single and multi-point excitation (synchronous / step-by-step) were used to test the time-history vibration curves of rock-coal and rock-rock interfaces under impact load, and the dynamic attenuation law of amplitude was obtained. Based on Fast Fourier transform (FFT), the spectrum structures of amplitude-frequency of interfaces vibration were studied. Based on Hilbert-Huang transform and energy equation, the time-history curves were decomposed by Ensemble Empirical Mode Decomposition (EEMD) and the vibration modes were obtained. According to the distribution laws of marginal spectrum and energy proportion, the effective and main vibration modes and the predominant frequencies were obtained. And the vibration response characteristics of the interfaces between coal and rock mass under impact load were preliminarily revealed.

Experimental model. The two-dimensional similar material simulation experiment platform was often used to simulate the deformation, damage and failure laws of overlying strata in the process of mining [17–18], and the size of similar material simulation experiment platform was 1800mm×160mm×1100mm in the lab; the multi-layer combined coal and rock mass was composed of five layers, each with a thickness of 200mm; from top to bottom, they were fine sandstone, medium sandstone, coal, coarse sandstone and mudstone; the similarity density constant of rock mass is 1.6, and that of coal is 1; the composition and ratio of similar materials of each layer in coal and rock mass could be seen in Table 1. The vibration amplitude was measured by magnetoelectric speed sensors (2D001) with the size of 63mm×63mm×63mm; And the distributed network dynamic signal test system (DH5981) was used for data acquisition and analysis, as shown in Fig. 1.

Table 1

The composition and ratio of similar materials of each layer.
Serial number	Layers of coal and rock mass	Raw material compressive strength/MPa	Similar material compressive strength/MPa	Fine sand /Kg	Cement /Kg	Gypsum /Kg	Water /Kg
1	Fine sandstone	120	0.75	72.98	7.30	17.03	9.73
2	Medium sandstone	80.1	0.50	81.09	8.11	8.11	9.73
3	Coal	10	0.063	86.49	7.57	3.24	9.73
4	Coarse sandstone	61.5	0.384	83.40	6.95	6.95	9.73
5	Mudstone	27.4	0.171	88.46	6.32	6.32	10.11

Action points and sensors distribution. Four sensors (No.1-No.4) were distributed respectively at the interfaces of each layer of combined coal and rock mass, and each sensor was at the midpoint of each interface; the lower surface of the sensor (signal receiving surface) coincided with the each interface of coal and rock mass. An action point was set every 100mm on the upper surface of the fine sandstone for percussion excitation, and iron block with 80mm×80mm was placed at action point to prevent damage to fine sandstone during excitation; A total of five vertical action points (1#-5#) and four inclined action points with an angle of 45 ° to the horizontal direction (6#-9#) were arranged, as shown in Figure. 2.

Experimental process. Single point and multi-point excitation (synchronous / step-by-step) were used in the experiment, and the specific excitation steps were as follows: (1) the action point (1#~9#) was excited respectively; (2) Two action points were excitedsynchronously or step-by-step as follows: 1 # and 2 #, 1 # and 5 #, 2 # and 4 # (excitation step-by-step), 6 # and 7 #, 6 # and 8 #, 7 # and 8 #, 8 # and 9 #; (3) four action points (6#~9#) and five action points (1#~5#) were excited synchronously and respectively. Before the experiment, the data acquisition instrument needed to be zeroed firstly, and when the impact actions caused by the excitation became balanced, the data acquisition would be terminated and saved.

Amplitude variation of interface vibration under impact load

Amplitude variation of interface vibration under single point excitation. When a single point was excited, the dynamic variation laws of the vibration amplitude of each interface obtained from the four sensors were similar; and the amplitude time-history curves of 2#, 4#and 6# action points excited separately were shown in Figure. 3 ~ Figure. 5. It can be seen from Figure. 3 that when the 2# action point was excited alone, the amplitude curve (2#-1 in Figure.3) of No.1 reached the first extreme value s1=-0.005mm when t1 = 15ms, and reached the peak s6 = 0.014mm when t6 = 51ms; When 4# action point was excited alone (Figure.4), the amplitude curve of No. 1 (2#-1 in Figure. 4) reached the first extreme value s1=-0.004mm when t1 = 12ms and the peak s6 = 0.015mm when t6 = 49ms; similarly, when 6# action point was excited alone (Figure.5), the amplitude curve of No. 1(6#-1 in Figure. 5) reached the first extreme value s1=-0.001mm when t1 = 7ms and the peak value s6 = 0.005mm when t6 = 18ms. The extreme points of amplitude curves of single point excitation (2#, 4# and 6#) and their corresponding time could be seen in Table.2. The extreme values of the amplitude curves of these three action points showed two stages as follows: first increasing and then decreasing; the vibration curves of 2# and 4# action points reached the peak after 2.25 cycles, and that of 6# action point the peak after 1.25 cycles.

Table 2

The extreme points of amplitude curves of 2#, 4# and 6# action points.
Extreme value (mm) /Time (ms)	2#	4#	6#
s₁/t₁	0.005/15	0.004/12	0.001/7
s₂/t₂	0.014/18	0.009/15	0.002/13
s₃/t₃	0.011/21	0.007/22	0.005/18
s₄/t₄	0.010/33	0.012/29	0.005/25
s₅/t₅	0.011/42	0.013/38	0.005/33
s₆/t₆	0.014/51	0.015/49	0.005/43
s₇/t₇	0.014/61	0.015/58	0.005/52
s₈/t₈	0.013/70	0.014/67	0.004/62
s₉/t₉	0.011/80	0.011/78	0.003/72
s₁₀/t₁₀	0.008/90	0.008/86	0.003/82
s₁₁/t₁₁	0.006/99	0.007/97	0.002/92
s₁₂/t₁₂	0.004/109	0.004/117	0.002/101

Amplitude variation of interface vibration under multi-point excitation. When 2# and 4# action points were excited step by step, the curve of No. 1 (24#-1 in Figure. 6) reached the first extreme value s₁=-0.01mm when t₁ = 11ms, the peak s₂ = 0.029mm when t₂ = 14ms, and the second peak s₆ = 0.021mm when t₆ = 46ms. Compared with No. 3 and No. 4, No. 1 and No. 2 were close to the action points, and there were complex micro vibrations during step-by-step excitation (24#-1 and 24#-2 in Figure.6), but the whole dynamic change of all measuring points were similar. When 6# and 7# action points were excited synchronously, the curve of No. 1 (67#-1 in Figure. 7) reached the first extreme value s₁=-0.001mm when t₁ = 12ms, the peak s₆ = 0.016mm when t₆ = 48ms, and the whole dynamic change of all measuring points were also similar. The extreme values of the amplitude curves of these two groups of action points showed two stages as follows: first increasing and then decreasing, and the vibration curves reached the peak after 2.25 cycles. The extreme points of amplitude curves of multi-point excitation (2# and 4#, 6# and 7#) and their corresponding time could be seen in Table.3.

Table 3

The extreme points of amplitude curves of two groups of action points (2# and 4#、6# and 7#).
Extreme value (mm) /Time (ms)	2# and 4#	6# and 7#
s₁/t₁	0.010/11	0.001/12
s₂/t₂	0.029/14	0.004/17
s₃/t₃	0.027/18	0.009/22
s₄/t₄	0.016/27	0.010/28
s₅/t₅	0.019/37	0.008/34
s₆/t₆	0.021/47	0.016/48
s₇/t₇	0.021/56	0.016/57
s₈/t₈	0.018/66	0.014/67
s₉/t₉	0.013/76	0.012/77
s₁₀/t₁₀	0.010/86	0.010/86
s₁₁/t₁₁	0.008/96	0.007/97
s₁₂/t₁₂	0.006/107	0.005/106

Amplitude attenuation law of interface vibration under impact load

Dynamic attenuation law of amplitude under single point excitation. The analysis results of the amplitude extreme value under single point excitation showed that the whole dynamic changes were similar; the extreme values distribution of the test curves when 6# action point was excited alone could be seen in Table. 4, and the curve-fitting results were shown in Figure. 8. It could be concluded that the dynamic attenuation of amplitude under single point excitation conformed to the law of exponential variation y = y₀ + Aexp(x/k), and the fitting degree was as high as 0.99.

Table 4

Amplitude extreme points of No.1-No.4 under 2# action point excitation.
Extreme point	Time /ms	No.1 /mm	Time /ms	No.2 /mm	Time /ms	No.3 /mm	Time /ms
T₁	61	0.014	61	0.014	60	0.014	61
T₂	70	0.013	70	0.012	70	0.013	70
T₃	80	0.011	80	0.01	80	0.011	80
T₄	90	0.008	90	0.008	90	0.008	90
T₅	99	0.006	99	0.006	99	0.006	99

Dynamic attenuation law of amplitude under multi-point excitation. The analysis results of the amplitude extreme value under multi-point excitation showed that the whole dynamic changes were similar; the extreme values distribution of the test curves when 6# and 7# action points were excited synchronously could be seen in Table. 5, and the curve-fitting results were shown in Figure. 9. It could be concluded that the dynamic attenuation of amplitude under single point excitation also conformed to the law of exponential variation y = y₀ + Aexp(x/k), and the fitting degree was as high as 0.99.

Table 5

Amplitude extreme points of No.1-No.4 under 6# and 7# action points excited synchronously.
Extreme point	Time /ms	No.1 /mm	Time /ms	No.2 /mm	Time /ms	No.3 /mm	Time /ms
T₁	57	0.016	56	0.016	57	0.016	57
T₂	67	0.014	67	0.014	66	0.015	67
T₃	77	0.012	77	0.012	77	0.012	76
T₄	86	0.01	86	0.01	86	0.01	87
T₅	97	0.007	97	0.007	96	0.008	96

Amplitude-frequency distribution of interface vibration under impact load

Amplitude-frequency distribution of interface vibration under single point excitation. The amplitude-frequency distributions when the 2#, 4# and 6# action points were excited separately were shown in Figure. 10-Figure. 12. When the 2# action point was excited, the amplitude of No. 1 (2#-1 in Figure. 10) reached the peak 7.2×10^-3mm at p₁ = 50Hz;when the 4# action point was excited, the amplitude of No. 1 (4#-1 in Figure. 11) reached the peak 7.5×10^-3mm at p₁ = 50Hz༛when the 6# action point was excited, the amplitude of No. 1 (6#-1 in Figu. 12) reached the peak 1.6×10^-3mm at p₁ = 53.7Hz༛the amplitude variations of No. 2 ~ No. 4 were all similar to that of No.1.

Amplitude-frequency distribution under multi-point excitation step-by-step. The amplitude-frequency distributions when 2# and 4# action points were excited step-by-step were shown in Figure. 13. The amplitude of No. 1 (24#-1 in Figure. 13) reached the peak 5.4×10^-3mm at p₁ = 52.1Hz, compared with single point excitation, the vibration complexity of multi-point excitation step-by-step was relatively high, and the amplitude variations of No. 2 ~ No. 4 were all similar to that of No.1.

Amplitude-frequency distribution under multi-point synchronous excitation. The amplitude-frequency distributions when 2# and 4# action points were excited synchronously were shown in Figure. 14. The amplitude of No. 1 (67#-1 in Figure. 14) reached the peak 5.1×10^-3mm at p₁ = 48.9Hz, the second peak 1.3×10^-3mm at p₂ = 92.4Hz, and the amplitude variations of No. 2 ~ No. 4 were all similar to that of No.1.

Effective vibration modes and predominant frequency of interface vibration under impact load. Based on Hilbert Huang transform (HHT), the interface vibration waveforms were decomposed by EEMD [20-23], combined with energy formula: , the energy distributions and marginal spectrum of the decomposed waveforms were obtained [24-25].

Under 2# action point excitation, the decomposition result of vibration waveform was shown in Figure. 15, which was decomposed into five vibration modes (IMF1~IMF5), and the residual res<10^-3 (Figure. 15a). The energy proportions of modes IMF1, IMF2 and IMF3 were relatively high (Figure. 15b), which were the effective vibration mode. Among them, the energy proportion of IMF2 was the highest, accounting for about 96% of the total energy, which was the main vibration mode. By analyzing the marginal spectrum of the original waveform and effective vibration modes (Figure. 15c and 15d), it could be concluded that the vibration frequency of the original waveform was mainly concentrated in P₁~P₃=39.9Hz~89.8Hz, and the predominant frequency corresponding to the peak was P₂=52.9Hz. The predominant frequencies of effective vibration modes (IMF1、IMF2 and IMF3) were P₄=236.8Hz、P₅=50.2Hz and P₆ = 35.9Hz respectively.

Under 4# action point excitation, the decomposition result of vibration waveform was shown in Figure. 16, which was decomposed into six vibration modes (IMF1 ~ IMF6), and the residual res < 10^− 3 (Figure. 16a). The energy proportions of modes IMF1, IMF2 and IMF3 were relatively high (Figure. 16b), which were the effective vibration mode. Among them, the energy proportion of IMF2 was the highest, accounting for about 95% of the total energy, which was the main vibration mode. By analyzing the marginal spectrum of the original waveform and effective vibration modes (Figure. 16c and 16d), it could be concluded that the vibration frequency of the original waveform was mainly concentrated in P₁ ~ P₃ = 38.9Hz ~ 108.8Hz, and the predominant frequency corresponding to the peak was P₂ = 50.4Hz. The predominant frequencies of effective vibration modes (IMF1、IMF2 and IMF3) were P₄ = 152.4Hz、P₅ = 49.2Hz and P₆ = 47Hz respectively.

Under 6# action point excitation, the decomposition result of vibration waveform was shown in Figure. 17, which was decomposed into six vibration modes (IMF1 ~ IMF6), and the residual res < 10^− 3 (Figure. 17a). The energy proportions of modes IMF1, IMF2 and IMF3 were relatively high (Figure. 17b), which were the effective vibration mode. Among them, the energy proportion of IMF2 was the highest, accounting for about 92% of the total energy, which was the main vibration mode. By analyzing the marginal spectrum of the original waveform and effective vibration modes (Figure. 17c and 17d), it could be concluded that the vibration frequency of the original waveform was mainly concentrated in P₁ ~ P₃ = 37.8Hz ~ 92.7Hz, and the predominant frequency corresponding to the peak was P₂ = 52.3Hz. The predominant frequencies of effective vibration modes (IMF1、IMF2 and IMF3) were P₄ = 91.3Hz、P₅ = 47.7Hz and P₆ = 47.7Hz respectively.

Under 2# and 4# action points excitation step-by-step, the decomposition result of vibration waveform was shown in Figure. 18, which was decomposed into seven vibration modes (IMF1 ~ IMF7), and the residual res < 10^− 4 (Figure. 18a). The energy proportions of modes IMF1, IMF2 and IMF3 were relatively high (Figure. 18b), which were the effective vibration mode. Among them, the energy proportion of IMF2 was the highest, accounting for about 86% of the total energy, which was the main vibration mode. By analyzing the marginal spectrum of the original waveform and effective vibration modes (Figure. 18c and 18d), it could be concluded that the vibration frequency of the original waveform was mainly concentrated in P₁ ~ P₃ = 37.5Hz ~ 99.9Hz, and the predominant frequency corresponding to the peak was P₂ = 49.4Hz. The predominant frequencies of effective vibration modes (IMF1、IMF2 and IMF3) were P₄ = 82.7Hz、P₅ = 48.6Hz and P₆ = 46.5Hz respectively.

Under 6# and 7# action points synchronous excitation, the decomposition result of vibration waveform was shown in Figure. 19, which was decomposed into six vibration modes (IMF1 ~ IMF6), and the residual res < 10^− 3 (Figure. 19a). The energy proportions of modes IMF1, IMF2 and IMF3 were relatively high (Figure. 18b), which were the effective vibration mode. Among them, the energy proportion of IMF2 was the highest, accounting for about 85% of the total energy, which was the main vibration mode. By analyzing the marginal spectrum of the original waveform and effective vibration modes (Figure. 19c and 19d), it could be concluded that the vibration frequency of the original waveform was mainly concentrated in P₁ ~ P₃ = 24.8Hz ~ 90.2Hz, and the predominant frequency corresponding to the peak was P₂ = 45.7Hz. The predominant frequencies of effective vibration modes (IMF1、IMF2 and IMF3) were P₄ = 201.3Hz、P₅ = 45.6Hz and P₆ = 47.4Hz respectively.

It could be seen that IMF1, IMF2 and IMF3 were effective vibration modes under single point excitation and multi-point excitation (synchronous/step-by-step). Among them, the energy of IMF2 accounted for the highest proportion (85%-94%), which was the main vibration mode, and its predominant frequencies were mostly concentrated in 45.6Hz ~ 50.2Hz. It could be concluded that IMF2 played a decisive role in the whole vibration process, so the predominant frequencies of coal-rock and rock-rock interfaces vibration under impact load were also concentrated in this range, and the vibration in this frequency range had an important effect on the dynamic response, damage and failure of coal and rock mass. Of course, in the actual conditions, the range of actual predominant frequencies could be obtained by converting according to the size and mechanical properties of coal and rock mass²⁶.

Under single and multi-point excitation (synchronous/step-by-step), the dynamic changes of amplitude curves of each interface vibration were obtained from the four sensors (No.1 ~ No.4) were similar, and the extreme value showed two stages as follows: first increase and then attenuation, most of which needed 2.25 cycles to reach the peak. The dynamic attenuation of amplitude conformed to the law of exponential variation y = y₀ + Aexp(x/k).

Based on FFT transform, the time-history curves of interface vibration under single point and multi-point excitation (synchronous/step-by-step) were analyzed, and the predominant frequencies distribution of amplitude were obtained. Among them, the two predominant frequencies were P₁ = 48.9Hz ~ 53.7Hz and P₂ = 92.4Hz.

The time-history curves of interface vibration under single point and multi-point excitation (synchronous/step-by-step) were decomposed by EEMD to obtain a total of 5 ~ 7 component modes (IMF), of which IMF1, IMF2 and IMF3 contained high energy and were effective vibration modes.

The energy of IMF2 accounted for the highest proportion (85%-94%), which was the main vibration mode, and its predominant frequencies were concentrated in 45.6Hz ~ 50.2Hz, which overlapped with that of the original waveform to a great extent. The vibration of IMF2 played a decisive role in the whole vibration process and had an important effect on the dynamic response, damage and failure of coal and rock mass. In the actual conditions, the range of actual predominant frequencies could be obtained by converting according to the size and mechanical properties of coal and rock mass.

EEMD Ensemble Empirical Mode Decomposition

FFT Fast Fourier transform

HHT Hilbert Huang transform

IMF Intrinsic Mode Functions

Data availability

The data presented in this paper is freely available from the corresponding author upon request.

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No competing interests reported.

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Vibration response of the interfaces in multi-layer combined coal and rock mass under impact load

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Experimental Design

Experimental Results

Amplitude variation of interface vibration under impact load

Conclusions

Abbreviations

Declarations

References

Additional Declarations

Status:

Version 1