Theoretical Study of Coupling Mechanism between FBG and Shock Waves of Rock Burst

Shiming Wei^1,2, Zesheng Zhang¹, Yao Wang¹

¹School of Energy Science and Engineering, Henan Polytechnic University, Jiaozuo, China.
²Collaborative Innovation Center of Coal Safety Production of Henan, Jiaozuo, China.

DOI: 10.4236/wjet.2020.84057                

Abstract

To achieve the monitor of rock burst in coal mine with fiber Bragg grating (FBG) sensing, the coupling mechanism between FBG and shock waves was theoretically analyzed. Based on Housner’s random shock model, the coupling mechanism between shock waves and FBG was theoretically analyzed. The result shows that the wave will change the period Ʌ and effective refractive index n of FBG, and further affect the initial wavelength value. The amplitude, phase and frequency of shock wave are directly related to the wavelength drifts of FBG. The transmitting velocity of shock wave in rock is affected by lithologic characteristics. The Elastic modulus, density and Poisson’s ratio of rock influence the initial wavelength value of FBG. This study provided a theoretical basis and practical application guidance for coal or rock burst monitoring with FBG sensing.

Keywords

Rock Burst, FBG, Shock Waves, Lithological Characteristics

1. Introduction

With mining depth of China increasing gradually, the occurrence rate of rock burst also increases [1] [2]. The study of mechanism and prevention of rock burst have always been the focus in the field of mining engineering [3] [4] [5] [6]. Rock burst is often accompanied with strong mine earthquake [7] [8] [9], which transmits in coal and rock in the form of seismic waves with random energy. The energy level of shock waves is closely related to the occurrence of rock burst, and the higher the level of waves energy is, the greater the possibility of rock burst is. Thus, it becomes an important means to monitor earthquake waves for rock burst warning [10] [11] [12]. The following methods are often used: micro seismic, acoustic emission, electromagnetic radiation, etc. Jiang Fuxing et al. [13] developed the explosion-proof microseismic positioning monitoring system and carried it out in field application, which proved its feasibility in coal mine. Pan Yishan et al. [14] developed a monitoring and positioning system with kilometer-scale for breaking mine earthquake and analyzed the location of mine earthquake by picking up the vibration wave signals. The monitor was consistent with the earthquakes, which provided bases for mine disaster relief and loss reduction. Xie et al. [15] monitored the parameters of rock burst through acoustic emission, and obtained that the spatial distribution of microseismic events had fractal characteristics. Li Yuanhui et al. [16] studied the variation of AE b and fractal dimension of spatial distribution under different stress levels in the process of rock fracture by acoustic emission, which improved the stability of stress monitoring of rock. Wang Enyuan et al. [17] [18] widely applied electromagnetic radiation technology in coal and rock dynamic disaster monitoring and early warning by studying electromagnetic radiation instrument. However, due to complex underground conditions, numerous large electrical equipments, serious electromagnetic interference, and the influence of water and gas, some of the above monitoring methods are invalid.

FBG is a kind of high-precision monitoring sensor sensing with wavelength drifts. Due to the merits of small size, anti-electromagnetic interference, corrosion resistance and so on, it has been widely used in many fields. Relevant researches show that the transmission process of shock waves after earthquake can be monitored by FBG. Peng Baojin et al. [19], based on tilted grating filter demodulation, studied a FBG microstrain sensing system, and the accuracy reached 0.009 με. Wu Jianhui et al. [20], based on FBG sensing, set up a monitoring system of seismic wave with sensitivity of 0.54 pm/ms². Because both earthquake and rock burst origin from sudden release of energy under high compressive stress concentration in rock, the shock waves generated are similar. Therefore, it is feasible to monitor rock burst of coal mine through FBG. Wang Jianda et al. [21] applied FBG sensing to underground coal mines, and developed early dynamic warning technology of rock burst as the early warning indexes of monitoring system of mining stress and stress gradient. Zhang Ningbo et al. [22] developed a multi-point stress and displacement monitoring system based on FBG sensing. Through experiments and engineering practice, the applicability of the system for rock burst in roadway was verified. Ginu Rajan et al. [23] adopted a high-frequency FBG testing system to monitor the high-frequency AE signals from stress-induced crack of rock samples with different shapes under compression load, and obtained the AE events consistent with the experiment, which revealed that high-frequency FBG can be used as a new technology for rock vibration monitoring. Gong H et al. [24] established a roof stability monitoring system in underground coal mine with FBG sensors, which verified the accuracy of FBG sensor in monitoring the strain of rock compression. Laudati et al. [25] designed a FBG triaxial acceleration sensor, and by measuring the axial deformation generated by dynamic acceleration of the fixture foundation, the lowest response frequency reached 0.1 Hz, providing a technical tool for underground microseismic monitoring.

In general, the study of rock burst monitoring with FBG sensing is still in development, and it is only achieved to receive the dynamic signal of rock burst. However, the research on mechanism of FBG sensing for rock burst, especially the transmission characteristics and influencing factors of shock waves in different rock are not involved.

In this paper, based on the transmission characteristics of shock waves and the sensing principle of FBG, the coupling mechanism between the waves and FBG was studied. The purpose of study is to realize the monitor of rock burst in coal mine with FBG sensing, and get the factors affecting the monitoring accuracy.

2. Mechanism of Lithologic Characteristics for Shock Wave Monitoring of Rock Burst with FBG Sensing

2.1. Coupling Mechanism between Shock Waves and FBG

According to Housner’s theory of random vibration [26], the ground motion was regarded as the superposition of randomly arriving pulses of a certain size:

$\alpha \left(t\right)={\displaystyle \underset{k=1}{\overset{N\left(t\right)}{\sum }}\eta \delta \left(t-t_k\right)}$ (1)

where $\eta$ is a constant, $N\left(t\right)$ is the total number of pulses arriving between [0, T], $t_k$ is the random time of pulse arrival.

R. H. Scanlan and K. Sachs proposed to use Fourier series to simulate ground motion time history [27]:

$\alpha \left(t\right)={\displaystyle \underset{k=1}{\overset{N\left(t\right)}{\sum }}{A}_k\cos \left({\omega }_{k}t-{\varphi }_k\right)}$ (2)

where $A_k$ is the amplitude spectrum value of the vibration time history; ${\varphi }_k$ is the phase spectrum value of the vibration time history; ${\omega }_k$ is the frequency.

The sensing principle of FBG was analyzed and deduced based on coupled mode theory. By solving the wave equation with Maxwell’s theory, the expression of wavelength of FBG was [28]:

${\lambda }_B=2\left(n_{eff}+\Delta n_{eff}\right)\Lambda$ (3)

where ${\lambda }_B$ is the FBG reflected center wavelength, $n_{eff}$ and Ʌ are the effective refractive index and grating period of the fiber core, respectively.

As shown in Figure 1, shock waves effect on FBG will change the period of the fiber core.

In combination with Equations (2) and (3), the changed refractive index period is [29]:

${\Lambda }^{\prime }=\Lambda \left[1+\gamma {\displaystyle \underset{k=1}{\overset{N\left(t\right)}{\sum }}{A}_k\cos \left({\omega }_{k}t-{\varphi }_k\right)}\right]$ (4)

where, $\gamma$ is the coupling coefficient of random shock wave coupled with FBG.

Figure 1. Coupling course between vibration shock wave and FBG.

From Equation (4), it can be obtained that when the random vibration wave is coupled with the fiber grating, the refractive index period of the original fiber grating will be redistributed.

Substitute ${\Lambda }^{\prime }$ into the central wavelength energy Formula (3):

${\lambda }_B=2\left(n_{eff}+\Delta n_{eff}\right){\Lambda }^{\prime }\approx 2n_{eff}\Lambda \left[1+\gamma {\displaystyle \underset{k=1}{\overset{N\left(t\right)}{\sum }}{A}_k\cos \left({\omega }_{k}t-{\varphi }_k\right)}\right]$ (5)

According to Equation (5), when shock waves of rock burst are monitored by the FBG sensor, the waves will be coupled with the FBG, and the initial wavelength of the FBG will be changed.

2.2. Analysis of Influence Mechanism of Lithologic Characteristics

According to Newton’s law and Hooke’s law, the rock generates volume and shape deformation under external forces. Two deformation spread in coal and rock by P and S wave. The movement direction of the P-wave is the same to the spreading direction, while the S-wave is perpendicular to the spreading direction.

The velocities $V_P$ of P-wave and $V_s$ of S-wave can be respectively expressed as following [30]:

$V_p=\sqrt{\frac{\lambda +2\mu }{\rho }}=\sqrt{\frac{E\left(1-\upsilon \right)}{\rho \left(1+\upsilon \right)\left(1-2\upsilon \right)}}$ (6)

$V_s=\sqrt{\frac{\mu }{\rho }}=\sqrt{\frac{E}{2\rho \left(1+\upsilon \right)}}$ (7)

where $\lambda$ and $\mu$ are Lamé Constants, E is the Elastic modulus, and υ is Poisson’s ratio. $\lambda =\frac{E\nu }{2\left(1+\nu \right)\left(1-2\nu \right)}$, $\mu =\frac{E}{2\left(1+\nu \right)}$.

When the vibration wave spreads, the relation between wavelength and wave velocity is expressed as following:

$V_k={\lambda }_k{\omega }_k$ (8)

where $V_k$ is wave speed, and ${\lambda }_k$ is wavelength.

By comprehensive analysis of waveguide and elastic-optic effect, sensitivity of FBG under uniform transverse stress is smaller than longitudinal [31]. However, the phase difference of shock waves makes the transverse stress on FBG not uniform, and this results in axial strain improvement of sensitivity. Moreover, the attenuation speed of P-wave is faster than S-wave, and the amplitude of S-wave is larger than P-wave. Therefore, only the influence of transverse wave on FBG is considerable. Put Equations (7) and (8) into (5), it can be gotten as following:

${\lambda }_B=2n_{eff}\Lambda \left[1+\gamma {\displaystyle \underset{k=1}{\overset{N\left(t\right)}{\sum }}{A}_k\cos \left(\sqrt{\frac{2E}{\rho \left(1+\upsilon \right)}}\frac{t}{2{\lambda }_k}-{\varphi }_k\right)}\right]$ (9)

In order to study the influence of lithology characteristics on FBG monitoring shock wave, one random shock wave was taken for analysis, it meant that assuming k = 1 in Equation (9). Assume ${\varphi }_k=0$, and then get:

${\lambda }_B=2n_{eff}\Lambda \left[1+\gamma A\cos \left(\sqrt{\frac{2E}{\rho \left(1+\upsilon \right)}}\frac{t}{2\lambda }\right)\right]$ (10)

According to Equation (10), when shock waves are monitored by FBG, the Elastic modulus, density, Poisson’s ratio and other parameters of rock will affect its initial wavelength. That also means that when shock waves with same parameters spreads in different rock, the wavelength drifts are different, and the influence is in the form of cosine, as shown in Figure 2.

3. Conclusions

According to the analysis of the coupling mechanism between FBG and shock waves, the factors influencing initial wavelength of FBG are obtained, and the conclusions are as follows:

• The shock wave has coupling effect with FBG which will change its grating period and effective refractive index, thus finally affecting its initial wavelength. The amplitude, phase and frequency of the shock wave will directly affect the wavelength of FBG.

Figure 2. Relationship between lithologic parameters of rock and initial wavelength of FBG.

• When shock waves with the same parameters in different rocks are monitored by FBG, the wavelength will be affected by the lithological characteristic parameter I, and has a cosine correlation with it. Therefore, as long as the rock mechanics parameters are obtained, the degree of influence of the lithological characteristics on the FBG monitoring can be obtained. This provides an important theoretical basis for coal or rock burst monitoring with FBG sensing, and can promote the application of optical test method for coal mine dynamic disaster.

Acknowledgements

This research was funded by National Natural Science Foundation of China (51674099).

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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