To achieve the monitor of rock burst in coal mine with fiber Bragg grating (FBG) sensing, the coupling mechanism between FBG and shock waves w as 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.
With mining depth of China increasing gradually, the occurrence rate of rock burst also increases [
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. [
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.
According to Housner’s theory of random vibration [
α ( t ) = ∑ k = 1 N ( t ) η δ ( t − t k ) (1)
where η is a constant, N ( t ) 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 [
α ( t ) = ∑ k = 1 N ( t ) A k cos ( ω k t − ϕ k ) (2)
where A k is the amplitude spectrum value of the vibration time history; ϕ k is the phase spectrum value of the vibration time history; ω 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 [
λ B = 2 ( n e f f + Δ n e f f ) Λ (3)
where λ B is the FBG reflected center wavelength, n e f f and Ʌ are the effective refractive index and grating period of the fiber core, respectively.
As shown in
In combination with Equations (2) and (3), the changed refractive index period is [
Λ ′ = Λ [ 1 + γ ∑ k = 1 N ( t ) A k cos ( ω k t − ϕ k ) ] (4)
where, γ is the coupling coefficient of random shock wave coupled with 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 Λ ′ into the central wavelength energy Formula (3):
λ B = 2 ( n e f f + Δ n e f f ) Λ ′ ≈ 2 n e f f Λ [ 1 + γ ∑ k = 1 N ( t ) A k cos ( ω k t − ϕ k ) ] (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.
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 [
V p = λ + 2 μ ρ = E ( 1 − υ ) ρ ( 1 + υ ) ( 1 − 2 υ ) (6)
V s = μ ρ = E 2 ρ ( 1 + υ ) (7)
where λ and μ are Lamé Constants, E is the Elastic modulus, and υ is Poisson’s ratio. λ = E ν 2 ( 1 + ν ) ( 1 − 2 ν ) , μ = E 2 ( 1 + ν ) .
When the vibration wave spreads, the relation between wavelength and wave velocity is expressed as following:
V k = λ k ω k (8)
where V k is wave speed, and λ k is wavelength.
By comprehensive analysis of waveguide and elastic-optic effect, sensitivity of FBG under uniform transverse stress is smaller than longitudinal [
λ B = 2 n e f f Λ [ 1 + γ ∑ k = 1 N ( t ) A k cos ( 2 E ρ ( 1 + υ ) t 2 λ k − ϕ k ) ] (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 ϕ k = 0 , and then get:
λ B = 2 n e f f Λ [ 1 + γ A cos ( 2 E ρ ( 1 + υ ) t 2 λ ) ] (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
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.
• 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.
This research was funded by National Natural Science Foundation of China (51674099).
The authors declare no conflicts of interest regarding the publication of this paper.
Wei, S.M., Zhang, Z.S. and Wang, Y. (2020) Theoretical Study of Coupling Mechanism between FBG and Shock Waves of Rock Burst. World Journal of Engineering and Technology, 8, 784-791. https://doi.org/10.4236/wjet.2020.84057