Spatial and temporal microseismic evolution before rock burst in steeply dipping thick coal seams under alternating mining of adjacent coal seams

Abstract

Due to the complex geological conditions and special mining approach of the steeply dipping thick coal seam in the south mining area of the Wudong coal mine, dynamic hazards are frequently encountered during horizontal section top-coal caving. Identification of rock burst precursor information can help effectively avoid its occurrence, decrease unnecessary loss, and ensure personal safety of underground workers. The B3+6 coal seam working face of the south mining area of the Wudong coal mine at +475 m level and +450 m level is monitored using a microseismic (MS) monitoring system. The spatial and temporal evolution patterns of MS parameters before rock burst occurrence are investigated and compared with the evolution pattern of precursor characteristics in the gently inclined coal seam. The results show the following data: (1) The daily MS total energy and event count exhibited a sudden decrease and abnormal fluctuation before rock burst occurrence in the steeply dipping thick coal seam of the south mining area of the Wudong coal mine, which can be employed as an effective precursor signal for rock burst early warning. (2) The MS sources were mainly concentrated around the rock pillar, which created a high static stress condition for the occurrence of rock burst and served as the force source of rock burst. The rock pillar was also the main cause of rock burst in the B3+6 coal seam. (3) The MS event aggregation index is defined, which shows sudden fall and rise variation and reaches an extremely low value immediately before the rock burst occurrence. This phenomenon can be considered as a rock burst precursor in the steeply dipping thick coal seam of the south mining area of the Wudong coal mine. (4) For the steeply dipping thick coal seam, the sharp rise and fall of the daily MS average energy does not necessarily mean rock burst occurrence, while the abnormal fluctuation of the daily MS average energy is very likely the precursor of rock burst occurrence. (5) More attention should be paid to the floor (rock pillar) rather than the roof in the study of rock burst in the steeply dipping thick coal seam under similar conditions.

Appendices

Appendix 1

• (1) Lack of shock b value

Previous studies show that the relation between the magnitude and frequency of earthquakes induced by human mining activities (shock bump and rock burst) and natural earthquakes follow the G-R relational expression (Gutenberg and Richter 1994):

$$ \lg N\ \left(\ge M\right)=a- bM $$

(2)

where N is the cumulative number of earthquakes with magnitudes greater than M; the parameter a represents the seismicity; and the parameter b (b-value) is the slope of the log-linear relation for the level of seismic tectonic activity in the region.

The methods for calculating the b-value mainly include the linear least square method (LSQ) and the maximum likelihood method (MLM)(Aki 1965). To calculate the b-value, the MLM is generally used for spatial scanning of b-value, while the LSQ is commonly used for temporal scanning of b-value (Xia et al. 2010b). The smaller the b-value is, the higher the MS activity and the higher the risk of rock burst (Li et al. 2017).

LSQ:

$$ b=\frac{\sum \limits_{i=1}^m\ {M}_i\sum \limits_{i=1}^m\lg {N}_i-m\sum \limits_{i=1}^m\ {M}_i\lg {N}_i}{m\ \sum \limits_{i=1}^m{M}_i^2-{\left(\sum \limits_{i=1}^m Mi\right)}^2} $$

(3)

MLM:

$$ b=\frac{0.4343N}{\sum \limits_{i=1}^N\left({M}_i-M\right)} $$

(4)

where M₀ is the initial value, and N is the total number of MS events.

• (2) A(b) value and P(b) value

A(b) value is a quantitative parameter that describes the seismicity of each region. This parameter takes into account factors such as the seismicity, magnitude, and frequency of a region and can directly reflect whether the seismicity is “increasing” or “quiet” (Cai et al. 2018). This value can be calculated using the following formula:

$$ A(b)=\frac{1}{b}\lg \sum \limits_{i=1}^N{10}^{b{M}_i} $$

(5)

where b is the b-value of the region and M_i is the magnitude of the seismic event. As shown in the formula, A(b) is essentially the reduced magnitude of a set of seismic events, the main components of which are those with large magnitudes in the set. This value is related to the b-value of this set. The smaller the b-value is, the larger the A(b) value, and vice versa.

P(b) is defined as a small-earthquake dynamic parameter, which can comprehensively represent the combined effect of the frequency N and average magnitude(Xia et al. 2010a):

$$ P(b)=\frac{N}{b}\left(\lg \sum \limits_{i=1}^N{10}^{b{M}_i}-\lg N\right) $$

(6)

• (3) Z value

The average magnitude of MS event n_j in the local observation area is (Lu et al. 2015)

$$ \overline{n_j}=\frac{1}{k}\lg \sum \limits_{i=1}^k{n}_i $$

(7)

where n_i is the magnitude of each event. The Z value is defined as

$$ z=\frac{\overline{N}-\overline{n}}{\sqrt{\left({\sigma}_N^2/B\right)+\left({\sigma}_N^2/b\right)}} $$

(8)

where $\overline{N}$ is the average microseismic occurrence rate in the whole historical period of the selected area, that is, the number of microseisms per unit time, $\overline{n}$ is the average microseismic occurrence rate in a certain period of time, B and b are the number of $\overline{N}$ and $\overline{n}$ samples respectively, and σ_N and σ_n are their standard deviations , respectively.

Appendix 2

Let x₁, x₂, ··· x_i be independent n samples from continuous distribution f(x), then the probability density of any point x is estimated to be (Fukunaga and Hostetler 1975)

$$ \hat{f}(x)=\frac{1}{nh^d}\sum \limits_{i=1}^nK\left(\frac{x-{x}_i}{h}\right) $$

(9)

where h is the window width and K is the kernel function. K is a radial symmetric kernel function satisfying the following conditions

$$ K(x)={c}_k,{d}^k\left({\left\Vert x\right\Vert}^2\right)\kern0.5em \left\Vert x\right\Vert \le 1 $$

(10)

is an adaptive nonparametric estimator of x position density in feature space. The density is calculated in the user-defined size kernel of x point in the feature space, which can be described as (AbdAllah and Shimshoni 2014):

$$ \hat{f}(x)=\frac{c_k}{nh^d}\sum \limits_{i=1}^nK\left({\left\Vert \frac{x-{x}_i}{h}\right\Vert}^2\right) $$

(11)

where c_k is a constant, n is the number of data points, h is kernel size, k is the kernel, and d is the dimension in the feature space. In order to get the maximum position of probability density function, the gradient of density function needs to be estimated. The local maximum density is identified at $\nabla \hat{f}(x)=0$ by moving the kernel by gradient rising in the feature space.

In Eq. (11), take the shadow G(x) of kernel function K(x) (Cheng 1995), that is, there are corresponding contour functions g(x) = −k'(x) at the same time, and Eq. (11) becomes (Ai and Xiong 2016; Comaniciu and Meer 2002):

$$ \nabla \hat{f}=\frac{2{c}_k}{nh^{d+2}}\left[\sum \limits_{i=1}^ng\left({\left\Vert \frac{x-{x}_i}{h}\right\Vert}^2\right)\right]\left[\frac{\sum \limits_{i=1}^n{x}_ig\left({\left\Vert \frac{x-{x}_i}{h}\right\Vert}^2\right)}{\sum \limits_{i=1}^ng\left({\left\Vert \frac{x-{x}_i}{h}\right\Vert}^2\right)}-x\right] $$

(12)

The second term of Eq. (11) (Ai and Xiong 2016; Wu and Yang 2007):

$$ \mathrm{m}(x)=\left[\frac{\sum \limits_{i=1}^n{x}_ig\left({\left\Vert \frac{x-{x}_i}{h}\right\Vert}^2\right)}{\sum \limits_{i=1}^ng\left({\left\Vert \frac{x-{x}_i}{h}\right\Vert}^2\right)}-x\right] $$

(13)

is the mean shift vector where x is the mean estimate inside the kernel, and x_i is the element inside the kernel, g is the kernel, h is the kernel size. The mean shift vector m(x) defines how the kernel moves along the density gradient to the local maximum corresponding to the dense region in the feature space (Ai and Xiong 2016). If the distribution of data set x_i, i=1,…n conforms to the probability density function f(x), given an initial point x_i, the mean shift vector will move step by step and eventually converge to the local peak point.