Introduction

With the increase of depth and intensity, the rock burst damage range and intensity have been increasing significantly (Braeuner 1994; Dou et al. 2012; Jiang et al. 2014). Each year, rock bursts cause considerable economic loss and enormous casualties. For instance, on February 14, 2005, as the rock burst caused a serious gas explosion, 214 people were killed in Sunjiawan Coal Mine in Fuxin, Liaoning Province, China (Li et al. 2015).

Forecasting rock burst hazard regions is a prerequisite for rock burst control. Many traditional methods of evaluating rock burst hazard have been proposed, such as seismic energy and event correlations, velocity tomography, the aggregate index, and multifactor coupling (Dou et al. 2006; Dou et al. 2014; Eneva et al. 1998; Chen et al. 2012; Peng et al. 2002; Zhao et al. 2000). As micro seismic systems can accurately, and constantly, reflect the cracking, stresses in the coal and surrounding rock and geologic structures, they are widely used to assess rock burst hazard. Many scholars have verified the correlation between seismic events and stress. (Kracke and Heinrich 2004; Abdul-Wahed et al. 2006; Srinivasan et al. 1997; Driad-Lebeau et al. 2005). Since a power-law relationship is found between the P-wave velocity and stress, seismic velocity tomography based on a micro-seismic system has been used in various fields. It is confirmed that seismic hazard zones and high abutment stresses are combined not only with zones of high velocity values, but also with zones of high velocity gradient values. (Lurka 2005; Gong et al. 2012a, b).

Although micro-seismic methods have been proposed to assess rock burst hazard, there are no seismic data records where a coal seam has not been mined, and in that situation, we can only use the aggregate index and multi-factor coupling instead of micro-seismic methods. The aggregate index and multi-factor coupling methods are empirical; they consider many extrinsic factors related to rock bursts. For example, mining depth, the mechanical properties of both coal and rock masses, the structural features of both floor and roof, variations in coal seam thickness, faulting, geological structure, and overall disposition of the working faces (Bukowska 2006). Under the influence of the same extrinsic factors, such as faulting, the stress concentration coefficient of two faults may differ significantly. The concentration coefficient of one may be 2, however, that of the other may be 1, or even less. The rock burst hazard zones obtained by these empirical methods do not always match the cases seen in actual mines (Zhang et al. 2013). The aggregate index and multi-factor coupling based on the empirical analogy method suffer from this limitation and is subject to even bigger errors when it is used to rock burst hazard evaluation.

Aiming at multi seam mining, we used micro-seismic data to establish the energy density risk index (EDRI), and proved that the EDRI was more able to reflect the potential rock burst region more accurately than the multi-factor coupling analysis method. Then a rock burst hazard assessment method for use in multi-seam mining was established according to the experience analogy method. Eventually, we introduced the SSIM to quantify the effectiveness and practicability of this assessment method.

Evaluation method

The feasibility of evaluation

In the generation of rock structure, and mineral composition, rocks are changed under the actions of alteration and weathering, which lead to inhomogeneity in geologic media. Various structural planes, such as faults, are formed under the action of tectonic movement, which results in discontinuities in the rock. Some rock stress boundaries are relieved, and the other rock stresses are locked-in during geological evolution, which leads to differences in the stress distributions therein.

With the increase of rock mass size, the physical properties and mechanical properties of rock will become more complicated. The theoretical results usually show significant deviation from actual data and the empirical analogy method is more practical than theoretical calculation in geotechnical engineering practice.

The strata in this coal mine are almost all sedimentary rocks. The area of the coal seam covers several square kilometres or even several hundreds of square kilometres. Differences in the physical properties of the rocks and their surrounding environment are readily seen at such a large scale, and the accuracy of any empirical analogy is greatly reduced. Conversely, compared with the horizontal direction, the distance between the strata is small, and differences in the vertical direction are small. Therefore, it is reasonable to determine the rock burst hazard zone in the lower coal seam by using monitored data from the upper coal seam.

Establishment of evaluation method

(1) The energy density risk index

According to rock mechanics theory, a shock event is defined as a sudden inelastic deformation within a certain volume which causes detectable vibration waves (Cai et al. 2014). The energy released by each tremor is proportional to the square of the strain in the rock before the tremor, and the strain is directly proportional to the stress in the elastic stage. Therefore, strain energy could reflect the stress state before a tremor (Benioff 1951; Kracke and Heinrich 2004). Friedel et al. (1995, 1997) and Bańka and Jaworski (2010) proved that the energy released by tremors is positively correlated with stress, and the tremors are closely related to rock burst occurrence.

Seismic events were considered as point sources when calculating earthquake, tremor, or source locations (Frankel 1995; Frankel et al. 2000), which could not be directly reflected by the magnitude of the energy in a certain region. Here, the EDRI method was proposed to assess the tremor characteristics of a region.

The tremor energy E, which was obtained from the micro-seismic monitoring system, was used in (1) to obtain the energy per unit area. As the energy in a large tremor was thousands, or even millions, of times than that of a small tremor, differences among low-energy tremors were hard to resolve. By drawing lessons from the method of using the earthquake magnitude (M ∝ log10 E) to express to earthquake intensity in seismology, the energy index was used to represent the magnitude of the energy, which could be obtained by using (2). According to the theoretical analysis, laboratory experiments and a large number of field tests (Dou and He 2007), the risk level associated with a tremor was quantified into four grades (Table 1). Therefore, the EDRI, which was obtained by normalising formula (3), was divided into four grades. The EDRI varies from zero to one and was sub-divided into four categories: 0≤ EDRI <0.25, 0.25≤ EDRI <0.5, 0.5≤ EDRI <0.75, and 0.75≤ EDRI ≤1, respectively, indicating no risk, weak risk, moderate risk, and high risk. Consequently, the risk evaluation criterion for a rock burst is established (Table 1).

$$ {E}_i=\frac{\sum {E}_j}{A} $$
(1)
$$ {e}_i={ \log}_{10}\left({E}_i\right) $$
(2)
$$ {EDRI}_i=\frac{e_i-{e}_{\min }}{e_{\max }-{e}_{\min }} $$
(3)
Table 1 Relationship between the energy density risk index and rock burst risk
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Where E i is the energy value per unit area of the i th statistical region, ∑E j represents the total energy of the j th seismic event in the i th statistical region, and A is the area of the i th statistical region, m 2; e i is the energy index of the i th statistical region, log10(J), e max is the maximum value of all e i , e min is the minimum value of all e i , and EDRI i denotes the energy density risk index of the i th statistical region.

To reduce the range between the maximum and minimum values of the energy index, the average of the five biggest values was set to e max, and the average of the five minimum values was set toe min.

(2) Generation of the EDRI

To map the EDRI, the sketch map of the spatial, statistically smoothed model was established, as shown in Fig. 1. Seismic events belonging to each statistical region are selected to calculate the EDRI using Eqs. (1), (2), and (3), which are then considered as the value at its corresponding grid node. Finally, the EDRI map can be generated by interpolation. To avoid a lack of fidelity in the results induced by omitting individual seismic events, the relationship between the grid spacing S and the statistically smoothed radius R should satisfy: \( S\le \sqrt{2} R \) (Cai et al. 2015). The statistically smoothed radius R was determined by the hypocentre location error calculated by the numerical emulation method in the process of the statistical calculation (Gong et al. 2010). The map of hypocentre location errors is shown in Fig. 2: the hypocentre location error of the working face under investigation was less than 20 m. So, the statistically smoothed radius R of 20 m could be obtained, and grid spacing S was set to 28 m accordingly.

Fig. 1
figure 1

Sketch map of the spatial, statistically smoothed model: S is the grid spacing and R is the statistically smoothed radius such that \( S\le \sqrt{2} R \)

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Fig. 2
figure 2

The map of hypocentre location error

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The validity of the evaluation method

To quantify the effectiveness of the prediction method, we introduced structural similarity theory to calculate the similarity ratio between the predicted rock burst risk map and the actual rock burst risk map.

Under the assumption that human visual perception is highly adapted for extracting structural information from a scene, an alternative complementary framework is used for quality assessment based on the degradation of structural information. Structural similarity indexing is a specific example of this concept (Wang et al. 2004). Structural similarity index, which is a particular implementation of the philosophy of structural similarity, reflects the properties of object brightness, contrast, and structure. The index of structural similarity is defined (in (4)) as

$$ SSIM\left( X, Y\right)=\frac{\left(2{\mu}_x{\mu}_y+{C}_1\right)\left(2{\sigma}_{x y}+{C}_2\right)}{\left({\mu}_x^2+{\mu}_y^2+{C}_1\right)\left({\sigma}_x^2+{\sigma}_x^2+{C}_2\right)} $$
(4)

where μ x and μ y are the mean values of image signals X and Y, respectively, estimated as the signal luminance; σ x and σ y are the standard deviations, estimated as the signal contrast; σ xy is the covariance, estimated as the signal structure; C 1 = (K 1 L)2 and C 2 = (K 2 L)2, L is the dynamic range of the pixel values, K 1 = 0.01 and K 2 = 0.03 by default (Wang et al. 2004).

When the two images are the same, the value of the SSIM index is one (its maximum value): the larger the value of the SSIM index, the greater the consistency of the two images.

Case study

Site description

The Zhangshuanglou coal mine is located in the northwest of Jiangsu Province, China. The study area was chosen as the west district of the coal mine. Seams 7 and 9, whose seam dips are 25°, formed the main mineable coalbed. The strata between two seams comprise 3 m of mudstone and 20 m of sandstone. The working faces in this district are at depths ranging from 970 to 1100 m. Caving mining was adopted throughout this district, and the No. 7 seam mining is a priority for excavation compared to the No. 9 seam. The KJ20 microseismic system, which includes three groups of 3-component (Nos. 1, 2, and 3) probes and one group of 1-component probes (Nos. 4, 5, and 6), was installed by Xilin Ltd. on 6 April 2011. Before installation, LW7419, 421, 422, 423, and LW9419 had been mined. Fig. 3 shows the panel geometry and relative receiver locations.

Fig. 3
figure 3

Layout of the micro-seismic monitoring system in the western district. a Plane graph. b Profile 1–1′. c Profile 2–2′

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The critical energy of a rock burst

(1) The discriminating method of critical value

When analysing the Gurtenberg-Richter power-law for earthquake, rock burst, and acoustic emissions, Amitrano et al. (2012) reports are deviating from the power-law at high energies. The inflexion point of the power-law relationship is regarded as the dividing line denoting high-energy shock, which can be treated as a critical value for a rock burst. The Gurtenberg-Richter power-law equation is as follows:

$$ \lg N\left(\ge \lg E\right)= a- b \lg E $$
(5)

Where E is the energy of the shock; N(≥ lg E) is the number of shocks which are greater than, or equal to, E; and a and b are constant.

To identify the inflexion point of Gurtenberg-Richter power rate curve, the correlation coefficient is introduced here. According to the Gurtenberg-Richter power distribution equation, lgN and lgE are completely linearly correlated with a correlation coefficient R of 1 in theory. However, there is a certain deviation between lgN and lgE, which are not a complete linearly correlation in reality (see Fig.4).

Fig. 4
figure 4

lgE − R and lgE − lg N curves

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As the discreteness of tremors is large in the high-energy region, the correlation coefficient R decreases gradually with the increasing number of events for which the correlation coefficient R between lgN and lgE is calculated. After the energy fell below the inflexion point demarcating high- and low-energy tremors, the drift rate between lgN and lgE gradually decreased, which meant that the correlation coefficient R increased.

Therefore, the energy value corresponding to the minimum R can be used as the inflexion point demarcating high- and low-energy tremors. A tremor with an energy greater than the inflexion point are called The characteristic mining tremor. The characteristic mining tremor is statistically an abnormal shock, which is the critical energy required to induce a rock burst (Cai et al. 2014). The correlation coefficient is given by the following equation:

$$ {R}_i=\frac{\sum_{j= i-1}^n\left({x}_j-\overline{x}\right)\left({y}_j-\overline{y}\right)}{\sqrt{\sum_{j= i-1}^n{\left({x}_j-\overline{x}\right)}^2\sum_{j= i-1}^n{\left({y}_j-\overline{y}\right)}^2}} $$
(6)

Where i = 2 , 3 ,  ⋯  , n; R i is the correlation coefficient for lgE i in the Gurtenberg-Richter power-law curve; x is lgE i − 1 , lg E i  , lg E i + 1 ,  ⋯  , lg E n ; y was lgN i − 1 , lg N i  , lg N i + 1 ,  ⋯  , lg N n ; \( \overline{x} \) is the mean average of all x, and \( \overline{y} \) is the average value of all y.

When \( {R}_k= \min \left\{{R}_{\frac{n-1}{2}},{R}_{\frac{n+1}{2}},{R}_{\frac{n+3}{2}},{R}_k,\cdots, {R}_n\right\} \), the corresponding point (R k , lgE k ) is the inflexion point of the Gurtenberg-Richter power-law, and E k is the critical energy required to induce a rock burst.

According to micro-seismic data from Zhangshuanglou coal mine, we can plot lgE − R and lgE − lg N curves (Fig. 4). The shock energy corresponding to inflexion point of the Gurtenberg-Richter power-law was 105 J, therefore this was also the critical energy required to induce a rock burst.

(2) The energy of a rock burst

A rock burst is induced by the interaction of static and dynamic load regimes, and a large energy shock is needed to cause a rock burst (Dou et al. 2006). We could effectively forecast the potential risk zone associated with a rock burst by predicting the zone with high-energy shock risk. The micro-seismic monitoring system can record the waveform generated by rock mass fracture and record the energy and position of each high-energy shock. By using the seismic monitoring system, the data relating to rock bursts (since the coal mine was established) and the corresponding source energies of Zhang Shuanglou mine are listed in Table 2. The recorded energies inducing rock bursts all exceeded 1.0 × 105 J. The rock burst energy released on 30 July 2010 is unknown because the micro seismic monitoring system was not installed at that time. According to descriptions from site workers, the intensity and damage area exceeded any one rock burst occurring in Zhangshuanglou coal mine, so it was believed that the rock burst energy released on 30 July 2010 exceeded 1.0 × 105 J.

Table 2 The energy released by rock bursts in Zhangshuanglou coal mine
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According to the field observation results, it was concluded that only energies exceeding 1.0 × 105 J could induce a rock burst, which confirmed the conclusion obtained in the last section.

The EDRI method and the multi-factor coupling method

Correlation between the EDRI and rock burst hazard

Figure 5 was obtained by the monitoring of seismic events in the mining process of coal seams Nos. 7 and 9 (except for panels LW7419, 421, 423, 422, and LW9419). Symbols show positions of tremors with an intensity exceeding 105 J, and Ellipses delineate the damage area induced by each rock burst.

Fig. 5
figure 5

EDRI map. Four different colours were used to represent four risk grades of EDRI: the light blue zone (0 to 0.25), the blue zone (0.25 to 0.5), the green zone (0.5 to 0.75), and the red zone (0.75 to 1), respectively, representing no risk, weak risk, moderate risk, and high risk

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According to the monitoring results, there were 20 tremors with an intensity above 105 J in this district during the mining process, and 19 of them were located in the high-risk zone. Moreover, all the damage regions of the four rock bursts were located in the high-risk zone. From the statistical results, it was concluded that the high-risk zone of EDRI map could reasonably and effectively forecast the critical shock and the damage zone of each rock burst. This matched previous results, in which microseismic activity recorded during mining, could pinpoint zones of a risk of rock bursting (Senfaute et al. 2014).

Comparison with the multi-factor coupling method

The multi-factor coupling analysis method is based on the effect of those rock burst influencing factors in a coal mine, such as faulting, folding, coal pillars, coal seam roadway intersections, mergers, and roof lithologies. Firstly, different influencing factors are used to determine the rock burst hazard zones. Then, the final rock burst hazard map is obtained by the superposition of each rock burst hazard zone. Multi-factor coupling analysis has been widely used in coal mine burst risk assessment (Dou et al. 2006, PATYNSKA 2013). According to the mining conditions prevailing in the research area, we can obtain the overall rock burst hazard map (Fig. 6) by using the multi-factor coupling analysis method.

Fig. 6
figure 6

The rock burst hazard zone found using the multi-factor coupling analysis method

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As seen from Fig. 6, the critical shock and damage zone, of the rock burst, are located near the rock burst hazard zone, which suggested that the multi-factor coupling analysis method can be used to predict the hazard risk zone; however, compared to the EDRI, this method suffers from a large relative error. For example, there are damage areas induced by rock bursts occurring in region A, but that region was not a rock burst hazard zone according to the multi-factor coupling analysis method. There is no critical shock or damage in region A; however, region B was a rock burst hazard zone according to the multi-factor coupling analysis method.

Compared with the multi-factor coupling analysis method, the EDRI can more accurately reflect the rock burst risk.

Discussion of the validity of the evaluation method

Consistency between the evaluation data and critical tremors in the lower seam

As seen from Fig. 7, the map of EDRI, which was obtained by the monitoring of seismic events in the mining process of coal seam No. 7 (except for panel LW 7419, 421, 423, and 422), was used to predict the risk zone during the mining process of coal seam No. 9. Symbols show positions of critical tremors in the mining process of the No. 9 seam.

Fig. 7
figure 7

Comparison of prejudged danger areas and critical tremors inducing rock bursts in the No. 9 seam

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There were a total of 10 critical tremors inducing rock bursts seen in this district during the mining of the No. 9 seam, and all of them were located in the high-risk zone. We can conclude that the established EDRI map of the upper seam could effectively predict the position, and extent, of critical tremors inducing rock bursts in the lower coal seam.

Consistency between the evaluation data and the rock burst-damaged area in the lower seam

As seen from Fig. 8, the map of EDRI, which was obtained by the monitoring of seismic events in the mining process of coal seam No. 7 (except for panels LW7419, 421, 423, and 422), was used to predict the risk zone during the mining process of coal seam No. 9. Ellipses delineate the damage area induced by each rock burst in the mining process of the No. 9 seam.

Fig. 8
figure 8

Comparison of prejudged danger areas and the area damaged by rock bursts in seam No. 9

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There were four rock bursts during mining of seam No. 9, with three rock bursts (Nos. 2, 3, and 4) located in high-risk zones on the EDRI map, as seen in Fig. 8. Coal in the vicinity of the first damaged area was not extracted during mining of the No. 7 seam. In contrast, the area was extracted during mining of the No. 9 seam, which increased the abutment stresses therein and induced the first rock burst.

From the above analysis, the rock burst damaged area of the lower coal seam can be predicted through the proposed assessment method. However, consideration should be given to the different mining disturbances between the two coal seams—increased mining disturbance will increase the rock burst hazard.

Quantitative evaluation

As seen from Fig. 9 a1 and a2, the map of EDRI and high-risk zone of EDRI, which were obtained by the monitoring of seismic events in the mining process of coal seam No. 7 (except for panels LW7419, 421, 423, and 422), were called the predicted risk map; in Fig. 9 b1 and b2, the map of EDRI and high-risk zone of EDRI, which were obtained by the monitoring of seismic events in the mining process of coal seam No. 9 (except for panel LW9419), was called the actual risk map.

Fig. 9
figure 9figure 9

Rock burst risk maps. (a1) Plan view of the predicted rock burst hazard zone. (a2) Plan view of the predicted high-risk zone. (b1) Plan view of the actual rock burst hazard zone. (b2) Plan view of the actual high-risk zone

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From Fig. 9, the predicted high-risk zones are located in regions A and B, and the actual high-risk zones are also located therein. Almost all of the zones in LW9418, 420, 422, and 424 were non-high-risk according to predicted risk results—the actual risk results showed a similar trend.

To quantify the similarity, SSIM is introduced. To ensure the assessment accuracy of the SSIM index between the predicted rock burst risk map and actual rock burst risk map in the No. 9 seam, images were cropped to the same size, and the same colour should be selected in the same risk section, as shown in Fig. 9. Table 3 lists the values of SSIM between the predicted and actual risk maps.

Table 3 SSIM data
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The value of SSIM between the predicted, and actual, rock burst risk maps is 0.4726 (see Fig. 9 a1 and a2). However, the value of SSIM between the predicted high-risk zone and actual high-risk zone is 0.8581 (see Fig. 9 b1 and b2).

It was concluded that the established rock burst hazard assessment method can accurately forecast the extent and position of the high-risk zone.

Conclusion

  1. (1)

    According to the discriminating method of critical value and the field observation results, the critical energy required to induce a rock burst exceeded 1.0 × 105 J in each case, which confirmed the feasibility of the discriminating method of critical energy-induced rock burst prediction.

  2. (2)

    Through practical application, the EDRI can accurately reflect rock burst risk to a better extent than the multi-factor coupling analysis method.

  3. (3)

    All critical tremors induced rock bursts, and the damage zones induced by rock bursts in the lower coal seam were located in high-risk hazard zones, which were predicted by this rock burst hazard assessment method for use in multi-seam mining. The value of SSIM between the predicted high-risk zone and the actual high-risk zone is 0.8581, which indicates that the established rock burst hazard assessment method used in multi-seam mining can accurately forecast the extent and position of the high-risk zone.