Introduction

Rock burst refers to the dynamic phenomenon of sudden and severe damage caused by the instantaneous release of elastic deformation energy in the coal and rock mass surrounding mine shafts or working faces. It is often accompanied by the ejection of coal and rock mass, loud noises, and air blasts, and is highly destructive, making it one of the major disasters in coal mining1,2,3,4. As the depth and intensity of coal mining increase, rock burst has become one of the main hazards faced by coal mining domestically and internationally5,6,7. During the excavation of mine workings and the retreat mining of workfaces, the original rock stress equilibrium state is disrupted, causing the internal stress of the coal and rock mass to redistribute to form a new stress equilibrium state. The force acting on the surrounding rock and support structures during mining activities is known as mining-induced stress. After mining, the stress state at each point in the original rock stress field will change. Thus, understanding accurately the evolution of the mining-induced stress field during the coal extraction process is crucial for evaluating and predicting dynamic disasters such as rock burst8,9,10.

Borehole stress monitoring is commonly used for monitoring mining-induced stress. The borehole stress principle monitoring involves installing pressure sensors, such as elastic elements, or hollow inclusion bodies, inside boreholes in the coal body. The borehole deformation caused the device case deformation and via sensors (e.g. vibrating wires, strain gauges). It is recalculated on stress value. This allows for the monitoring and forecasting of the risk of rock burst. The values of borehole stress are mainly read by digital manometers. The value of borehole stress consists of two main components, one is the artificial initial installation stress and the other is the coal body stress. Wei et al. proposed a method for setting critical early warning indicator values for coal seam stress monitoring to predict rock burst11. This method addressed the absence of differentiation among mines and laboratory theoretical basis in existing rock burst prediction through coal seam borehole stress monitoring. However, the method was unable to provide differentiated guidance for mines in conducting monitoring and early warnings. Lan et al. proposed a rock burst early warning method for coal mine retreat roadways12. This method applied the dynamic failure stress index (Cd) and the coal body impact failure stress index (Dd) to predict the risk of roadway rock burst. Chen et al. and Li et al. separately introduced different borehole stress sensor devices and monitoring methods, respectively13,14. Jiang et al. comprehensively summarized the key technology system of the rock burst monitoring and early warning system15. In addition, the “vibration field-stress dynamics” integrated monitoring and early warning system has been adequately applied in the field. Jiang et al. proposed a method of pressure measurement by sealing holes with polyurethane pre-injection and high-pressure grouting. It was successful in the field test at Baiyangling Coal Mine16. Petr Konicek et al. using borehole monitoring technology to measure stress at different mining stages, revealed that elastic deformation accounts for a significant proportion of total deformation. This indicates that coal seams are prone to rock burst17. Wang et al. using a steel strain gauge borehole stress meter at the 93–03 working face of Nantun Coal Mine, identified areas most likely to induce rock burst by monitoring stress values at different depths within the coal body18. Cao et al. demonstrated the real-time application of various borehole stress monitoring technologies for rock burst taking the 4401 working face of Yangquan Coal Mine. Importantly, he provided valuable theoretical and practical references for similar mining areas19. Tan et al. focusing on the characteristics of rock burst under the condition of hard roof, conducted in-depth research on its occurrence mechanism and early warning information through theoretical analysis and on-site borehole testing20. Rong et al. used microseismic monitoring, geosound monitoring, and mining-induced stress among other early warning methods, combined with effective prevention and control measures, achieved effective monitoring and prevention of rock burst, ensuring the safe production of the mine21. Zhao et al. and Lubomir Stas et al. independently developed a new type of long-term stress monitoring borehole deformation sensor for coal mine rocks, significantly improving monitoring accuracy22,23. Song et al., obtaining the stress distribution in the surrounding rock mass caused by mining activities during field stress monitoring working24. And then he proposed a model for predicting mining-induced rock burst. Zhan et al. introduced a novel predictive model for rock burst by utilizing amplitude, frequency of coal body vibrations, and the proportion of coarse to fine coal particles25. Certainly, he had conducted its verification through a borehole stress meter. The aforementioned studies have enriched the methods and means of borehole stress monitoring. However, they have only defined the risk assessment indicators and methods for using borehole stress in predicting rock burst, and have not proposed a method to determine the critical values of borehole stress warning indicators from a theoretical perspective. Accurately determining the warning indicators of borehole stress monitoring for rock burst is of significant importance for the prediction of rock burst26,27,28,29. Field research indicates that the critical values for borehole stress warning indicators across different mines are typically established through empirical or engineering analogy methods. This results in the inability to determine the critical values according to the unique geological and mining condition science of each mine due to the different regions’ critical values are uniform.

To address the issue of existing borehole stress warning indicators being determined by past experience and simple analogies without theoretical support. This paper proposes a theoretical calculation method for the critical values of borehole stress monitoring warning indicators for rock burst based on the theory of disturbance response instability. Taking into account the geological and mining conditions of coal mines, the paper further proposes a theoretical calculation formula for the critical values of warning indicators for borehole stress monitoring in rock burst that is more aligned with actual production taking into account the geological and mining conditions of coal mines. It provides theoretical guidance for the precise monitoring and targeted prevention of rock burst disasters.

Theoretical basis and indicators

Disturbance response instability theory

(1) Mechanical criterion of rock burst

For the deformation system of coal and rock mass, under the action of external load P, the characteristic depth of the plastic softening deformation zone is ρ and the characteristic displacement is u. u can be roof subsidence or roadway convergence displacement30,31. Assuming that the system is in equilibrium at some time, for a small disturbance ∆P of external load, or a small disturbance ∆p of roadway excavation, or a small disturbance ∆p of working face mining penetration, the plastic softening deformation area of coal and rock mass increases from ρ to ρ + ∆ρ. The displacement increases from u to u + ∆u. If the response ∆ρ or ∆u is bounded or finite, then the equilibrium state is stable. It means that for any given decimal ε >0, there always exists δ >0 such that when the perturbation ∆P or ∆p satisfies the condition:

$$\left| {\Delta P} \right| \le \delta \,\,or\,\,\left| {\Delta p} \right| \le \delta$$
(1)

The response ∆ρ or ∆u always satisfies the following inequality:

$$\left| {\Delta \rho } \right| \le \varepsilon \,or\,\left| {\Delta u} \right| \le \varepsilon$$
(2)

If the system is in unstable equilibrium, no matter how small the disturbance ∆P or ∆p is, it will result in an infinite increase in the plastic softening deformation region or characteristic displacement:

$$\frac{\Delta \rho }{{\Delta P}} = \frac{d\rho }{{dP}} = \infty$$
(3)

Or

$$\frac{\Delta u}{{\Delta P}} = \frac{du}{{dP}} = \infty$$
(4)

Or

$$\frac{\Delta \rho }{{\Delta p}} = \frac{d\rho }{{dp}} = \infty$$
(5)

Or

$$\frac{\Delta u}{{\Delta p}} = \frac{du}{{dp}} = \infty$$
(6)

The above are the criteria for determining extreme value points of disturbance response instability when rock burst occurs.

(2) The theoretical solution to rock burst occurrence

According to the mechanical model of roadway with rock burst in two zones as shown in Fig. 1, the radius of roadway a, the radius of plastic softening zone is ρ, and the supporting stress of roadway inner wall is ps, which is acted by ground stress P at a distance. The deformation damage stress–strain curve of coal rock is simplified as a bilinear model, where λ is the plastic softening modulus of coal rock and E is the elastic modulus of coal rock. The ratio of the softening modulus to the elastic modulus is defined as the coal rock impact propensity index K. Define the impact tendency index K = λ/E. For calculation, the failure of roadway surrounding rock adopts the Mohr–Coulomb yield failure criterion and regards it as the axisymmetric plane strain problem under hydrostatic pressure32,33.

Fig. 1
figure 1

Analysis model of roadway rock burst.

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Based on the elastic theory, the Mohr–Coulomb criterion is satisfied at the junction of the elastic and softening zones \(\sigma_{{\uptheta }}\left(\rho\right)=m\sigma_{{\text{r}}}(\rho)+\sigma_{{\text{c}}}\).Therefore, the radial stress and circumferential stress in the elastic region are:

$$\left\{ \begin{gathered} \sigma_{{\text{r}}} = P - \left( {\left. {P - \frac{{2P - \sigma_{{\text{c}}} }}{m + 1}} \right)\frac{{\rho^{2} }}{{r^{2} }}} \right. \hfill \\ \sigma_{{\uptheta }} = P + \left( {\left. {P - \frac{{2P - \sigma_{{\text{c}}} }}{m + 1}} \right)\frac{{\rho^{2} }}{{r^{2} }}} \right. \hfill \\ \end{gathered} \right.$$
(7)

Among, \(m = \frac{1 + \sin \varphi }{{1 - \sin \varphi }}\).

When the material is damaged in the plastic softening zone (a < r < ρ), the effective stress component is \(\tilde{\sigma }_{{\text{r}}} = \frac{{\sigma_{{\text{r}}} }}{1 - D}\),\(\tilde{\sigma }_{{\uptheta }} = \frac{{\sigma_{{\uptheta }} }}{1 - D}\).By replacing the stress in the Mohr–Coulomb yield criterion with the effective stress, we get \(\tilde{\sigma }_{{\uptheta }} = m\tilde{\sigma }_{{\text{r}}} + \sigma_{{\text{c}}}\):

$$\frac{{\sigma_{{\uptheta }} }}{1 - D} = m\frac{{\sigma_{{\text{r}}} }}{1 - D} + \sigma_{{\text{c}}}$$
(8)

In the softening zone, the equivalent strain in the softening zone is obtained from the geometric equation and the assumption of incompressibility of volume \(\overline{\varepsilon }\):

$$\overline{\varepsilon } = \frac{{\rho^{2} }}{{r^{2} }}\varepsilon_{{\text{c}}}$$
(9)

The damage evolution equation in the softening zone can be further obtained as follows:

$$D = \frac{\lambda }{E}\left( {\frac{{\rho^{2} }}{{r^{2} }} - 1} \right)$$
(10)

Regardless of the volume force, it is brought \(\sigma_{{\uptheta }} = m\sigma_{{\text{r}}} + \left( {1 - D} \right)\sigma_{{\text{c}}}\) into the equilibrium equation:

$$\frac{{{\text{d}}\sigma_{{\text{r}}} }}{{{\text{d}}r}} - \frac{{\sigma_{{\uptheta }} - \sigma_{{\text{r}}} }}{r} = 0$$
(11)

According to \(\sigma_{{\text{r}}}(a)=p_{{\text {s}}}\) the boundary conditions, the radial stress component in the softening region is:

$$\sigma_{{\text{r}}} = \left[ {p_{{\text{s}}} - \frac{{K\sigma_{{\text{c}}} }}{m + 1} + \left( {1 + K} \right)\frac{{\sigma_{{\text{c}}} }}{m - 1}} \right]\left( \frac{r}{a} \right)^{m - 1} + \frac{{K\sigma_{{\text{c}}} }}{m + 1}\frac{{\rho^{2} }}{{r^{2} }} - \left( {1 + K} \right)\frac{{\sigma_{{\text{c}}} }}{m - 1}$$
(12)

From the continuous condition of radial stress at r = ρ, the equation of roadway system in two zones is obtained:

$$\frac{P}{{\sigma_{{\text{c}}} }} = \frac{m + 1}{2}\left[ {\frac{{p_{{\text{s}}} }}{{\sigma_{{\text{c}}} }} + \left( {1 + K} \right)\frac{1}{m - 1}} \right]\left( {\frac{\rho }{a}} \right)^{m - 1} - \frac{K}{2}\left( {\frac{\rho }{a}} \right)^{m + 1} - \left( {1 + K} \right)\frac{1}{m + 1}$$
(13)

According to the instability criterion of disturbance response, \(\frac{\text{d}\rho}{\text{d}P}=\infty\), the critical softening zone radius ρcr when rock burst occurs is obtained:

$$\frac{{\rho_{{{\text{cr}}}} }}{a} = \sqrt {1 + \frac{1}{K} + \frac{1}{K}\left( {m - 1} \right)\frac{{p_{{\text{s}}} }}{{\sigma_{{\text{c}}} }}}$$
(14)

By substituting Eq. (14) back to Eq. (13), the critical load Pcr when rock burst occurs is obtained:

$$\frac{{P_{{\text{cr}}} }}{{\sigma_{{\text{c}}} }} = \frac{1}{m - 1}\left\{ {K\left[ {1 + \frac{1}{K} + \frac{1}{K}\left( {m - 1} \right)\frac{{p_{\text{s}}}}{{\sigma_{{\text{c}}} }}} \right]^{{\frac{m + 1}{2}}} - K - 1} \right\}$$
(15)

Generally, take the internal friction Angle of 30° and bring it into the above formula to obtain:

$$P_{{{\text{cr}}}} = \frac{{n\sigma_{{\text{c}}} }}{2}\left( {1 + \frac{1}{K}} \right)\left( {1 + \frac{{4p_{{\text{s}}} }}{{\sigma_{{\text{c}}} }}} \right)$$
(16)

In the equation, Pcr is the critical stress for rock burst in tunnels; n is a correction factor; σc is the strength of coal; ps is the strength of tunnel support.

Borehole stress monitoring is the near-field mining stress, so it is necessary to transform the far-field critical stress into the near-field critical stress Pmcr for impact development. Based on the theoretical deduction in research literature34, the following results can be obtained:

$$P_{{\text{mcr}}} = \left( {\frac{{3P_{{\text{cr}}} }}{2} + \frac{{\sigma_{{\text{c}}} }}{4}} \right)$$
(17)

In the equation, Pmcr is the near-field critical stress of roadway rock burst. Pcr is the far field critical stress of roadway impact.

Disturbance response instability theory underpins borehole stress indicators

The critical stress indicating rock burst in tunnels can be identified based on the Disturbance Response Instability Theory, with its magnitude reflecting the ease or difficulty of rock burst occurrences in the coal rock deformation system. The hazard level of rock burst are assessed and warned in mined coal rock in real time compared with the sum of real-time monitoring results of actual and mining-induced stresses in the surrounding rock of tunnels with the critical stress level for rock burst. The actual stress in surrounding rock typically does not change after excavation. Whereas mining-induced stress varies dynamically with the advancing mining face, and dynamic loads from roof fractures also modify this stress. In real field conditions, changes in mining-induced stress are fully captured by borehole stress meters. The critical values for borehole stress warning indicators are determined based on the difference between the critical stress for rock burst in tunnels and the actual post-excavation stress, as shown in Fig. 2.

Fig. 2
figure 2

Stress relationship diagram.

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Determination of critical value

The actual near-field stress P0 can be obtained by using the self-weight stress of overlying strata of coal seam and the stress concentration coefficient of in-situ coal seam mining:

$$P_{0} = k\gamma h$$
(18)

In the equation, k is the stress concentration coefficient; γ is the rock density; h is the buried depth of the roadway.

According to the near-field critical stress and actual stress caused by rock burst, the critical mining stress σ'cr of coal body caused by rock burst in roadway is calculated:

$$\sigma ^{\prime}_{{\text{cr}}} = P_{{{\text{mcr}}}} - P_{0}$$
(19)

Existing studies show that the borehole stress can basically reflect the change of mining stress. According to the critical mining stress σ'cr of coal body and the initial installation stress σ0 of the borehole stress meter, the critical value σcr of the borehole stress monitoring and warning index of coal seam with rock burst is calculated:

$$\sigma_{{\text{cr}}} = \sigma ^{\prime}_{{\text{cr}}} + \sigma_{0}$$
(20)

By combining formula (19), formula (18), formula (17) and formula (16), we can finally get:

$$\sigma_{{{\text{cr}}}} = \frac{{3n\sigma_{{\text{c}}} }}{4}\left( {1 + \frac{1}{K}} \right)\left( {1 + \frac{{4p_{{\text{s}}} }}{{\sigma_{{\text{c}}} }}} \right) + \frac{{\sigma_{{\text{c}}} }}{4} - k\gamma h + \sigma_{{0}}$$
(21)

The above formula indicates that the critical stress index for drilling holes relates to the correction factor n, which connects to the occurrence of dynamic pressure, the uniaxial compressive strength σc of the coal body, the impact tendency index K, the support strength ps of the roadway, the stress concentration factor k of the surrounding rock, the bulk density γ of the rock layers, the depth h of the roadway, and the initial installation stress σ0 of the borehole strain gauge. Among these, n can be determined by the actual occurrences of dynamic pressure in the mine. Parameters σc and K can be measured through tests on coal body mechanical properties. The value of ps can be calculated based on the support conditions of the roadway. The parameters K, γ, and h can be defined by the geological and mining conditions of the roadway. Finally, σ0 can be determined based on the initial installation conditions of the borehole strain gauge.

In summary, the calculation process for the critical indicators of coal seam drilling hole stress monitoring for dynamic pressure can be illustrated as shown in Fig. 3.

Fig. 3
figure 3

Calculation Process for Critical Indicators of Borehole Stress.

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Field practice

Study area

This document focuses on the 1100 working face of a mine in Shanxi, China, as shown in Fig. 4. To the north of the 1100 working face lies solid coal, while to the south are five main galleries of the West Wing mining area. The east is adjacent to the gob area of the 1101 working face, which retains a 30 m coal pillar, and solid coal bounds the west. The working face is situated at a depth ranging from 531 to 535 m. The coal seam is 6.2 m thick, directly overlaid by 6.2 m of sandy mudstone, serving as the immediate roof, and at 18.4 m depth, medium-grained sandstone acts as the main roof.

Fig. 4
figure 4

Layout of 1100 working face stress monitoring equipment.

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The working face is equipped with a borehole stress monitoring system and a microseismic monitoring system. The borehole stress monitoring system is the KJ24 roof monitoring system made in China, which consists of pressure sensors and display, the monitoring accuracy is 0.1 MPa, the measurement time is 5 min/times, and the pressure sensors are initially installed at a pressure of 3.5 ~ 5.5 MPa. The microseismic monitoring system is the ARAMIS M/E microseismic monitoring system made in Poland, which consists of a ground central station, a data logger, a data processing computer, a downhole vibration picker and a probe sensor. server, data processing computer, downhole vibration pickup and probe sensors. The sensitivity of the pickup is 120 V/(m × s) and the sensitivity of the probe is 90 V/(m × s). The effective distance to receive 100 J of microseismic energy is 1800 m for the pickup and 800 m for the probe. The positioning accuracy of this microseismic system for the ___location of the seismic source is ± 20 m for horizontal deviation and ± 50 m for vertical deviation.

In the intake roadway of the 1100 working face, researchers installed 11 sets of borehole stress meters. Each set was spaced 40 m apart. One set included a measurement point at a depth of 15 m, while another featured a 9-m shallow measurement point. This configuration mirrored the setup in the return airway, which also had 11 sets of borehole stress meters. Each borehole is marked as depicted in Fig. 4, with measurement point 005 situated 250 m from the heading. Micro-seismic probes T27 and T28 were deployed in the intake roadway of the 1100 working face, while the T26 probe and S4 micro-seismic receiver were positioned in the return airway. Furthermore, the S5 micro-seismic receiver was installed at a high extraction point within the 1100 working face. Collectively, these five probes effectively encapsulate the recovery area of the 1100 working face, yielding robust micro-seismic monitoring outcomes.

Borehole stress monitoring index critical value

Based on the test results of the coal and rock mechanics parameters, the uniaxial compressive strength of the coal body is 4.26 MPa, and the impact energy index is 1.57.

The formula for estimating the stresses in the roadway support is:

$$p_{{\text{s}}} = \frac{F}{A}$$
(22)

where, F is the support force of the minimum support unit, N; A is the support area corresponding to the minimum support unit, m2.

The support form adopted for the 1100 working roadway is the combined support of anchor rods and anchor cables, as shown in Fig. 6, and the specific support parameters are shown in Table 1.

Table 1 Supporting parameters of roadway.
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According to Eq. (22), the 1100 working roadway support stress is calculated as:

$$p_{{\text{s}}} = \frac{F}{A} = \frac{{\left( {0.4 \times 7 \times 180 + 0.6 \times 2.5 \times 450} \right){\text{N}}}}{{\left( {5.3 \times 0.9} \right){\text{m}}^{2} }} = 0.25{\text{MPa}}$$

where, 0.4 is the anchor support efficiency; 0.6 is the anchor cable support efficiency; 5.3 is the width of the roadway, m; and 0.9 is the row spacing of the anchor rods and anchor cables, m.

The modification coefficient n in Eq. (16) is determined to be 4.1 considering the geological and mining conditions associated with the occurrence of rock burst events in the mine. Meanwhile, we incorporated the modification coefficient, the near-field critical stress where rock burst occurs in roadways, the strength of the coal mass, the support strength of the roadway surrounding rock, and the coal mass’s propensity index for rock burst into Eq. (16). And next, we calculated the far-field critical stress is 17.52 MPa for the occurrence of rock burst in the 1100 working face roadways. Furthermore, the near-field critical stress for rock burst occurrence in this example of roadways is calculated to be 27.35 MPa using Eq. (17).

The 1100 working face tunnel is buried at a depth of 550 m, with an overlying rock unit weight of 25kN/m3. It is calculated that the stress concentration factor k due to tunnel excavation is about 1.3 through numerical simulation. Therefore, under the action of self-weight stress, the near-field actual stress after tunnel excavation is calculated to be 17.88 MPa according to Eq. (19). The critical mining-induced stress σ'cr for the occurrence of rock burst in the coal mass is 9.47 MPa according to Eq. (20). Since the initial installation pressure of the borehole stress measurement in the 1100 working face generally ranges from 3.5 to 5.5 MPa, the critical value of the borehole stress warning indicator is determined to be 12.97 to 14.97 MPa. A range of 12 to 14 MPa is adopted for safety.

For the 1100 working face, shallow borehole stress measurement points are located at 9 m and deep borehole stress measurement points at 15 m. The coal body at shallow measurement points experiences relatively lower confining pressure and has lower compressive strength, making it more susceptible to instability and failure. Conversely, the coal body at deep measurement points is subjected to higher confining pressure and has higher compressive strength, allowing it to withstand greater loads. Therefore, the stress warning value for shallow boreholes is set at 12 MPa, and for deep boreholes set at 14 MPa. Additionally, yellow and red stress warning threshold values are established for both shallow and deep measurement points, as shown in Table 2.

Table 2 Critical value table of borehole stress warning index.
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Field test and verification

The stress variation curve of the deep measurement point of borehole No. 005 in the coal wall of the belt roadway of the 1100 working face, from June 15, 2022, to July 13, 2022, as shown in Fig. 5. It can be observed that there were two warning signals in the stress curve. The first warning started around June 15, 2022, when the borehole stress measurement point was approximately 130 m from the working face, which is the initial stage affected by mining stress. As the working face retreated, the borehole stress gradually increased, reaching the warning value of 12 MPa on June 22, 2022. Afterward, the stress continued to rise, and following the release of pressure, the borehole stress decreased. On June 26, 2022, the stress at the deep measurement point of borehole No. 005 increased again, at this time 75 m from the working face. The borehole stress reached the warning value of 12 MPa, at this point 60 m from the working face on July 3. Subsequently, the stress continued to increase, being in the peak area of the advanced support pressure, and after the release of pressure, the borehole stress gradually decreased.

Fig. 5
figure 5

Stress change curve at stress measurement point of borehole 005# (2022.6.15 ~ 2022.7.13).

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Starting in May 2022, after advancing about 60 m from the 1100 working face, the tape conveyor gradually exhibited failures in support from the roof bolts and anchoring cables. This primarily manifested as broken and ejected bolts and cables, with nuts separating from trays. Since June, influenced by the 30 m coal pillar and the N1101 goaf area, significant deformations were observed within 100 m ahead of the working face, with the maximum floor heave reaching 1.2 m and the maximum rib bulging reaching 0.8 m. Specific situations of anchor bolt and cable failures and roadway deformation are shown in Fig. 6. April-august anchor bolt and cable failure began on May 8, 2022, as shown in Fig. 7. The damage were rarely existent between May 8 and July 6, 2022. The incidence of anchor bolt and cable failures began to increase, with the cumulative number curve initially rising slowly, then growing rapidly, and finally leveling off again starting from July 6. Notably, the number of failed anchor bolts and cables reached 31 on July 10. And anchor bolts and cables almost continuous occurrences of fault either daily or every few days. The monitoring indicators for borehole stress, derived from this study, issued a warning on July 3. This indicated the critical value for borehole stress warning based on the disturbance response instability theory can effectively predict high-stress environments in coal masses. The appearance of strong mining pressure in the roadway after the warning confirms the accuracy of the theoretical analysis of the borehole stress warning critical value. In other words, it applicable for monitoring and early warning of dynamic disasters in coal and rock, such as rock burst.

Fig. 6
figure 6

Failure of anchor bolts and cables and the deformation of the tunnel, (a) Normal support state of anchor bolts and cables, (b) Anchor bolt and cable failure status (c) The tunnel remains in a state of no significant deformation (d) State of significant deformation in tunnels.

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Fig. 7
figure 7

Change of the number of failure cables of the roof bolt with duct grooving on 1100 working face with time.

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The plane projection of partial microseismic energy events from June 12 to June 21, 2022, is shown in Fig. 8. Starting from June 12, the microseismic energy gradually increased in magnitude and number, progressively concentrating towards the stress monitoring point of borehole No. 005. The frequency and energy of microseismic events on that day increased significantly compared with the previous days by the plane of the microseismic energy event on June 19. From June 12 to June 21, the stress curve of the borehole No. 005 stress monitoring point showed a continuous upward trend, especially on June 19, when a significant spike occurred. Therefore, the concentration and migration of microseismic events are consistent with the increase in borehole stress measurements. The migration of these events towards the monitoring point No. 005 before reaching the critical warning value of borehole stress through analyzing from the distribution of microseismic events on June 22. This further confirms the accuracy of the critical warning value for borehole stress.

Fig. 8
figure 8

1100 projections of microseismic event planes at the working face (2022.6.12 ~ 2022.6.21). (a) 12th. June, (b) 14th. June, (c) 16th. June, (d) 17th. June, (e) 19th. June, (f) 20th. June.

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The planar projection of some microseismic energy events from June 26 to July 3, 2022, is illustrated in Fig. 9. Microseismic energy events were mainly concentrated near the working face from June 28 to June 30. Starting from July 1, these events began to gradually concentrate towards the borehole No. 005 stress monitoring point. From June 30, the microseismic energy events gradually transitioned from minor to major energy events, and concurrently, the increasing trend in borehole stress monitoring became more pronounced. Analyzing from the perspective of microseismic event distribution, before reaching the borehole stress warning critical value again on July 3, the microseismic events once more migrated towards the direction of monitoring point No. 005. This phenomenon further confirms the accuracy of the critical value for borehole stress warning.

Fig. 9
figure 9

1100 projections of microseismic event planes at the working face (2022.6.28 ~ 2022.7.3). (a) 28th. June, (b) 29th. June, (c) 30th. June, (d) 1st. July, (e) 2nd. July, (f) 3rd. July

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The statistical analysis of microseismic daily cumulative frequency and total energy during the two phases mentioned are shown in Figs. 10 and 11. The variation curves of both microseismic daily cumulative frequency and total energy display two rising phases, showing good consistency with the stress changes presented in Fig. 5. On June 25, 2022, the stress in borehole No. 005 once again increased, reaching a warning level of 12 MPa on July 3, and then continued to rise, peaking at 26.49 MPa on July 8, which falls within the peak pressure area for advanced support. The consistency between daily microseismic frequency, total energy, and stress changes were consistent during this period. When the borehole stress reached the warning value of 12 MPa on July 3, both the microseismic daily cumulative frequency and total energy reached the red warning levels. Therefore, the yellow warning value for deep borehole stress measurement points set on 12 MPa can verify the accuracy of the theoretical analysis results of the borehole stress warning indicator. This is more in line with the actual situation.

Fig. 10
figure 10

Daily cumulative microseismic frequency variation curve.

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Fig. 11
figure 11

Daily accumulated microseismic energy variation curve.

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Conclusions

  1. (1)

    When the sum of the stress in the coal seam roadway surrounding rock and the mining-induced stress exceeds the critical stress at which rock burst disasters occur, a rock burst disaster happens. The critical value for the borehole stress warning indicator can be theoretically calculated based on the critical stress for the occurrence of rock burst and the stress in the roadway surrounding rock.

  2. (2)

    The critical value of the borehole stress warning indicator for rock burst is related to the mechanical properties of the coal body, coal body impact susceptibility, support strength of the roadway, mining depth, concentration coefficient of mining-induced stress, and the initial installation pressure of the stress meter. This encompasses both geological factors and mining technical factors involved in the coal seam extraction process.

  3. (3)

    According to the theoretical formula for the critical value of the borehole stress warning indicator, the critical value for the shallow boreholes in the 1100 working face is set at 10 MPa, and for deep boreholes, it’s 12 MPa. During the coal seam mining process, when the monitored borehole stress exceeds these critical values, dynamic phenomena such as the breaking of anchor rods and cables in the roadway roof occur. Meanwhile, the micro-seismic monitoring indicators also reached the warning level.

  4. (4)

    This article proposes a method for determining the critical value of rock burst borehole stress warning indicators based on the disturbance response instability theory. This method, compared to traditional empirical or engineering analogy methods, takes into account geological and mining technological factors during the coal seam mining process, aligning more closely with actual mine production realities. However, further refinement and correction of the theoretical formula for the critical values are needed through extensive field applications.