Introduction

Rockburst is a dynamic phenomenon in which the unstable surrounding rock structure of underground roadways suddenly releases elastic deformation energy under external disturbances, leading to instability1,2,3,4. Characterized by high destructive intensity, rockbursts can cause damage ranging from several meters to hundreds of meters, posing significant challenges to the safe and efficient mining of many coal mines. As a result, rockburst has become a prominent research topic in the coal industry5,6,7. In rockburst monitoring, the drilling cuttings method is a widely used local monitoring and prediction technique. By analyzing variations in drilling cuttings quantity per unit depth and dynamic phenomena during drilling, the risk of rockburst can be assessed, enabling the prediction of rockburst events8,9,10,11,12. Typically, the drilling cuttings quantity is limited, with normal values generally not exceeding 6 kg/m13,14. However, with increasing mining depth and intensity, the actual drilling cuttings quantity in the field can far exceed normal levels, with drilling cuttings multiples reaching tens or even thousands, resulting in ultra-large drilling cuttings quantities of over one ton per meter. Intuitively, the phenomenon of ultra-large drilling cuttings quantity reflects the abnormal stress state of the coal and the instability of the drilling hole structure. What, then, is the specific mechanism behind the occurrence of ultra-large drilling cuttings quantity? Can it be used to assess the rockburst risk of roadways, i.e., what is the relationship between the ultra-large drilling cuttings quantity phenomenon and rockburst risk? It is necessary to investigate this phenomenon, especially as deep mining becomes more prevalent, where complex mining environments may make the ultra-large drilling cuttings quantity phenomenon more pronounced.

The key to studying the drilling cuttings method lies in establishing a more accurate relationship between the drilling cuttings quantity and coal stress. Many scholars have conducted in-depth research on this topic and achieved significant results. Pan Yishan15 established an elastic-plastic softening and dilatation model for coal, deriving an analytical expression for the drilling cuttings quantity. Wen Guangcai et al.16 developed a drilling cuttings quantity analysis model for gas-bearing coal seams, obtaining the relationship between drilling cuttings quantity around the borehole and factors such as borehole diameter, in-situ stress, coal strength, and gas pressure through numerical calculations. Cui Naixin17 considered the influence of gas on coal seams and micro-damage, deriving a formula for drilling cuttings quantity per unit depth in gas-bearing coal seams. Li Zhonghua18 proposed a drilling cuttings risk index formula for predicting rockburst in high-gas coal seams. Yin Guangzhi19 combined theories of longwall mining pressure and gas pressure distribution to analyze the relationship between drilling cuttings quantity, mining pressure, and gas pressure. Qu Xiaocheng20 conducted field tests and numerical simulations to establish the correspondence between borehole surrounding rock stress and drilling cuttings quantity. Yin Yongming et al.21 derived coal stress from the drilling cuttings quantity formula and established an evaluation index for drilling cuttings quantity. Tang Jupeng et al.22,23 introduced effective stress to account for horizontal in-situ stress in deep mining, resulting in a new drilling cuttings quantity formula. Recent theoretical research on drilling cuttings quantity has primarily focused on establishing relationships between drilling cuttings quantity and coal stress for conventional drilling cuttings quantities, with little attention paid to the phenomenon of ultra-large drilling cuttings quantity.

In fact, Cook24 discussed the phenomenon of ultra-large drilling cuttings quantity as early as the 1960s, providing a simple explanation for its occurrence conditions but without a clear definition or detailed analysis. This paper first defines the ultra-large drilling cuttings quantity phenomenon based on field observations. Building on previous theoretical research, a plastic strain softening model for coal seam drilling holes considering damage is established. Using the disturbance response instability theory, the initiation conditions, main influencing factors, and relationship with rockburst are explored, revealing the mechanism behind the ultra-large drilling cuttings quantity phenomenon and its role in rockburst monitoring.

Definition of ultra-large drilling cuttings quantity in coal seams

Drilling cuttings method

The drilling cuttings method is a localized prediction technique for rockburst that simultaneously detects multiple factors related to rockburst25,26. It involves using handheld electric drills or pneumatic drills with 1.0 m extension drill rods and typically a Φ42 mm drill bit to construct drilling holes perpendicular to the coal wall, extending beyond the peak stress zone of the coal wall, as shown in Fig. 1. The drilling cuttings quantity per meter of drilling depth is measured using either the weight method or the volume method. The weight method measures the weight of cuttings per meter (unit: kg/m), while the volume method measures the volume of cuttings per meter (unit: L/m). The measured drilling cuttings data are compared with standard indicators to assess rockburst risk. Additionally, dynamic phenomena such as drill jamming, noises, and blowouts during drilling are used to evaluate the risk of rockburst.

Fig. 1
figure 1

Schematic diagram of the working principle of drill cuttings.

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Drilling cuttings quantity

The drilling cuttings quantity consists of two parts: one is the volume of coal within the drill hole diameter that is not subjected to stress, and the other is the volume of coal generated due to deformation under stress. In rockburst monitoring and early warning, the normal drilling cuttings quantity refers to the quantity measured in areas unaffected by mining activities or geological structures. Typically, the normal drilling cuttings quantity is small, generally not exceeding 6 kg/m.

Ultra-large drilling cuttings quantity

Based on field statistics, this paper defines the phenomenon of ultra-large drilling cuttings quantity as occurring when the actual drilling cuttings quantity is ten times or more than the normal value. Although research on this phenomenon is limited, it is not uncommon in coal mining sites. Literature and field investigations have revealed that this phenomenon has occurred in several coal mines, such as Zhangshuanglou Coal Mine, Pingmei No. 8 Mine, Pingmei No.12 Mine, Hegang Xingshan Mine, a mine in Kailuan, and a mine in Tuokexun, Xinjian.

Case study: ultra-large drilling cuttings quantity in Zhangshuanglou coal mine

Detailed records of the ultra-large drilling cuttings quantity phenomenon are scarce, partly because it has not yet garnered sufficient attention from field personnel and researchers. Often, this phenomenon is simply attributed to excessive drilling cuttings caused by high stress or hole collapse. Below, the ultra-large drilling cuttings quantity phenomenon in Zhangshuanglou Coal Mine is analyzed as a case study.

Overview of Zhangshuanglou coal mine

Zhangshuanglou Coal Mine, operated by Xuzhou Mining Group, has a long mining history and complex production conditions. The main coal seams mined are the No. 7 and No. 9 seams, which have been identified as having a strong propensity for rockburst. The mine has experienced multiple rockburst incidents, including a significant event on July 30, 2010, at 3:15 AM, in the − 1200 m east mining area, which resulted in 6 fatalities, multiple injuries, and substantial economic losses. The 7123 working face, located only 80 m vertically from the site of the “7.30” incident, exhibited the ultra-large drilling cuttings quantity phenomenon multiple times during mining.

Drilling hole layout at the 7123 working face

The 7123 working face is located in the east mining area and features a monocline structure with a dip angle of approximately 22°. The mining depth ranges from 931.7 m to 961.7 m, with a coal seam thickness of 4.05 m. The immediate roof consists of 8 m of mudstone or sandy mudstone, while the main roof is 3.25 m of medium-fine sandstone. The immediate floor is 3.48 m of gray-black mudstone, and the main floor is 26.62 m of fine sandstone. Drilling measurement points were arranged along the mining side of the 7123 working face material roadway. Within a 90 m advance range of the working face, drilling holes were spaced every 15 m, with a drill bit diameter of 42 mm and a hole depth of 10 m, drilled perpendicular to the roadway side.

Ultra-large drilling cuttings quantity phenomenon

The 7123 working face material roadway recorded 42 instances of drilling cuttings quantities exceeding normal values within an 80 m advance range. These occurrences were mostly observed at depths of 6 ~ 10 m. Typically, the drilling cuttings quantity was normal for the first 7 m, but at the 8 m mark, the quantity suddenly increased dramatically, accompanied by large coal particles, noises, vibrations, and other dynamic phenomena. Beyond 10 m, the drilling cuttings quantity returned to normal.

Drilling holes 16#, 17#, 18#, 20#, and 21# were drilled sequentially along the upper side of the 7123 working face material roadway, starting 1350 m from the open-off cut. During drilling, the drilling cuttings quantity exceeded normal values multiple times, as shown in Fig. 2. From Fig. 2, it can be seen that the drilling cuttings quantities for holes 16#, 17#, 18#, 20#, and 21# at depths of 8 ~ 10 m were more than 10 times the normal value. Notably, the drilling cuttings quantity for hole 17# reached 180 kg, approximately 57 times the normal value. Additionally, during the monitoring period, a drilling hole 20 m ahead of the working face recorded a drilling cuttings quantity of 1027 kg at 8 m depth, about 473 times the normal value. Another hole 59 m ahead of the working face recorded 1548 kg at 8 m depth, approximately 713 times the normal value. These are typical examples of the ultra-large drilling cuttings quantity phenomenon.

Fig. 2
figure 2

Measure drilling cuttings of 16#, 17#, 18#, 20# and 21# in the Material Haulageway 7123.

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Characteristics of ultra-large drilling cuttings quantity

General patterns of ultra-large drilling cuttings quantity

Based on literature and field data analysis, the ultra-large drilling cuttings quantity phenomenon occurs under various hardness conditions. For example, it has been observed in both soft coal seams (e.g., a mine in Shenyang) and hard coal seams (e.g., Zhangshuanglou Coal Mine). It has also been reported in both deep and shallow mining operations. For instance, Zhangshuanglou Coal Mine first observed this phenomenon at -990 m, while a mine in Xinjiang recorded it at around − 350 m. Within the same mine, the phenomenon is more likely to occur in deeper mining areas. In the same drilling hole, the phenomenon typically occurs near the peak abutment pressure zone. For example, at the 7123 working face of Zhangshuanglou Coal Mine, the phenomenon was frequently observed at around 8 m depth (near the peak abutment pressure). The occurrence of ultra-large drilling cuttings quantity is often accompanied by dynamic phenomena such as noises, drill jamming, drill suction, and large coal particles.

Differences between ultra-large drilling cuttings quantity, hole collapse, and blowout

The drilling hole and its surrounding rock in coal seams form a deformable structure with stability issues. Under stable conditions, the hole wall remains intact, and the drilling cuttings quantity consists of the coal volume within the hole diameter and the volume generated by hole deformation, varying regularly with coal stress. However, when the coal stress reaches a critical value, the surrounding rock of the drilling hole transitions from a shallow plastic zone to a deep elastic zone, becoming unstable. Under disturbances such as drilling and rotation, the deformable structure of the hole and its surrounding rock becomes unstable, causing the plastic zone to expand continuously. The coal in the plastic zone flows into the roadway, resulting in a drilling hole impact phenomenon similar to roadway rockburst. This leads to a sudden, irregular increase in drilling cuttings quantity, i.e., the ultra-large drilling cuttings quantity phenomenon. Therefore, ultra-large drilling cuttings quantity can be regarded as the result of drilling hole impact, caused by stress and disturbances, and is characterized by suddenness.In contrast, hole collapse, similar to roadway roof fall, occurs when the surrounding coal undergoes shear failure, developing fractures that collapse under gravity, representing a progressive failure27. Blowouts, typically occurring in high-gas coal seams, are similar to coal and gas outbursts. They involve the ejection of broken coal from the hole under the combined action of gas pressure and stress, exhibiting distinct gas-related characteristics. Thus, the mechanisms behind ultra-large drilling cuttings quantity, hole collapse, and blowouts differ, leading to different increments in drilling cuttings quantity. Figure 3 illustrates the mechanisms of ultra-large drilling cuttings quantity, hole collapse, and blowout.

Fig. 3
figure 3

Schematic diagram of the mechanism of the ultra-large drilling cuttings quantity, hole collapse, and drilling blowout occurrence.

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Theoretical analysis of ultra-large drilling cuttings quantity phenomenon

Plastic strain softening model for coal seam drilling holes

Assuming the coal wall in front of the drilling hole is a homogeneous, isotropic elastic body, the failure of the surrounding coal follows the Mohr-Coulomb yield criterion, and gravity is neglected, the problem can be treated as an axisymmetric plane strain under hydrostatic pressure. The drilling hole radius is denoted as a, the far-field stress as P, and the radius of the plastic zone as ρ. Outside the plastic zone lies the elastic zone, as shown in Fig. 4. To derive the initiation conditions for the ultra-large drilling cuttings quantity phenomenon, the constitutive relationship of coal deformation and failure is simplified as bilinear. Before peak strength, the deformation is linearly elastic with an elastic modulus E, and the peak strength corresponds to the uniaxial compressive strength σc and strain εc. After peak strength, the strain softening stage is simplified as a linear decline with an absolute slope equal to the softening modulus, as shown in Fig. 5.

Fig. 4
figure 4

Mechanical analysis model of drilling cuttings hole.

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Fig. 5
figure 5

Stress-strain relation of coal.

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The constitutive equation established based on Fig. 5 is as follows:

$$\sigma =\left\{ \begin{gathered} E\varepsilon \begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {}&{} \end{array}}&{}&{\begin{array}{*{20}{c}} {}&{(\varepsilon \leqslant {\varepsilon _c})} \end{array}} \end{array} \hfill \\ {\sigma _c} - \lambda (\varepsilon - {\varepsilon _c})\begin{array}{*{20}{c}} {}&{(\varepsilon >{\varepsilon _c})} \end{array} \hfill \\ \end{gathered} \right.$$
(1)

The equilibrium equation is as follows:

$$\frac{{d{\sigma _r}}}{{dr}}+\frac{{{\sigma _r} - {\sigma _\theta }}}{r}=0$$
(2)

In the equation, σr and σθ represent the radial stress and tangential stress, respectively;

The geometric equation is as follows:

$${\varepsilon _r}=\frac{{du}}{{dr}},{\varepsilon _\theta }\frac{u}{r}$$
(3)

In the plastic zone near the wall of the drilling cuttings hole, it is assumed that the volume of coal is incompressible. For the plane strain problem, the following holds:

$${\varepsilon _r}+{\varepsilon _\theta }=0$$
(4)

Substituting Eq. (3) into Eq. (4) yields:

$$u=\frac{B}{r}$$
(5)

Where B is the integration constant. Given the radial displacement at the borehole boundary r = a as ua, we have:

$${\varepsilon _r}= - \frac{{{u_a}a}}{{{r^2}}},{\varepsilon _\theta }=\frac{{{u_a}a}}{{{r^2}}}$$
(6)

Based on the equivalent strain formula:

$$\overline {\varepsilon } =\sqrt {\frac{2}{9}\left[ {{{\left( {{\varepsilon _1} - {\varepsilon _2}} \right)}^2}+{{\left( {{\varepsilon _2} - {\varepsilon _3}} \right)}^2}+{{\left( {{\varepsilon _3} - {\varepsilon _1}} \right)}^2}} \right]}$$
(7)

The effective strain in the plastic zone can be obtained as:

$$\bar {\varepsilon }=\frac{{2{u_a}a}}{{\sqrt 3 {r^2}}}$$
(8)

From the condition \(\bar {\varepsilon }\left( \rho \right)={\varepsilon _c}\), the contraction displacement of the borehole wall is derived as:

$${u_a}=\frac{{\sqrt 3 }}{2}\frac{{{\varepsilon _c}{\rho ^2}}}{a}$$
(9)

According to the analysis of the source of drilling cuttings in Sect. 1.2, combined with Eq. (9) and the expression for drilling cuttings quantity, the total drilling cuttings quantity \({M_0}\)per unit depth can be obtained as:

$${M_0}=\gamma \left( {\pi {a^2}+2\pi a{u_a}} \right)=\gamma \left( {\pi {a^2}+\sqrt 3 \pi {\varepsilon _c}{\rho ^2}} \right)$$
(10)

where γ is the unit weight of coal.

Let the stresses at the interface between the elastic and plastic zones be σr and σθ, then:

$$\left\{ \begin{gathered} {\sigma _r}{\text{=}}\frac{{{\rho ^2}}}{{{r^2}}}\sigma _{r}^{P}+\left( {1 - \frac{{{\rho ^2}}}{{{r^2}}}} \right)P \hfill \\ {\sigma _\theta }{\text{=-}}\frac{{{\rho ^2}}}{{{r^2}}}\sigma _{r}^{P}+\left( {1+\frac{{{\rho ^2}}}{{{r^2}}}} \right)P \hfill \\ \end{gathered} \right.$$
(11)

At the interface between the elastic and plastic zones, the coal is in the initial yield state. Using the Coulomb yield criterion:

$${\sigma _\theta }{\text{=}}m{\sigma _r}+{\sigma _c}$$
(12)

Where \(m{\text{=}}\frac{{1{\text{+}}\sin \varphi }}{{1 - \sin \varphi }}\),and ϕ is the internal friction angle.

Assuming that damage evolution occurs in the softening zone, the damage variable D is linearly related to the equivalent strain \(\bar {\varepsilon }\), i.e.,\(D={D_1}+{D_2}\bar {\varepsilon }\). When \(\bar {\varepsilon }={\varepsilon _c}\),\(\bar {\sigma }={\sigma _c}\),\(D=0\) ; when \(\bar {\varepsilon }={\varepsilon _u}\),\(\bar {\sigma }=0\), where \(D={D_{cr}}\) is the critical damage value. Thus, we have:

$$D=\frac{\lambda }{{{\sigma _c}}}\left( {\bar {\varepsilon } - {\varepsilon _c}} \right)$$
(13)

Replacing the stress in Eq. (12) with effective stress:

$$\frac{{{\sigma _\theta }}}{{1 - D}}=m\frac{{{\sigma _r}}}{{1 - D}}+{\sigma _c}$$
(14)

Neglecting body forces, the equilibrium equation and yield condition in the plastic zone satisfy:

$$\frac{{d{\sigma _r}}}{{dr}} - \left( {m - 1} \right)\frac{{{\sigma _r}}}{r}=\frac{{{\sigma _c}+\lambda {\varepsilon _c}}}{r} - \frac{{\lambda {\varepsilon _c}}}{{{r^3}}}{\rho ^3}$$
(15)

Solving this yields:

$${\sigma _r}{\text{=}}R{r^{m - 1}}+\frac{{\lambda {\varepsilon _c}}}{{m+1}}\frac{{{\rho ^2}}}{{{r^2}}} - \frac{{{\sigma _c}+\lambda {\varepsilon _c}}}{{m - 1}}$$
(16)

where R is the integration constant.

Combining Eq. (16) with the boundary conditions \({\sigma _r}\left( \rho \right)=\frac{{2P - {\sigma _c}}}{{1+m}}\) and \({\sigma _r}\left( a \right)=0\) we obtain:

$$\frac{{{\rho ^{m - 1}}}}{{{a^{m - 1}}}}\frac{{{\sigma _c}+\lambda {\varepsilon _c}}}{{m - 1}} - \frac{{\lambda {\varepsilon _c}}}{{m+1}}\frac{{{\rho ^{m+1}}}}{{{a^{m+1}}}}=\frac{{2P - {\sigma _c}{\text{-}}\lambda {\varepsilon _c}}}{{m+1}}+\frac{{{\sigma _c}+\lambda {\varepsilon _c}}}{{m - 1}}$$
(17)

Initiation conditions for the ultra-large drilling cuttings quantity phenomenon

The occurrence of the ultra-large drilling cuttings quantity phenomenon depends on whether the deformation structure of the surrounding rock of the drilling hole is stable. When disturbances such as roadway excavation, working face advancement, blasting, drill rod rotation, and advancement occur near the drilling hole, the deformation structure of the surrounding rock will inevitably be affected. If the deformation of the drilling hole caused by any disturbance is limited, the deformation structure of the surrounding rock remains stable. However, if the deformation structure becomes uncontrollable under any disturbance, the deformation structure of the surrounding rock is in an unstable state28.

For a drilling hole in equilibrium under the action of coal stress P, the drilling cuttings quantity is\({M_0}\). If a minor disturbance\(\Delta P\)to the coal stress P increases the drilling cuttings quantity from \({M_0}\) to\({M_0}{\text{+}}\Delta {M_0}\), and the response \({M_0}\)is finite, the equilibrium state of the coal wall is stable. The system simply transitions to a new equilibrium state after the disturbance. That is, for any given small number \(\varepsilon >0\), there exists a\(\delta >0\), such that when the disturbance \(\Delta P\) satisfies \(\left| {\Delta P} \right| \leqslant \delta\), the response \(\Delta {M_0}\) satisfies the inequality:

$$\left| {\Delta {M_0}} \right| \leqslant \varepsilon$$
(18)

If the coal wall of the drilling hole is in an unstable equilibrium state, no matter how small the disturbance\(\Delta P\), it will lead to an infinite increase in the drilling cuttings quantity\(\Delta {M_0}\), i.e.,

$$\frac{{\Delta {M_0}}}{{\Delta P}}=\frac{{d{M_0}}}{{dP}}=\infty$$
(19)

Equation (19) represents the initiation condition for the ultra-large drilling cuttings quantity under the disturbance response instability theory.

From the stress continuity condition at the interface between the elastic and plastic zones (r=ρ), we obtain:

$$\frac{P}{{{\sigma _c}}}=\frac{{m+1}}{{2\left( {m - 1} \right)}}\left( {1+\frac{\lambda }{E}} \right){\left( {\frac{\rho }{a}} \right)^{m - 1}} - \frac{\lambda }{{2E}}{\left( {\frac{\rho }{a}} \right)^{m+1}} - \left( {1+\frac{\lambda }{E}} \right)\frac{1}{{m - 1}}$$
(20)
$$\frac{P}{{{\sigma _c}}}=\left( {1+\frac{\lambda }{E}} \right){\left( {\frac{P}{a}} \right)^2} - \frac{\lambda }{{2E}}{\left( {\frac{P}{a}} \right)^4} - \frac{1}{2}\left( {1+\frac{\lambda }{E}} \right)$$
(21)

The solution is:

$${\rho ^2}={a^2}{\frac{{1+\frac{\lambda }{E} \pm \left[ {\left( {1+\frac{\lambda }{E}} \right) - \frac{{2\lambda P}}{{E{\sigma _c}}}} \right]}}{{\frac{\lambda }{E}}}^{\frac{1}{2}}}$$
(22)

Substituting Eq. (22) into Eq. (17), the relationship between the drilling cuttings quantity and coal stress is obtained as: `

$$\begin{aligned} {M_0}= & \gamma \left( {\pi {a^2}+\sqrt 3 \pi {\varepsilon _c}{\rho ^2}} \right) \\ = & \gamma \pi {a^2}\left[ {1+\sqrt 3 {\varepsilon _c}\frac{{{{\left( {1=\frac{\lambda }{E} - \frac{{2\lambda P}}{{E{\sigma _c}}}} \right)}^{\frac{1}{2}}}}}{{\frac{\lambda }{E}}}} \right] \\ \end{aligned}$$
(23)

Taking the derivative of Eq. (23) with respect to the coal stress P, we get:

$$\frac{{d{M_0}}}{{dP}}=\sqrt 3 \frac{{{a^2}\gamma \pi {\sigma _c}}}{E}\frac{{\frac{1}{{{\sigma _c}}}}}{{{{\left( {1+\frac{\lambda }{E} - \frac{{2\lambda P}}{{E{\sigma _c}}}} \right)}^{\frac{1}{2}}}}}$$
(24)

Based on Eq. (24) and Eq. (19), the critical stress for the initiation of the ultra-large drilling cuttings quantity can be derived as:

$${P^*}=\left[ {{{\left( {\frac{\lambda }{E}} \right)}^{ - 1}}+1} \right]\frac{{{\sigma _c}}}{2}$$
(25)

From Eq. (25), it can be seen that the initiation condition for the ultra-large drilling cuttings quantity is determined by the inherent physical and mechanical properties of the coal. When the actual coal stress P ≥ P∗, the ultra-large drilling cuttings quantity phenomenon can occur, and the drilling cuttings quantity far exceeds the normal value. Otherwise, the drilling hole remains stable, and the drilling cuttings quantity has a one-to-one correspondence with the stress.

When the coal stress reaches the critical stress, the critical value of the ultra-large drilling cuttings quantity can be obtained from Eq. (23) as:

$$M_{0}^{*}=\gamma \pi {a^2}\left\{ {1+\sqrt 3 {\varepsilon _c}\left[ {\left( {\frac{\lambda }{E}} \right)+1} \right]} \right\}$$
(26)

Equation (26) reflects that the coal properties, burst propensity, and drilling hole size are the main factors influencing the critical value of the ultra-large drilling cuttings quantity.

Analysis of main influencing factors for the ultra-large drilling cuttings quantity phenomenon

The key criterion for judging the initiation of the ultra-large drilling cuttings quantity phenomenon is whether the coal stress reaches the critical stress. From Fig. 3 and the definition of bursting energy index KE, under ideal conditions, the ratio of the softening modulus λ to the elastic modulus E equals the bursting energy index KE. Therefore, λ/E can be approximated as the bursting energy index KE. From Eqs. (25) and (26), it can be seen that the bursting energy index KE, uniaxial compressive strength σc, and unit weight γ are the factors controlling the ultra-large drilling cuttings quantity and its critical stress. Based on Eq. (23), the relationship between drilling cuttings quantity and coal stress under different values of bursting energy index KE, compressive strength σc, and unit weight is plotted, as shown in Figs. 6, 7 and 8. According to the mechanism of the ultra-large drilling cuttings quantity phenomenon, once the stress in the surrounding rock of the drilling hole reaches the critical stress, the drilling hole becomes unstable, and the drilling cuttings quantity increases disorderly. Therefore, to represent the disordered increase in drilling cuttings quantity beyond the critical stress, an upward straight line is used in the plots. According to the mechanism of ultra-large drilling cuttings quantity, when the surrounding rock stress of the borehole reaches the critical stress, the borehole becomes unstable, and the plastic zone undergoes theoretically uncontrollable expansion, triggering a disordered increase in drilling cuttings quantity. In practice, the expansion of the plastic zone does not continue indefinitely but ceases once the system structure enters a new stability point. However, due to the uncertainty in the spatiotemporal distribution of these stability points, the magnitude of ultra-large drilling cuttings quantity remains finite.

Fig. 6
figure 6

The relationship between the drilling cuttings and the stress of the coal for different bursting energy index KE.

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Fig. 7
figure 7

Relationship between critical cuttings quantity, critical cuttings stress and bursting energy index KE.

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Fig. 8
figure 8

The relationship between the drilling cuttings and the stress of the coal for different compressive strength σc.

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Influence of the bursting energy index K E

Figure 6 illustrates the variation of drilling cuttings quantity with coal stress P under different bursting energy index KE. It can be observed that as the coal stress increases, the drilling cuttings quantity also increases. However, once the stress reaches a certain critical value, the drilling cuttings quantity no longer increases in a regular manner but rather exhibits disordered growth due to instability. This critical stress value represents the threshold at which the drilling hole becomes unstable, leading to the occurrence of the ultra-large drilling cuttings quantity phenomenon.

By analyzing Eq. (25) in conjunction with Fig. 6, it is evident that when the brittleness of the coal seam is stronger, the softening modulus λ is larger, resulting in a higher bursting energy index KE and greater impact tendency. Consequently, the critical stress for the ultra-large drilling cuttings quantity phenomenon decreases, making it easier for the phenomenon to initiate. Conversely, when λ is smaller, the bursting energy index KE decreases, the impact tendency diminishes, and the critical stress for the ultra-large drilling cuttings quantity phenomenon increases, making it less likely to occur.In the extreme case, When λ approaches infinity, the bursting energy index KE also approaches infinity. In this scenario, the ultra-large drilling cuttings quantity phenomenon can occur when the coal stress P reaches half of the uniaxial compressive strength σc. When λ is zero, the bursting energy index KE becomes zero, and the coal behaves as an ideal elastic-plastic material. In this case, the critical stress for the ultra-large drilling cuttings quantity phenomenon approaches infinity, meaning the phenomenon will never occur.

Figure 7 illustrates the relationship between the critical drilling cuttings quantity, critical drilling cuttings stress, and the bursting energy index KE. It can be observed that as the bursting energy index KE increases, both the critical drilling cuttings quantity and the critical drilling cuttings stress decrease. Overall, there is a negative correlation between KE and the critical drilling cuttings quantity as well as the critical drilling cuttings stress. However, the sensitivity of the critical drilling cuttings quantity and critical drilling cuttings stress to changes in KE differs significantly before and after KE=1.Before KE=1, as the bursting energy index KE decreases, the absolute value of the slope of the curves for the critical drilling cuttings quantity and critical drilling cuttings stress increases. This indicates that the critical drilling cuttings quantity and critical drilling cuttings stress are highly sensitive to changes in KE in this range. In other words, for coal with lower KE values, small changes in KE lead to significant changes in the critical drilling cuttings quantity and critical drilling cuttings stress.After KE=1,as the bursting energy index KE increases, the absolute value of the slope of the curves for the critical drilling cuttings quantity and critical drilling cuttings stress decreases. This suggests that the critical drilling cuttings quantity and critical drilling cuttings stress become less sensitive to changes in KE for brittle coal with higher KE values. In other words, for coal with higher KE values, changes in KE have a relatively smaller impact on the critical drilling cuttings quantity and critical drilling cuttings stress. In summary, the relationship between the bursting energy index KE and the critical drilling cuttings quantity as well as the critical drilling cuttings stress is characterized by a negative correlation. However, the sensitivity of these critical values to changes in KE varies significantly depending on whether KE is below or above 1. For KE<1, the critical values are highly sensitive to changes in KE, while for KE>1, the critical values become less sensitive, particularly for brittle coal.

$$\frac{{{\rho _{cr}}}}{b}=\sqrt {1+\frac{1}{{{K_E}}}}$$
(27)

In the equation, b represents the radius of the roadway, and ρcr is the critical depth of the softening zone

According to reference28, Eq. (27) provides the calculation formula for the critical depth of the softening zone at which rockburst occurs. When the roadway radius remains constant, the more brittle the coal, the higher the bursting energy index KE, and the smaller the critical depth of the softening zone, making rockburst more likely to occur. Combined with Fig. 7, the influence of the bursting energy index KE on rockburst and the ultra-large drilling cuttings quantity follows the same pattern, indicating that the ultra-large drilling cuttings quantity phenomenon can serve as a dynamic indicator for predicting rockburst.

Influence of uniaxial compressive strength Σc

Figure 8 illustrates the variation of drilling cuttings quantity with coal stress P under different values of uniaxial compressive strength σc. Similarly, once the coal stress reaches the critical stress, the drilling cuttings quantity enters a state of disordered growth due to instability.

From the different values of uniaxial compressive strength σc, it can be observed that the larger the σc, the greater the critical value and critical stress for the ultra-large drilling cuttings quantity phenomenon. This indicates that the higher the uniaxial compressive strength σc, the more difficult it is to initiate the ultra-large drilling cuttings quantity phenomenon. However, once initiated, as the amount of discharged cuttings increases, the severity of the situation escalates. This explains why the ultra-large drilling cuttings quantity phenomenon often occurs in soft coal but is more severe when it occurs in hard coal. For example, the hardness coefficient of the No. 7 coal seam in Zhangshuanglou Coal Mine is 2.3, which is classified as hard coal. Therefore, the ultra-large drilling cuttings quantity phenomenon is more severe in this case.

Influence of unit weight

Figure 9 illustrates the variation of drilling cuttings quantity with coal stress P under different unit weight conditions.

Fig. 9
figure 9

The relationship between the drilling cuttings and the stress of the coal for different bulk densityγ.

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From Fig. 9, it can be observed that an increase in unit weight does not alter the critical stress for the ultra-large drilling cuttings quantity phenomenon. However, it increases the drilling cuttings quantity under the same stress conditions and raises the critical value for the ultra-large drilling cuttings quantity. This indicates that changes in the unit weight of the coal do not affect the ease of initiating the ultra-large drilling cuttings quantity phenomenon or the rate of change in drilling cuttings quantity caused by variations in coal stress.

Field application and analysis

Based on physical and mechanical experiments, the physical and mechanical parameters of the No. 7 coal seam in the Zhangshuanglou Coal Mine are presented in Table 1. Using Eqs. (23), (25), and (26), the relationship between the drilling cuttings quantity and coal stress for Zhangshuanglou Coal Mine can be derived, as illustrated in Fig. 10.

Table 1 Physico-mechanical properties of the No. 7 coal seam in Zhangshuanglou coal mine.
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Fig. 10
figure 10

The relationship between the drilling cuttings and the stress of the coal.

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From Fig. 10, it can be observed that the critical stress for the occurrence of the ultra-large drilling cuttings quantity phenomenon in the No.7 coal seam of Zhangshuanglou Coal Mine is 44.6 MPa. Based on the geological and mining technical conditions of the 7123 working face in Zhangshuanglou Coal Mine, the burial depth H at the location where the ultra-large drilling cuttings quantity occurred is approximately 950 m. The unit weight of the overlying strata is taken as 25kN/m³, the stress concentration coefficient k0 for the advance influence of the working face is 1.6, and the stress concentration coefficient k1 for the lateral abutment pressure of the roadway is 1.2. The actual stress P0 at the location where the ultra-large drilling cuttings quantity occurred can be estimated as:

\(P0=H \times \gamma \times ({k_0}+{k_1} - 1)=42.75\operatorname{MPa}\)

It can be seen that the estimated actual stress differs from the theoretical calculation by approximately 4%, which is a negligible difference. Additionally, the trend of drilling cuttings quantity with depth at the measurement points of the ultra-large drilling cuttings quantity in Fig. 11 matches that in Fig. 10, indicating that the theoretical derivation aligns well with the actual conditions.

Fig. 11
figure 11

Drilling cuttings before and after pressure relief blasting.

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For the area in Fig. 10 where the ultra-large drilling cuttings quantity occurred, pressure relief blasting was conducted. After the blasting, three drilling inspection holes were constructed, and it was found that the drilling cuttings quantity still exceeded the standard. A second round of pressure relief blasting was performed, and subsequent inspections showed that the drilling cuttings quantity returned to normal, as illustrated in Fig. 11. It took two rounds of intensive pressure relief for the area to return to normal, indicating that the region where the ultra-large drilling cuttings quantity phenomenon occurred was under high stress and at significant risk of rockburst. This further demonstrates that the ultra-large drilling cuttings quantity phenomenon can be used to assess the risk of roadway rockburst.

Discuss

In this study, a plastic strain softening model for coal seam drilling holes is established. And the analytical solution for the initiation conditions of the ultra-large drilling cuttings quantity phenomenon is derived. Then, the controlling factors for the critical stress of ultra-large drilling cuttings in coal were analyzed, and it was found that the bursting energy index KE and uniaxial compressive strength σc have a significant impact on the critical stress of ultra large drilling cuttings in coal.

Extensive research has shown that the external cause of rockburst in roadways is stress concentration in the coal body due to mining activities, while the internal cause lies in the physical and mechanical properties of the coal itself29,30. As indicated by Eqs. (25) and (26), the ultra-large drilling cuttings quantity phenomenon is influenced by the physical and mechanical properties of the coal and occurs when the coal stress reaches the critical stress for the phenomenon. Therefore, both the ultra-large drilling cuttings quantity and roadway rockburst are controlled by the same factors, suggesting a certain relationship between the ultra-large drilling cuttings quantity phenomenon and the risk of roadway rockburst.

Reference28 provides the initiation conditions for roadway rockburst. A comparison with the initiation conditions for the ultra-large drilling cuttings quantity reveals that the critical stress for initiating roadway rockburst is the same as that for initiating the ultra-large drilling cuttings quantity. Both are determined by the physical and mechanical properties of the coal and share the same value. Thus, when the ultra-large drilling cuttings quantity phenomenon occurs in a drilling hole, the stress in the surrounding rock of the drilling hole reaches the critical stress for initiating the phenomenon. Since the stress in the surrounding rock of the drilling hole represents the stress in the surrounding rock of the roadway, this implies that the roadway stress has reached the critical level for rockburst occurrence. At this point, the roadway is at risk of rockburst.Therefore, the occurrence of the ultra-large drilling cuttings quantity phenomenon can be used to assess a high risk of rockburst in the drilling area. Similar to dynamic phenomena such as vibrations, noises, and drill jamming, the ultra-large drilling cuttings quantity phenomenon serves as an early warning indicator for rockburst risk during drilling. However, it reflects a localized state of excessive stress in the coal and is a sufficient but not necessary condition for rockburst occurrence.

Conclusions

(1) The definition of the ultra-large drilling cuttings quantity phenomenon is provided. Based on the analysis of its initiation conditions, it is found that this phenomenon can occur under various conditions, including coal seams of different strengths and at different mining depths.

(2) A plastic strain softening model for coal seam drilling holes is established. Based on the disturbance response instability theory, the analytical solution for the initiation conditions of the ultra-large drilling cuttings quantity phenomenon is derived, including the formulas for the critical value and critical stress of the phenomenon.

(3) Analysis of the influencing factors of the ultra-large drilling cuttings quantity reveals that the bursting energy index KE and uniaxial compressive strength σc significantly affect both the critical value and critical stress of the phenomenon. In contrast, the unit weight primarily influences the critical value.

(4) The relationship between the ultra-large drilling cuttings quantity and rockburst is analyzed. It is found that both phenomena are controlled by the same factors. The occurrence of the ultra-large drilling cuttings quantity phenomenon indicates that the stress in the surrounding rock of the roadway has reached the critical condition for rockburst, placing the roadway in a state of rockburst risk. Furthermore, based on the actual conditions of Zhangshuanglou Coal Mine, the theoretically calculated stress at the occurrence of the ultra-large drilling cuttings quantity closely matches the estimated actual stress. This comprehensive analysis demonstrates that the ultra-large drilling cuttings quantity phenomenon can serve as a dynamic indicator for assessing rockburst risk during drilling operations.