Introduction

With the rapid increase in coal demand in China over the past few decades, coal production has gradually shifted towards the western and deeper regions. As the mining depth increases, the difficulty of mining rises, and the likelihood and risk of rock bursts also increase significantly. Therefore, the prevention and control of rock bursts have become crucial. Local prevention and control of rock bursts in coal mines typically involve artificial intervention methods. The primary goal is to reduce energy accumulation and stress concentration in the surrounding rock, as well as to improve its mechanical properties, thereby decreasing its tendency to experience rock bursts. Commonly used prevention measures include large-diameter pressure relief drilling1,2,3,4, roof directional hydraulic fracturing5,6, deep-hole blasting for roof control7,8,9,10,11,12, and coal body pressure relief blasting13. Among these, pressure relief drilling is widely used due to its advantages of minimal disturbance, ease of construction, broad applicability, and significant effectiveness.

The key to pressure relief drilling lies in determining the optimal borehole parameters. If the borehole arrangement is too dense, it can lead to excessive pressure relief, compromising the stability of the support system. Conversely, if the boreholes are too sparsely arranged, insufficient pressure relief may occur, resulting in new stress concentration and increasing the risk of rock bursts. Conventional drilling has limited effectiveness in relieving pressure and transferring stress in the surrounding rock. Additionally, excessively large borehole diameters may damage the support structure, leading to conflicts with surrounding rock control. Kang14 discussed the method of reasonable design of pressure relief borehole group by analyzing the zoning characteristics of disturbance stress field after excavation of deep rock mass. The study found that the appropriate drilling pressure relief method can effectively reduce the stress concentration, which is conducive to the stable control of the roadway and the prevention of large deformation disasters. Zhang15 discussed the influence of pressure relief holes on the mechanical properties of surrounding rock, including drilling with different numbers and arrangement parameters. It is pointed out that the greater the drilling density, the richer the crack propagation and evolution around the borehole, the more sufficient the energy release, and the better the pressure relief effect. Wang16 deeply discussed the influence of drilling technology on the stability of coal structure through the designed prefabricated drilling experiment. The research results show that the implementation of drilling pressure relief in coal seam can slow down the severe vibration and impact caused by the concentration of ground stress, and can also effectively control the crack propagation and deformation of surrounding rock. Wang17 discussed the relationship between the mechanical and impact performance parameters of the sample and the number of boreholes and the arrangement form. The results show that with the increase of the number of boreholes, the elastic modulus, stress peak and impact energy index decrease gradually, and the pressure relief effect is more significant. Zhu18 believed that in the process of pressure relief of large diameter boreholes, in order to avoid the occurrence of rock burst, the borehole layout parameters must be reasonably determined. Gai19 conducted an in-depth study on the pressure relief effect of boreholes under high stress environment. The research results show that with the decrease of borehole spacing, the interaction between boreholes is enhanced, and the pressure relief area of boreholes also increases accordingly. Jia2 discussed the influence of parameters such as borehole diameter, borehole spacing and borehole depth on the strength of the sample through laboratory experiments. It was found that with the increase of borehole diameter and borehole depth, the number of cracks around the borehole increased, and the main crack path became clearer, thus realizing the improvement of pressure relief effect.

The aforementioned scholars have conducted extensive and in-depth research on the parameters and actual effects of conventional drilling pressure relief technology. These studies have highlighted the crucial role of this method in coal mine safety, while also revealing several urgent issues that need to be addressed. On the one hand, conventional borehole pressure relief can be insufficient due to its limitations. For instance, pressure relief may be inadequate, resulting in rock bursts even after intervention. On the other hand, excessive pressure relief can lead to excessive deformation of the surrounding rock, compromising roadway stability and potentially causing more severe disasters. The key issue of how to implement drilling pressure relief in rock burst risk areas while maintaining the integrity and strength of the surrounding roadway rock requires further study. In response, The variable diameter drilling method is adopted. To prevent damage to the supporting structure, small diameter drilling is conducted at the roadway sides, while large diameter reaming is performed deeper within the surrounding rock. After drilling and reaming, the boreholes in the roadway’s anchorage zone are sealed to minimize their impact on the supporting structure. This approach provides a reference for optimizing pressure relief drilling parameters and its practical engineering application.

Stress distribution characteristics of coal around variable-diameter borehole

Calculation of distribution radius of coal pressure relief area around borehole

According to the superposition principle of elastic mechanics, the vertical stress and horizontal stress of the conventional drilling section and the deep reaming section can be decomposed into two parts: The first part is affected by the uniform compressive stress (1 + λ)p/2 in the vertical direction and the uniform compressive stress (1 + λ)p/2 in the horizontal direction; The second part is affected by the uniform compressive stress (1–λ)p/2 in the vertical direction and the uniform tensile stress (1–λ)p/2 in the horizontal. According to the theory of elastic mechanics, the polar coordinate stress component expression under the stress of coal around the borehole is obtained:

$$\left\{ \begin{gathered} \sigma_{r} = - \frac{{\left( {1 + \lambda } \right)p}}{2}\left( {1 - \frac{{a^{2} }}{{r^{2} }}} \right) + \frac{{\left( {1 - \lambda } \right)p}}{2}\left( {1 - \frac{{a^{2} }}{{r^{2} }}} \right)\left( {1 - 3\frac{{a^{2} }}{{r^{2} }}} \right)\cos 2\theta \hfill \\ \sigma_{\theta } = - \frac{{\left( {1 + \lambda } \right)p}}{2}\left( {1 + \frac{{a^{2} }}{{r^{2} }}} \right) - \frac{{\left( {1 - \lambda } \right)p}}{2}\left( {1 + 3\frac{{a^{2} }}{{r^{2} }}} \right)\cos 2\theta \hfill \\ \tau_{r\theta } = - \frac{{\left( {1 - \lambda } \right)p}}{2}\left( {1 - \frac{{a^{2} }}{{r^{2} }}} \right)\left( {1 + 3\frac{{a^{2} }}{{r^{2} }}} \right)\sin 2\theta \hfill \\ \end{gathered} \right.$$
(1)

In the formula: \(r\), \(\theta\) are the polar coordinates of any point around the borehole, \(\sigma_{r}\) is the radial stress at any point around the borehole, \(\sigma_{\theta }\) is the tangential stress at any point around the borehole, \(\tau_{r\theta }\) is the shear stress at any point around the borehole, \(\lambda\) is the lateral pressure coefficient, \(a\) is the borehole radius.

According to the stress component Eq. (1) in polar coordinates, the expression of the principal stress at a point of coal around the borehole is obtained:

$$\left\{ \begin{gathered} \sigma_{1} = \frac{{\sigma_{p} + \sigma_{\varphi } }}{2} + \frac{1}{2}\sqrt {\left( {\sigma_{p} - \sigma_{\varphi } } \right)^{2} + 4\tau_{\rho \varphi }^{2} } \hfill \\ \sigma_{3} = \frac{{\sigma_{p} + \sigma_{\varphi } }}{2} - \frac{1}{2}\sqrt {\left( {\sigma_{p} - \sigma_{\varphi } } \right)^{2} + 4\tau_{\rho \varphi }^{2} } \hfill \\ \end{gathered} \right.$$
(2)

In the formula: \(\sigma_{1}\), \(\sigma_{3}\) are the maximum and minimum principal stress at a point.

According to the principal stress at a point of coal around the borehole, the Mohr–Coulomb yield condition is substituted into Eq. (2) to obtain the yield condition at a point of coal around the borehole:

$$\frac{1}{2}\sqrt {\left( {\sigma_{p} - \sigma_{\varphi } } \right)^{2} + 4\tau_{\rho \varphi }^{2} } = C\cos \phi - \frac{1}{2}\left( {\sigma_{\rho } + \sigma_{\varphi } } \right)\sin \phi$$
(3)

In the formula: \(C\) is the cohesion of coal body, \(\phi\) is the internal friction angle of coal.

The boundary equation of the plastic zone of the coal body around the borehole, that is, the pressure relief zone, is derived by substituting the formula (1) into the formula (3):

$$b + h\frac{{\rho^{2} }}{{a^{2} }} + d\frac{{\rho^{4} }}{{a^{4} }} + e\frac{{\rho^{6} }}{{a^{6} }} + f\frac{{\rho^{8} }}{{a^{8} }} = 0$$
(4)
$$\begin{aligned} {\text{In}}\;{\text{the}}\;{\text{formula}}: & b = 9\left( {1 - \gamma } \right)^{2} ; \\ & h = 6\left( {1 - \gamma^{2} } \right)\cos 2\varphi - 12\left( {1 - \gamma } \right)^{2} ; \\ & d = \left( {1 + \gamma } \right)^{2} + 10\left( {1 - \gamma } \right)^{2} \cos^{2} 2\varphi - 2\left( {1 - \gamma } \right)^{2} \sin^{2} 2\varphi - 4\left( {1 - \gamma^{2} } \right)\cos 2\varphi \\ & \quad - 4\left( {1 - \gamma } \right)^{2} \cos^{2} 2\varphi \cdot \sin^{2} \phi ; \\ & e = 4\left( {1 - \gamma } \right)^{2} \left( {\sin^{2} 2\varphi - \cos^{2} 2\varphi } \right) + 2\left( {1 - \gamma^{2} } \right)\cos 2\varphi \\ & \quad - 4\frac{C}{p}\left( {1 - \gamma } \right)\sin 2\phi \cos 2\varphi - 4\left( {1 - \gamma^{2} } \right)\cos 2\varphi \cdot \sin^{2} \phi ; \\ & f = \left( {1 - \gamma } \right)^{2} - 4\frac{{C^{2} }}{{p^{2} }}\cos^{2} \phi - \left( {1 + \gamma } \right)^{2} \sin^{2} \phi - 2\frac{C}{p}\left( {1 + \gamma } \right)\sin 2\phi ; \\ \end{aligned}$$

\(\rho\)—the radius of the pressure relief zone at the corresponding corner \(\varphi\).

Through the above analysis, it can be known that the distribution of the pressure relief zone around the borehole is affected by the vertical stress \(p\), the lateral pressure coefficient \(\gamma\), borehole radius \(a\), coal cohesion \(C\) and internal friction angle \(\phi\) of the coal body. Among them, the cohesion \(C\), internal friction angle \(\phi\) and lateral pressure coefficient \(\gamma\) of the coal body are determined by the working face environment, and the drilling radius determines the size of \(a\). Therefore, the pressure relief effect of the variable-diameter borehole and the radius of the plastic zone of the surrounding coal body are affected by the radius of the borehole.

The influence of borehole diameter on the distribution of pressure relief area

According to the coal properties and stress distribution of typical coal mines, the internal friction angle \(\phi\) of coal is 26.9°, the vertical stress \(p\) is 25 MPa, the lateral pressure coefficient \(\gamma\) is 0.8, and the borehole diameters are 100 mm, 150 mm, 200 mm, 250 mm and 300 mm, respectively. The parameters mentioned above are entered into the calculation software to determine the maximum radius and direction of the pressure relief zone for various borehole diameters. The results are presented in Table 1, and the relationship between borehole diameter and the boundary of the pressure relief area is illustrated in Fig. 1.

Table 1 Calculation results of pressure relief zone parameters of different borehole diameters.
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Fig. 1
Fig. 1
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Borehole pressure relief zone boundary with borehole diameter variation diagram.

From Table 1, Figs. 1 and 2, it can be concluded that the maximum radius of the pressure relief zone increases with the increase of the borehole diameter, and increases linearly. When the borehole diameter increases from 100 to 150 mm, the maximum radius of the pressure relief zone increases by 46%. When the borehole diameter increases from 100 to 200 mm, the maximum radius of the pressure relief zone doubles. When the borehole diameter increases from 100 to 200 mm, the maximum radius of the pressure relief zone doubles. With a borehole diameter of 250 mm, the maximum radius increases by 146% compared to 100 mm. At a borehole diameter of 300 mm, the maximum radius is three times larger than at 100 mm.

Fig. 2
Fig. 2
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The variation trend of the maximum radius of the pressure relief zone with the borehole diameter.

Numerical simulation

Scheme of numerical simulation

Compared to conventional borehole pressure relief, variable-diameter borehole pressure relief involves more influencing factors, primarily including deep borehole diameter, position of the diameter change, and borehole spacing. To investigate the impact of these three key parameters on the stability of roadway surrounding rock, FLAC3D numerical simulation software was employed to analyze the vertical stress distribution and energy dissipation patterns associated with different variable-diameter borehole parameters, based on the engineering context.

A numerical calculation model is established for a typical rock burst coal mine, with dimensions of 70 m × 20 m × 41 m (length × width × height). The model uses hexahedral grid units, with a total of approximately 386,400 grid units and 399,200 grid nodes. The bottom and periphery of the model are fixed, and the displacement is limited. The corresponding vertical stress is applied to the upper part of the model. According to the buried depth of the coal seam, the average bulk density of the overlying rock mass is 25kN/m3, and the applied weight of the overlying rock mass is 25 MPa. A survey line is placed above the borehole, with monitoring points arranged from the left side of the roadway. The distance between adjacent measuring points is 1 m, resulting in a total of 26 monitoring points. The grid units are hexahedral, and a representative three-dimensional numerical model is selected, as shown in Fig. 320.

Fig. 3
Fig. 3
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Numerical simulation model.

Scheme 1: The conventional borehole diameter for the shallow section is 100 mm, the shallow borehole depth is 4 m, the deep reaming depth is 12 m, the borehole spacing is 1.0 m, and the total borehole length is 20 m, as shown in Table 2.

Table 2 Numerical simulation schemes of different deep reaming diameters.
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Scheme 2: The shallow borehole diameter is fixed at 100 mm, the deep reaming diameter is 250 mm, the borehole spacing is 1.0 m, and the total borehole length is 20 m, as shown in Table 3.

Table 3 Numerical simulation schemes for different deep reaming depths.
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Scheme 3: The shallow conventional borehole diameter is fixed at 100 mm, the deep reaming diameter at 250 mm, the shallow borehole depth at 4 m, the deep reaming depth at 16 m, and the total borehole length at 20 m, as shown in Table 4.

Table 4 Numerical simulation schemes for different deep reaming spacings.
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Numerical simulation results analysis

Numerical simulation scheme of different deep reaming diameter

  1. (1)

    The influence of deep reaming diameter on the vertical stress distribution of roadway side.

Figure 4 shows the vertical stress distribution in the roadway sidewalls at different deep reaming diameters, and Fig. 5 presents the corresponding vertical stress distribution curves. Without borehole pressure relief, the peak vertical stress in the surrounding rock is 43.66 MPa at a distance of 5.0 m from the sidewall. When the deep reaming diameters are 100 mm, 150 mm, and 200 mm, the vertical stress at the original stress peak location decreases by 4.33%, 4.74%, and 8.11%, respectively, compared to the no-borehole case, indicating a relatively weak pressure relief effect; When the deep reaming diameter is 250 mm, the vertical stress peak at the roadway side is 35.60 MPa, with the vertical stress at the original peak position decreasing to 35.72 MPa, representing an 18.19% reduction compared to the undrilled condition. The pressure relief zone created by the reaming is connected to the low-stress area, while a high-stress region forms at the reaming end, with a peak value of 31.34 MPa. The stress redistribution effect is more pronounced, and the pressure relief effect is enhanced; When the deep reaming diameter is increased to 300 mm, the vertical stress peak at the roadway side is 39.94 MPa, while the vertical stress at the original peak location decreases to 23.20 MPa, a 46.86% reduction compared to the undrilled condition. The reaming-induced pressure relief zone fully connects to the low-stress area, and the stress transfer to the deeper region becomes more significant. The maximum stress in the high stress zone at the reaming end is 38.2 MPa. MPa, further improving the pressure relief effect.

Fig. 4
Fig. 4
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Vertical stress distribution of roadway surrounding rock under different deep reaming diameters.

Fig. 5
Fig. 5
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Vertical stress distribution curve of roadway surrounding rock under different deep reaming diameters.

When the deep reaming diameter ranges from 100 to 200 mm, the pressure relief and stress transfer effects on the roadway surrounding rock are limited. However, when the deep reaming diameter exceeds 250 mm, the high-stress zone at the roadway side shifts to the distal and lower parts of the deep reaming, significantly enhancing both the pressure relief and stress transfer effects. As the deep reaming diameter increases, the vertical stress monitoring curve exhibits a gradual decline, while the degree of stress transfer to the deeper parts of the reaming zone progressively increases. This phenomenon is primarily due to the position of the variable-diameter borehole, which lies between the stress concentration zone of the surrounding rock and the roadway. The deep reaming through this stress concentration zone, significantly influencing the stress redistribution and pressure relief in the surrounding rock.

  1. (2)

    The effect of deep reaming diameter on energy dissipation.

As shown in Fig. 6, when the diameter of deep reaming is 100–250 mm, there is a small range of dissipation energy density cloud area around the reaming, and the concentration area of dissipation energy density and the maximum value of dissipation energy appear near the side of the roadway. The pressure relief effect and energy dissipation degree are general. With a 300 mm diameter for deep reaming, there is a wide, concentrated area of dissipated energy density surrounding the drilling and reaming site, resulting in optimal pressure relief and a noticeable energy dissipation effect. The concentration area of dissipated energy density is concentrated to the roadway, which is due to the stress concentration at the roadway side caused by the excavation of the roadway. After the pressure relief by reaming, the stress concentration at the roadway side is reduced, and the dissipation effect of reaming on the stress concentration is the most obvious, and the energy dissipation degree is the highest.

Fig. 6
Fig. 6
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Dissipative energy density cloud diagram of roadway surrounding rock under different deep reaming diameters.

As shown in Fig. 7, the dissipated energy density increases with the diameter of the deep reaming. When the diameter of the deep reaming is 100 mm, that is, the full length of the borehole is a conventional borehole, the maximum dissipated energy density is 0.696 kJ/m3. For deep reaming diameters of 150 mm, 200 mm, and 250 mm, the maximum dissipated energy densities are 1.508 kJ/m3, 5.052 kJ/m3, and 14.84 kJ/m3, respectively. The energy density increases by 116.38%, 626.44%, and 2031.61% compared to the 100 mm diameter. When the deep reaming diameter reaches 300 mm, the maximum dissipated energy density increases to 49.45 kJ/m3, an increase of 7004.31% compared to the 100 mm diameter.

Fig. 7
Fig. 7
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Dissipative energy density distribution trend diagram of roadway surrounding rock under different deep reaming diameter.

  1. (3)

    Influence of deep reaming diameter on roadway deformation.

As shown in Fig. 8, when no drilling is applied for pressure relief, the maximum deformation of the roadway sides is 246.8 mm, the maximum deformation of the floor is 224.9 mm, and the maximum deformation of the roof is 180.3 mm. With deep reaming diameters of 100 mm, 150 mm, 200 mm, and 250 mm, the maximum deformation of the sides is 251.0 mm, 252.1 mm, 252.5 mm, and 253.2 mm, respectively, while the maximum deformation of the floor is 229.6 mm, 229.8 mm, 229.6 mm, and 229.7 mm, respectively. When the deep reaming diameter is 300 mm, the maximum deformation of the sides increases to 267.6 mm, the maximum deformation of the floor is 233.8 mm, and the maximum deformation of the roof is 192.4 mm. At this point, the deformations of the roadway sides, roof, and floor all increase significantly.

Fig. 8
Fig. 8
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Curves of roadway surface deformation under different deep reaming diameters.

When the deep reaming diameter is 100 mm, 150 mm, 200 mm, and 250 mm, the deformation of the two sides increases by 1.70%, 2.15%, 2.31%, and 2.59%, respectively, compared to the undrilled case. As the diameter of the deep borehole increases, The deformation of the two sides, floor, and roof of the roadway is generally on the rise, albeit not significantly. When the diameter of deep reaming is 300 mm, the deformation of the two sides increases by 8.43%, with notable deformation occurring on the roadway surface. When the borehole diameter exceeds 300 mm, the surface deformation of the roadway increases significantly. The analysis shows that although the variable diameter position is outside the anchorage zone of the roadway, the borehole diameter is too large, and the pressure relief range gradually affects the anchorage structure. This leads to a conflict between pressure relief and the control of the surrounding rock. Therefore, the diameter of the deep reaming should not exceed 300 mm.

Numerical simulation scheme for different deep reaming depths

  1. (1)

    Effect of deep reaming depth on vertical stress distribution in roadway sides.

From Figs. 9 and 10, it can be seen that without borehole pressure relief, the peak vertical stress of the roadway side is 43.66 MPa, at a distance of 5.0 m from the roadway side. When the deep reaming depth is 0 m, the vertical stress peak of the roadway side is 41.85 MPa, and the vertical stress at the original stress peak position is 41.84 MPa, which is 4.17% lower than that of the undrilled pressure relief. When the deep reaming depth is 4 m, 8 m, and 12 m, the vertical stress peaks of the roadway side are 41.88 MPa, 42.00 MPa, and 42.37 MPa, respectively, and the vertical stress at the original stress peak position is reduced to 41.85 MPa, 41.12 MPa, and 42.26 MPa, respectively. Compared with the undrilled pressure relief, the reduction ranges are 4.15%, 5.82%, and 3.21%, respectively. When the deep reaming depths are 16 m and 20 m, the vertical stress peaks of the roadway side are 35.60 MPa and 35.26 MPa, respectively. The vertical stress at the original stress peak position is 35.62 MPa and 34.51 MPa, respectively. Compared with the undrilled pressure relief, the reductions are 18.42% and 20.96%, respectively. The pressure relief zone formed by the reaming is connected to the low stress zone over a range of 8.1 m and 8.7 m, respectively. A large stress concentration area appears around the deep reaming, and the peak vertical stress at the end of the deep reaming is 32.05 MPa and 32.12 MPa, respectively, showing a high degree of stress transfer.

Fig. 9
Fig. 9
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Distribution of vertical stress around the roadway at different deep reaming depths.

Fig. 10
Fig. 10
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Vertical stress distribution curves of the roadway surrounding rock at different deep reaming depths.

When the deep reaming depths are 16 m and 20 m, the variable diameter position is located within the original vertical stress peak position of the undrilled roadway (5.0 m from the roadway side). The vertical stress at the original stress peak position is reduced to 34.51 MPa, a decrease of 20.96%, indicating a good pressure relief effect. When the deep reaming depth is 12 m, the variable diameter position lies between the original vertical stress peak of the undrilled roadway and the roadway itself. The vertical stress at the original stress peak position decreases to 42.26 MPa, a reduction of only 3.21%, showing a less effective pressure relief. This is primarily due to the overlapping of the stress concentration zones at both ends of the deep reaming with the original stress concentration zone, resulting in the superposition of the two stress concentration areas. When the deep reaming depths are 8 m, 4 m, and 0 m, the variable diameter position lies outside the peak of the vertical stress of the undrilled roadway. The vertical stress at the original stress peak position decreases to 41.12 MPa, representing a reduction of 5.82%, indicating a moderate pressure relief effect. Considering the influence of deep reaming depth on the pressure relief effect, it is determined that the variable diameter position should be located between the vertical stress peak of the surrounding rock and the roadway, so that the deep reaming passes through the original stress concentration zone, that is, the variable diameter position should be within 5.0 m from the roadway side.

  1. (2)

    Effect of deep reaming depth on energy dissipation.

As shown in Fig. 11, when the deep reaming depths are 4 m, 8 m, and 12 m, the dissipated energy density concentration zones appear around the deep reaming, in contrast to shallow small-diameter boreholes. This indicates that deep reaming has a more significant energy dissipation effect on the surrounding rock of the roadway. When the deep reaming depths are 16 m and 20 m, the borehole length is essentially a large-diameter reaming. In these cases, both the concentration zones of dissipated energy density and the maximum values of dissipated energy are located at the roadway side. The dissipation effect on the stress concentration at the roadway side is more pronounced, and the degree of energy dissipation is higher.

Fig. 11
Fig. 11
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Dissipated energy density cloud map of the surrounding rock of the roadway at different deep reaming depths.

As shown in the trend chart of Fig. 12, the dissipated energy density increases with the depth of deep reaming. When the depth of deep reaming is 0 m, meaning the borehole is a conventional borehole, the maximum dissipated energy density is 1.187 kJ/m3. When the deep reaming depths are 4 m, 8 m, and 12 m, the maximum dissipated energy densities are 4.042 kJ/m3, 4.381 kJ/m3, and 4.448 kJ/m3, respectively. Compared to the deep reaming depth is 0 m, the dissipated energy density increases by 2.86 kJ/m3, 3.19 kJ/m3, and 3.261 kJ/m3, corresponding to increases of 240.94%, 268.74%, and 274.73%. When the deep reaming depths are 16 m and 20 m, the maximum dissipated energy densities are 14.83 kJ/m3 and 15.38 kJ/m3, respectively. Compared to the 0 m depth, the dissipated energy density increases by 13.64 kJ/m3 and 14.19 kJ/m3, resulting in increases of 1149.12% and 1195.45%.

Fig. 12
Fig. 12
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Dissipative energy density distribution trend of roadway surrounding rock under different deep reaming depths.

  1. (3)

    Influence of deep reaming depth on roadway deformation.

It can be observed from Fig. 13 that without borehole pressure relief, the maximum deformations of the two sides, floor, and roof of the roadway are 246.8 mm, 224.9 mm, and 180.3 mm, respectively. When the deep reaming depths are 0 m, 4 m, 8 m, 12 m, 16 m, and 20 m, the maximum deformations of the two sides are 247.6 mm, 247.7 mm, 248.2 mm, 249.4 mm, 253.2 mm, and 252.2 mm, while the maximum deformations of the floor are 227.9 mm, 227.9 mm, 228.5 mm, 228.8 mm, 229.7 mm, and 229.2 mm, respectively.

Fig. 13
Fig. 13
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Roadway surface deformation curve under different deep reaming depth.

Compared to the case without drilling, when the depth of deep reaming is 0 m, 4 m, 8 m, and 12 m, the deformation of the two sides increases by 0.32%, 0.36%, 0.57%, and 1.05%, respectively. As the depth of deep reaming increases, the deformation of the roadway’s two sides, floor, and roof generally rises, though the increase is relatively slow. When the deep reaming depth reaches 16 m and 20 m, the variable diameter position falls within the anchorage zone. Compared to the non-drilling scenario, the deformation of the two sides increases by 2.59% and 2.19%, respectively. On the whole, the deformation of roadway is less affected by the depth of deep reaming, but the position of variable diameter should be outside the anchorage zone.

Numerical simulation scheme for different deep reaming spacings

  1. (1)

    Effect of deep reaming spacing on the vertical stress distribution of the roadway side.

From Figs. 14 and 15, it can be observed that without borehole pressure relief, the peak vertical stress at the roadway side is 43.66 MPa, located 5.0 m from the roadway side. When the deep reaming spacing is 2.5 m, 2.0 m, and 1.5 m, the peak vertical stress at the roadway side is 41.34 MPa, 41.28 MPa, and 41.48 MPa, respectively. The vertical stress at the original peak stress position is 40.55 MPa, 40.77 MPa, and 40.74 MPa, respectively. These values represent reductions of 7.12%, 6.62%, and 6.69% compared to the undrilled condition. When the deep reaming spacing is 1.0 m, the peak vertical stress at the roadway side is 40.71 MPa, and the vertical stress at the original peak stress position is 39.77 MPa, representing an 8.91% reduction compared to the undrilled condition. The pressure relief zone created by deep reaming connects with the low-stress zone, with a penetration range of 8.6 m. When the deep reaming spacing is 0.5 m, the peak vertical stress at the roadway side is 39.38 MPa, and the vertical stress at the original stress peak position is 24.67 MPa, showing a 43.50% reduction compared to the undrilled condition. The pressure relief zone formed by deep reaming fully connects with the low-stress zone, and a high-stress region appears at the end of the deep reaming, with a peak value of 39.38 MPa.

Fig. 14
Fig. 14Fig. 14
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Distribution of vertical stress in the surrounding rock of the roadway at different deep reaming spacings.

Fig. 15
Fig. 15
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Vertical stress distribution curves of roadway surrounding rock at different deep reaming spacings.

When the deep reaming spacing exceeds 1.5 m, the decrease in the vertical stress peak at the roadway side is minimal. When the spacing is between 1.0 and 1.5 m, a high-stress zone begins to form at the end of the deep reaming, and the reduction in the original stress peak starts to increase. When the deep reaming spacing is less than 1.0 m, the vertical stress peak at the roadway side is entirely transferred to the end of the deep reaming. This occurs because the drilling is dense in a certain volume, and the pressure relief area generated by the drilling is completely connected with the low stress area. The shallow drilling and the full length of the deep reaming play a role in pressure relief.

  1. (2)

    Influence of deep reaming spacing on energy dissipation.

Figure 16 shows the distribution of dissipated energy density in the surrounding rock of the roadway at different deep reaming spacings, while Fig. 17 illustrates the trend of dissipated energy density under these conditions. When the borehole spacing is 2.5 m, 2.0 m, 1.5 m, and 1.0 m, the maximum dissipated energy densities are 2.701 kJ/m3, 2.850 kJ/m3, 5.704 kJ/m3, and 9.806 kJ/m3, respectively. When the borehole spacing is 0.5 m, the maximum dissipated energy density is 46.86 kJ/m3, which is 1634.91%, 1544.21%, 721.53% and 377.87% higher than that when the borehole spacing is 2.5 m, 2.0 m, 1.5 m and 1.0 m, and the energy dissipation effect is obvious. As shown in Fig. 16, when the borehole spacing is between 1.0 and 2.5 m, the concentrated area of dissipated energy density and the maximum dissipated energy are located at the side of the roadway. As the borehole spacing decreases, the degree of pressure relief at the roadway side increases, but the energy dissipation is moderate. When the borehole spacing is 0.5 m, due to the large number of reaming holes per unit volume, a large area of dissipated energy density concentration area appears around the full length of the reaming hole, the pressure relief effect is the best, and the energy dissipation effect is the most obvious.

Fig. 16
Fig. 16
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Dissipative energy cloud diagram of roadway surrounding rock under different deep reaming spacing.

Fig. 17
Fig. 17
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Dissipative energy density distribution trend of roadway surrounding rock under different deep reaming spacing.

As the borehole spacing decreases, the degree of pressure relief in the roadway increases significantly, leading to an increase in dissipated energy density. However, when the borehole spacing is reduced beyond a certain threshold, the bearing capacity of the surrounding rock structure sharply declines, causing the internal residual elastic energy to decline rapidly, which in turn leads to a decrease in dissipated energy density. This situation is extremely dangerous for the roadway, as the loss of bearing capacity in the surrounding rock will make future maintenance efforts extremely difficult.

  1. (3)

    Influence of deep reaming spacing on roadway deformation.

Figure 18 shows that, under the condition of no borehole pressure relief, the maximum deformations of the two sides, floor, and roof of the roadway are 246.8 mm, 224.9 mm, and 180.3 mm, respectively. When the deep reaming spacings are 1.0 m, 1.5 m, 2.0 m, and 2.5 m, the maximum deformations of the two sides are 251.8 mm, 245.7 mm, 244.3 mm, and 247.6 mm, respectively, while the maximum deformations of the floor are 229.4 mm, 227.2 mm, 226.3 mm, and 225.5 mm. As the deep borehole spacing decreases, the deformation of the two sides and the roof and floor tends to increase, although the increase is marginal, within this range, the effect of deep reaming spacing on roadway deformation is relatively minor. When the deep reaming spacing is 0.5 m, the maximum deformations of the two sides, floor, and roof reach 268.6 mm, 237 mm, and 193 mm, respectively. These represent increases of 8.83%, 5.38%, and 7.04% compared to the case without drilling. When the deep reaming spacing is less than 1.0 m, the support and bearing structure of the roadway sides are compromised, causing a sharp increase in deformation. In such cases, it is necessary to seal the boreholes within the anchorage zone to minimize the impact of the pressure relief holes on the anchoring structure.

Fig. 18
Fig. 18
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Roadway surface deformation curve under different reaming spacing.

Physical similarity simulation test

Test scheme

The experiment consists of two groups: conventional drilling and variable-diameter drilling. The conventional borehole has a diameter of 2 cm and a length of 40 cm. In the case of variable-diameter drilling, the shallow part has a small diameter of 2 cm and a length of 20 cm, while the deep part has a larger diameter of 8 cm and a length of 20 cm. Due to the variable diameter of the borehole, with a larger diameter at the deep part and a smaller diameter at the shallow part, excavation of the model is not feasible once it is constructed. If a metal pipe is pre-installed, it cannot be removed after the model dries. Therefore, a pre-installed wire method (using thick nylon rope) is employed to capture images at the location where the model aligns with the borehole. Conventional drilling method: Nylon rope is laid at the pre-designed drilling positions during the construction of the model. Variable diameter drilling Method: Nylon rope is also laid at the pre-designed drilling positions during model construction. For the deep large-diameter borehole, the nylon rope is folded several times to facilitate removal, preventing it from getting tangled. The nylon rope for the shallow small-diameter borehole is extended to the roadway to facilitate extraction, as shown in Fig. 19a20.

Fig. 19
Fig. 19
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Similar simulation test.

To investigate the impact of conventional drilling and variable diameter drilling on the stress changes in the surrounding rock of the roadway, a total of 10 stress monitoring points were arranged in the model. Each monitoring point used the LY-350 micro pressure transducer, as shown in Fig. 19b, to record the stress variations in the roadway sidewalls. A measurement line was placed 25 mm above the borehole to monitor the stress changes in the surrounding rock of the roadway after drilling. The LY-350 micro pressure transducers were arranged starting 50 mm from the roadway side, with a 50 mm spacing between adjacent monitoring points. The specific layout is shown in Fig. 20.

Fig. 20
Fig. 20
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Schematic diagram of the layout of the measuring line and borehole.

Stress change law of roadway surrounding rock with variable diameter borehole

For ease of discussion, the stress data measured from the two experimental groups—conventional drilling and variable diameter drilling—are converted and analyzed according to the designed stress similarity ratio, resulting in the vertical stress monitoring curve shown in Fig. 21. The maximum vertical stress recorded in both experimental groups occurred at the monitoring point located 10 cm from the roadway side, where stress concentration is observed. In the conventional drilling experiment, the maximum vertical stress measured was 28.74 MPa, while in the variable diameter drilling experiment, the maximum vertical stress measured was 28.69 MPa; The minimum vertical stress recorded in both experimental groups occurred at the monitoring point located 5 cm from the roadway side. This is because the stress in the surrounding rock near the roadway surface is released due to excavation. As a result, the vertical stress at this monitoring point is the lowest. In the conventional drilling experiment, the minimum vertical stress measured was 28.14 MPa, while in the variable diameter drilling experiment, the minimum vertical stress measured was 28.34 MPa. The monitoring points located at distances of 15 cm, 20 cm, 25 cm, 30 cm, 35 cm, and 40 cm from the roadway side are positioned above the boreholes. The surrounding rock and soil above the boreholes form cavities after drilling, resulting in the release of upper strata stress and loosening of the soil. As a result of the pressure relief from the drilling, the stress is reduced. Therefore, in both the conventional and variable diameter drilling experiments, the vertical stress measured at these six locations is lower. In both tests, conventional drilling is performed within 20 cm from the roadway side, while in the variable diameter drilling test, large diameter reaming is applied in the range of 20 cm to 40 cm from the roadway side. Therefore, the drilling in both tests is consistent within 20 cm from the roadway side, under ideal conditions, the data from the four monitoring points in this range should be identical. However, the final experimental results show that the vertical stress values at these four monitoring points in the variable diameter drilling test are slightly lower than those in the conventional drilling test. This discrepancy is likely due to the pressure relief effect of the large-diameter borehole behind the variable diameter borehole, which may have affected the conventional boreholes in front. Alternatively, the difference in stress values could be attributed to slight variations in the force and angle during the extraction of the coarse nylon rope, leading to minor differences in the hole formation between the two tests. Additionally, unavoidable errors during the model setup process may have contributed to the variation.

Fig. 21
Fig. 21
Full size image

Vertical stress monitoring curve.

There are significant differences between the two test schemes in the range of 20 cm to 40 cm from the roadway side. The four pressure gauges located at 25 cm, 30 cm, 35 cm, and 40 cm from the roadway side serve as the primary monitoring points in this study. At the monitoring points 25 cm, 35 cm, and 40 cm from the roadway side, the vertical stress values extracted in the conventional drilling test are 28.58 MPa, 28.49 MPa, and 28.51 MPa, respectively. In the variable diameter drilling test, the corresponding vertical stress values are 28.52 MPa, 28.32 MPa, and 28.40 MPa. Compared to the conventional drilling test, the vertical stress at these three monitoring points in the variable diameter drilling test decreases by 0.06 MPa, 0.17 MPa, and 0.11 MPa, with reduction rates of 0.21%, 0.60%, and 0.39%, respectively. The large diameter reaming in the variable diameter drilling test scheme has played a better pressure relief role. The data extracted from the monitoring point 30 cm from the roadway side in the variable diameter borehole test scheme is slightly higher than that in the conventional borehole test scheme, representing an anomaly in the data. The reason for this anomaly is that this point lies within the transition zone between the small diameter borehole and the large diameter reaming. Due to the stress release above the large diameter reaming, stress concentrations may form on either side, resulting in a slight increase in the vertical stress value at this point.

Discussion

In fact, variable diameter drilling pressure relief has been widely used in engineering, in Germany and some other countries, drilling pressure relief technology because of its simple operation, wide application is generally considered to be an efficient means of pressure relief, is also the only standard measures approved by the German National Inspectorate21,22,23,24. Hu et al.25 conducted an industrial test of variable diameter boreholes in the auxiliary transportation roadway (No. 19111) at Pingshuo No.1 Coal Mine of China Coal Group. Their study concluded that after employing variable diameter boreholes for pressure relief, stress concentration in the coal body significantly decreased, resulting in reduced deformation of the roadway roof. This measure ensures the safety and stability of the roadway. Ding et al.26 conducted an industrial test in the transportation crossheading of the 6307working face of Tangkou Coal Mine. In the area where the transportation crossheading of the 6307 working face is accompanied by a strong impact risk, 100 m was selected as the experimental area, and the drilling pressure relief method was used for the roadway side. It is concluded that the application of the variable-diameter drilling pressure relief technology reduces the maximum displacement of the roadway roof and floor compared with the large-diameter drilling, indicating that the variable-diameter drilling can relieve the pressure on the surrounding rock of the roadway while minimizing the impact on the deformation of the surrounding rock of the roadway. Through industrial tests, it has been demonstrated that variable diameter boreholes effectively mitigate and redistribute the pressure in roadway surrounding rock, thereby reducing or eliminating the risk of rock bursts and enhancing deep rock safety. The coal and rock around the pressure relief borehole undergo fragmentation, enhancing the natural physical conditions of the coal rock and alleviating surrounding stress. We hope that our theoretical analyses and numerical simulations can serve as a reference for preventing rock burst disasters.

Conclusions

Using a typical rock burst coal mine as the engineering background, the study investigates the impact of variable diameter drilling parameters—such as deep reaming diameter, reaming depth, and reaming spacing—on the stress, dissipated energy density, and deformation of the roadway surrounding rock through theoretical analysis, numerical simulation, and similar simulation tests. The following conclusions are drawn:

  1. (1)

    The distribution range of the pressure relief zone is related to the vertical stress acting on the coal body, the lateral pressure coefficient, the coal’s cohesion, and the internal friction angle. The maximum radius of the pressure relief zone increases with the drilling diameter.

  2. (2)

    As the deep reaming diameter increases and the deep reaming spacing decreases, the stress concentration in the surrounding rock of the roadway is more significantly transferred to greater depths, making it more likely to form a stress double-peak zone. This leads to a greater effect of pressure relief and stress transfer on the surrounding rock of the roadway, resulting in higher energy dissipation. However, due to the limitation of the overall borehole diameter, changes in deep reaming depth have little effect on the pressure relief and stress transfer in the roadway surrounding rock.

  3. (3)

    From the perspective of energy dissipation, it is concluded that when the deep reaming depth of the borehole is less than 16 m, the pressure relief borehole has little effect on the energy dissipation density of the roadway surrounding rock. At this depth, the action zone of the variable diameter borehole is located deeper within the surrounding rock, where the elastic energy reserves are low, resulting in limited available dissipated energy. At this depth, the area influenced by the variable diameter borehole is located deep within the surrounding rock of the roadway. Due to the low elastic energy reserves in the surrounding rock, the available dissipated energy is limited. As the deep reaming depth increases, when the depth exceeds 16 m, the change in dissipated energy density within the pressure relief zone of the surrounding rock gradually stabilizes. Therefore, the optimal position for the variable diameter borehole is within the peak vertical stress zone of the surrounding rock that has not yet been relieved.