Research on the pressure relief law of diamond beaded rope saw cutting seam: a numerical investigation

Abstract

As a new technology to mitigate the high outburst risk of the low permeability coal seam, it is essential to delve deeper into the law and mechanism of pressure relief associated with the diamond beaded rope saw slotting. The paper presents a numerical calculation model under small size that is based on the superimposed beam theory and the contact surface model. The model is compared with the experimental results of similar models in the laboratory to verify its applicability for simulating the numerical calculation of stress distribution in coal seam cut by diamond beaded rope saw. The study then goes on to investigate the influence of coal seam inclination, working face length, coal seam hardness, and seam advancing distance on the pressure relief effect of diamond beaded rope saw cutting seam under engineering scale. The mechanism of the diamond beaded rope saw cutting seam is also analyzed. The results indicate that the diamond beaded rope saw effectively reduces pressure in low permeability coal seams, with the impact range extending to the slit area. Additionally, stress concentration was observed at the front of the slit. Increasing the inclination of the coal seam, working face length, and advancing distance of the cutting seam enhances the pressure relief effect of the diamond beaded rope saw. The latter two factors’ influence is reflected in the direction along the working face and the direction of mining advance, respectively. The efficacy of pressure relief through this particular method is comparatively better in soft coal than in hard coal. This research is significant in promoting the widespread application of diamond beaded rope saws in the pressure relief of coal seam cutting.

1 Introduction

The continuous increase of coal mining depth in China has made coal seam occurrence characteristics and mining conditions more complex (Zhou et al 2022), and the "three high problems" (high gas, high ore pressure and high ground temperature) are becoming increasingly prominent, which seriously restricts the safe and efficient production of coal (Ding et al 2022). The characteristics of high pressure permeability in deep coal seams make gas extraction challenging (Lin et al 2023). To solve the potential risk of high gas and low permeability coal seam, the use of engineering means to release coal seam gas pressure has become a concern in the industry. One common idea is to destroy the complete structure of coal rock, which will release the stress of the coal seam and provide seepage channels for gas (Xu and Zhao 2022; Mou 2022). Currently, the mainstream coal seam relief technologies include technologies such as advanced drilling, hydraulic cutting and hydraulic fracturing (Lu et al 2009, 2017; Liu et al 2022).

Based on the technological idea of coal seam cutting and pressure relief, researchers are exploring a new method of creating fractures that is more efficient and reliable (Yan et al 2015; Tang et al 2021; Wang et al 2021a, b). Previous studies have demonstrated that the diamond beaded rope saw is effective in cutting through rock masses (Konstanty 2021). The technology for diamond beaded rope saw cutting was first proposed by the British in 1836 and was initially used in the feild like stone cutting (Wang and Xu 2021). With the development of diamond beaded rope saw production technology, more size and better performance diamond beaded rope saws have been provided, which also provides a possibility for applying the diamond beaded cutting technology to the field of low permeability seam.

It is easily for the diamond beaded rope saw cutting seam to create a large, continuous area of pressure relief (Wang et al 2023). Essentially, the mechanism behind this is that the diamond beaded rope saw cuts the coal seam, creating a large area of continuous slot, which is similar to the hollow area that is formed after traditionally mining the protected layer. The difference is that this method can directly act on the current coal seam, which effectively reduces the stress of the construction coal seam, making it more conducive to gas seepage. Using diamond beaded rope saw technology can be a feasible and efficient alternative to traditional protective layer mining techniques and avoid the complexities and high costs involved in the latter. The construction arrangement is illustrated in Fig. 1. A directional drill bit is utilized to drill holes in the coal wall located in front of the working face. The drill bit is controlled to move parallel to the working face and maintain a stable height direction until it pierces through to the roadway of the other side. Then, the diamond beaded rope saw is threaded through the hole to form a complete closed loop that runs along the lane-working face-roadway, with the turning point guided by a guide wheel. The rope saw is rotated at high speed to cut through the coal rock, shortening its length as the cutting seam moves forward. Figure 2a and c provide a visual representation of the working face and corner slit position, while Fig. 2b and d depict the cutting face and the size of the diamond beaded rope saw. As can be seen from the figure, it is envisaged that a large continuous section is formed in front of the working face through this technology, while its cutting surfaces are smooth and flat due to the high-speed cutting action.

Fig. 1

Diamond beaded rope saw slit construction layout diagram a stereogram, b Top view, c side view and d front view

Fig. 2

Diamond beaded rope saw cutting joint construction position and joint characteristics

At present, some scholars have conducted preliminary research in this field. The majority of the experimental data was provided by Li's team, they studied the stress and displacement distribution characteristics of the coal strata above and below the seam grooves with rope saw by using similar model tests (Li et al 2021). The monitoring results show that a small range of fracture zones and bending subsidence zones are formed above and below the seam grooves, and stress reduction zones are formed in the coal body above and below the seam grooves. The team has conducted various research studies, with several members approaching the topic from a unique angle. Tang (2021) and Zhu (2022) used the FLAC3D and UDEC method to examine the diamond bead slit pressure relief law, while Yang (2022) studied the gas migration law of coal seam after cutting. Despite the differences in their approaches, the research results confirm the positive impact of the diamond beaded rope saw on the pressure relief and permeability improvement of coal seam. It is indicates that the diamond beaded rope saw slit pressure relief technology has a good application prospect. However, the academic community lacks a clear understanding of the pressure relief mechanism of diamond beaded rope saw slit, and it is difficult to fully capture monitoring data by means of experimental means alone, and it is challenging to avoid the influence of coal-rock dispersion on the general law. Moreover, the existing numerical simulation methods have several issues, such as unreasonable contact settings and limited study conditions. These problems lead to calculated results that are significantly different from the actual ones, and there is a lack of large-scale engineering data for reference. Therefore, it is essential to utilize accurate numerical calculation methods and account for realistic influencing factors.

. This paper explores the use of numerical simulation to investigate the pressure relief and permeability improvement of low-permeability coal seams in the "three-high" characteristic (Wang et al 2021a, b) area of Pingdingshan, Henan, China. The study begins by constructing a finite difference model of a coal seam with a diamond beaded rope saw slit, based on Coulomb friction contact surface mesh. The accuracy of the numerical calculation model is verified by combining it with laboratory test monitoring data. The study then systematically analyzes the effects of coal seam inclination, working face length, hardness, and slitting advancing distance on the stress distribution of the coal seam. By analyzing the pressure relief law of coal seam under different slit parameters, the mechanism of pressure relief and permeability improvement of coal seam by diamond beaded rope saw is comprehensively and systematically expounded, which provides important theoretical support for further promoting the application of diamond beaded rope saw slit technology in the disaster prevention field of low permeability and high outburst coal seam.

2 Numerical model of diamond beaded rope saw cutting seam

There is no mature model on the numerical calculation of diamond beaded rope saw. Figure 3 shows that the displacement field of the seam with diamond beaded rope saw is different from that of the seam with a large and high groove. If there is only a roadway in the coal seam, the displacement field is mainly caused by roadway deformation, as depicted in Fig. 3a. When the coal seam is cut using the traditional method, the deformation of coal and rock is mainly the normal deformation of the cut due to the large groove height. However, this method has a drawback as the length of the joint is limited, and it is difficult to form a large area of continuous joint surface, as shown in Fig. 3b. In contrast, diamond beaded rope saw cutting seams have distinct characteristics, as illustrated in Fig. 3c. The red line segment in the figure indicates the position of slot. As cutting damages the integrity of coal and rock, it provides displacement space for coal and rock, and the displacement field of coal and rock is composed of normal displacement and tangential slip.

Fig. 3

Coal and rock deformation schematic a roadway deformation, b wide slot deformation, c diamond beaded rope saw cut seam deformation, d slot above and below contact

2.1 Theory of superimposed beam theory

The diamond beaded rope saw seam brings out coal and rock debris in the cutting process, which provides deformation space for the composite beam. Tang et al.'s work suggests that the coal seam and roof can be regarded as layered superimposed structures according to lithology stratification, and the problem of multi-layer composite beams (superimposed beams) under the condition of stress plane strain problem can be resolved (Wang et al 2019). Formula (1) gives the load formed by the layer $n$ of multi-layer composite rock beam on the first layer:

$$\left( {q_{n} } \right)_{1} = \frac{{E_{1} h_{1}^{3} \left( {\gamma_{1} h_{1} + \gamma_{2} h_{2} + \ldots + \gamma_{n} h_{n} } \right)}}{{E_{1} h_{1}^{3} + E_{2} h_{2}^{3} + \ldots + E_{n} h_{n}^{3} }}$$

(1)

where $E_{i} (i = 1,2,3, \ldots ,n)$ represents the elastic modulus of each layer of material, $h_{i} (i = 1,2,3, \ldots ,n)$ represents the height of each layer, and $\gamma_{{\text{i}}} (i = 1,2,3, \ldots ,n)$ represents the bulk density of each layer.

2.1.1 Load boundary condition above coal seam slot

In order to simplify the analysis of the problem, the upper coal seam has been simplified into a double-layer structure composed of coal seam and direct roof (Miao and Liu 2016). The load on the double-layer superimposed beam is illustrated in Fig. 4, with the top of beam 1 being subjected to a uniform load $q$ = $\left( {q_{2} } \right)_{1}$. The beam has a length of $L$, height of $h_{1}$ and $h_{2}$, and elastic modulus and Poisson's ratio of $E_{1} {, }\kappa_{1}$ and $E_{2} {, }\kappa_{2}$, respectively. A rectangular coordinate system has been established with the left side of the fitting place between the upper and lower layers as the origin, the right side as the $x$-axis forward, and the downward side as the $y$-axis forward.

Fig. 4

Double laminated beam structure

The boundary conditions for this force are:

$$\sigma_{1y} = - q, \, \tau_{1xy} = 0 \, \left( {y = - h_{1} } \right)$$

(2)

$$\sigma_{2y} = 0, \, \tau_{2xy} = 0 \, \left( {y = h_{2} } \right)$$

(3)

$$F_{s1} + F_{s2} = \frac{ql}{2} \, \left( {x = 0} \right)$$

(4)

$$F_{s1} + F_{s2} = - \frac{ql}{2} \, \left( {x = l} \right)$$

(5)

The displacement boundary condition is:

$$u_{1} = 0, \, v_{1} = 0, \, u_{2} = 0, \, v_{2} = 0, \, \theta_{i} = 0 \, \left( {x = 0, \, l} \right)$$

(6)

The deformation coordination between the two layers of beams is satisfies:

$$\sigma_{1y} = \sigma_{2y} , \, \tau_{1xy} = \tau_{2xy} = f \cdot \sigma_{1y} , \, v_{1} = v_{2} \, \left( {y = 0} \right)$$

(7)

According to the stress component expression, force and displacement, as well as the stress distribution characteristics of simply-supported beams (Xu 2006), a stress function expression of $\phi_{i}$ has been synthesized to meet the stress coordination equation:

$$\begin{aligned} \phi_{i} = & \frac{{x^{2} }}{2}\left( {C_{i1} y^{3} + C_{i2} y^{2} + C_{i3} y + A_{i4} } \right) \\ & \quad + x\left( {C_{i5} y^{3} + C_{i6} y^{2} + C_{i7} y} \right) \\ & \quad - \frac{1}{10}C_{i1} y^{5} - \frac{1}{6}C_{i2} y^{4} + C_{i8} y^{3} + C_{i9} y^{2} \\ \end{aligned}$$

(8)

Taking Eq. (8) into the stress coordination equation, we obtained:

$$\sigma_{ix} = x^{2} \left( {3C_{i1} y + C_{i2} } \right) + 2x\left( {3C_{i5} y + C_{i6} } \right) - 2C_{i1} y^{3} - 2C_{i2} y^{2} + 6C_{i8} y + 2C_{i9}$$

(9)

$$\sigma_{iy} = C_{i1} y^{3} + C_{i2} y^{2} + C_{i3} y + C_{i4}$$

(10)

$$\tau_{ixy} = - x\left( {3C_{i1} y^{2} + 2C_{i2} y + C_{i3} } \right) - 3C_{i5} y^{2} - 2C_{i6} y - C_{i7}$$

(11)

Equations (9)–(11) are introduced into the stress-displacement equation to obtain the deflection value of the superposed beam:

$$\begin{gathered} v_{i} = \frac{1}{{E_{i} }}\left\{ {\frac{1}{4}\left( {1 + 2\mu_{i} } \right)C_{i1} y^{4} + \frac{1}{3}\left( {1 + 2\mu_{i} } \right)C_{i2} y^{3} + \frac{1}{2}\left( {C_{i3} - 6\mu_{i} C_{i8} } \right)y^{2} } \right. \\ \quad + \left( {C_{i4} - 2\mu_{i} C_{i9} } \right)y - \mu_{i} x^{2} \left( {\frac{3}{2}C_{i1} y^{2} + C_{i2} y} \right) - \mu_{i} x\left( {3C_{i5} y^{2} + 2C_{i6} y} \right) \\ \left. {\quad - \frac{1}{4}C_{i1} x^{4} - C_{i5} x^{3} - x^{2} \left[ {3C_{i8} + \left( {1 + \frac{{\mu_{i} }}{2}} \right)C_{i3} } \right]} \right\} + \xi_{i0} x + v_{i0} \\ \end{gathered}$$

(12)

The undetermined constants $C_{in}$, $\xi_{in}$ and $\nu_{i0}$ ($i = 1,{ 2}$; $n = 1,2...9$) in Eq. (12) can be determined from the boundary conditions and continuous conditions of the mechanical model, and the specific parameters are expressed in Appendix.

2.1.2 Load boundary condition under coal seam slot

The formation of grooves leads to the creation of the structure shown in Fig. 5, as a result of the interaction between the lower bend of coal rock above the grooves and the coal rock beneath them (Zhu et al 2008). The following coal rock is taken as the research object, and the stress area between points $I$ and $J$ is divided into $i$–$j$ sections based on the load type. The maximum stress value in the support zone at both ends is denoted by $k_{1} q$ and $k_{3} q$ respectively, while the stress in the contact zone is represented by $k_{2} q$. The original stress outside the support zone is assumed to be $q$ by default. From the balance relationship of forces, it can be observed that (Xiao et al 2011):

$$\frac{1}{2}(a + b)k_{1} q + \frac{1}{2}(f + g)k_{3} q = Lq - dk_{2} q$$

(13)

$$(a + b)k_{1} + (f + g)k_{3} = 2\left( {L - dk_{2} } \right)$$

(14)

Fig. 5

Coal rock load distribution under the slit

Select a position point $H\left( {x,y} \right)$ and define the angle between the dash line and vertical direction of each segment point as $\theta_{1}$–$\theta_{8}$ from left to right, then the vertical stress component on each segment can be expressed as (Zhang et al 2013):

$$q_{AB} = \frac{{k_{1} qy^{2} \left( {\tan \theta_{1} - \tan \theta } \right)}}{a(z + q)} + q$$

(15)

$$q_{BO} = \frac{{k_{1} qy\left( {\tan \theta - \tan \theta_{3} } \right)}}{b}$$

(16)

$$q_{CD} = k_{2} q$$

(17)

$$q_{EF} = \frac{{k_{3} qy\left( {\tan \theta_{6} - \tan \theta } \right)}}{f}$$

(18)

$$q_{FG} = \frac{{k_{3} qy^{2} \left( {\tan \theta - \tan \theta_{8} } \right)}}{g(y + q)} + q$$

(19)

The tangent values corresponding to each angle can be obtained from the geometric relationship illustrated in Fig. 5. Hence, there is no need to delve into the specifics here. See the Appendix for the expressions of each angle.

2.1.3 Stress distribution in a semi-infinite plane

The stress component at point $H\left( {x,y} \right)$ shown in Fig. 6 is approximately equivalent to solving the semi-infinite in-plane stress under plane strain (Xiao and Che 2018). The three stress components $\sigma_{x} , \, \sigma_{y} , \, \tau_{xy}$ are calculated according to the following formula:

$$\sigma_{x} = \frac{2}{\pi }\int_{\alpha }^{\beta } q \sin^{2} \theta d\theta$$

(20)

$$\sigma_{y} = \frac{2}{\pi }\int_{\alpha }^{\beta } q \cos^{2} \theta d\theta$$

(21)

$$\tau_{xy} = \frac{2}{\pi }\int_{\alpha }^{\beta } q \sin^{2} \theta \cos \theta d\theta$$

(22)

Fig. 6

Definition of the Angle in a semi-infinite plane

Take paragraphs $IA$ and $AB$ as an example, the expressions corresponding to the three components are shown in Eqs. (23)–(28):

$$\sigma_{x}^{(i)} = \frac{q}{\pi }\left[ {\left( {\theta_{0} - \theta_{1} } \right) - \sin \theta_{0} \cos \theta_{0} + \sin \theta_{1} \cos \theta_{1} } \right]$$

(23)

$$\sigma_{y}^{(i)} = \frac{q}{\pi }\left[ {\left( {\theta_{0} - \theta_{1} } \right) + \sin \theta_{0} \cos \theta_{0} - \sin \theta_{1} \cos \theta_{1} } \right]$$

(24)

$$\tau_{xy}^{(i)} = \frac{2q}{{3\pi }}\left[ {\sin^{3} \theta_{0} - \sin^{3} \theta_{1} } \right]$$

(25)

$$\begin{gathered} \sigma_{x}^{(a)} = \frac{{k_{1} qy^{2} }}{\pi a(y + q)}\left[ {\sin^{2} \theta_{2} + \left( {\theta_{1} - \theta_{2} } \right)\tan \theta_{1} - \sin \theta_{2} \cos \theta_{2} \tan \theta_{1} } \right] \\ \quad + \frac{q}{\pi }\left[ {\left( {\theta_{1} - \theta_{2} } \right) + \sin \theta_{1} \cos \theta_{1} - \sin \theta_{2} \cos \theta_{2} } \right] \\ \end{gathered}$$

(26)

$$\begin{gathered} \sigma_{y}^{(a)} = \frac{{k_{1} qy^{2} }}{\pi a(y + q)}\left[ {\sin^{2} \theta_{2} + \left( {\theta_{1} - \theta_{2} } \right)\tan \theta_{1} - \sin \theta_{2} \cos \theta_{2} \tan \theta_{1} } \right] \\ \quad + \frac{q}{\pi }\left[ {\left( {\theta_{1} - \theta_{2} } \right) + \sin \theta_{1} \cos \theta_{1} - \sin \theta_{2} \cos \theta_{2} } \right] \\ \end{gathered}$$

(27)

$$\begin{gathered} \tau_{xy}^{(a)} = \frac{{2k_{1} qy^{2} }}{\pi a(y + q)}\frac{{\left( {\sin^{3} \theta_{1} - \sin^{3} \theta_{2} } \right)\tan \theta_{1} }}{3} \\ \quad - \frac{{2k_{1} qy^{2} }}{\pi a(y + q)}\left[ {\left( {\frac{{\cos^{2} \theta_{1} }}{3} - 1} \right)\cos \theta_{1} - \left( {\frac{{\cos^{2} \theta_{2} }}{3} - 1} \right)\cos \theta_{2} } \right] \\ \quad + \frac{2q}{{3\pi }}\left[ {\sin^{3} \theta_{1} - \sin^{3} \theta_{2} } \right] \\ \end{gathered}$$

(28)

The above theoretical formula summarizes the previous theoretical results based on the experimental results. However, it's worth noting that this formula only applies to horizontal coal seams with a single consideration factor. It's not sufficient to deal with the actual complex situations, such as stress calculation under inclined coal seams and complex lithology geological conditions (Li et al 2014). Therefore, it is necessary to conduct numerical simulation research on this basis to obtain more accurate results.

2.2 Theory of contact surface

According to the details in Fig. 3d, the coal seam has a slit that forms a slot on the coal wall, which remains open. Further to the middle of the coal seam, the self-weight deformation of the coal rock (similar to the bending of a beam) causes the two sides of the slot to gradually fit together and form contact (Wang et al 2013). To simulate the interaction between coal and rock along the joint surface in numerical calculations, a reasonable model is needed. FLAC3D utilizes the embedded contact surface to simulate joints, faults, bedding, and other geological structures. The Coulomb sliding model controls the mechanical behavior of the contact surface, and its mechanical parameters include normal and tangential stiffness, cohesion strength, internal friction angle, shear angle, and more (Li 2020). While contact surfaces can theoretically be created in any region of the model space, usually the generated contact surfaces are based on the existing zone unit surface, triangulating the quadrilateral mesh, and using the triangle mesh vertices as the contact surface mesh nodes. Each contact node has its corresponding representative region, and the area of the region is allocated to the corresponding node according to the weight.

The behavior of the contact surface defined in the software is composed of the contact between the target surface and the point. The size of the contact force is calculated based on the normal penetration of the node and the target surface, as well as the relative shear velocity. The Coulomb shear strength criterion sets the upper limit of the shear force on the joint. When the limit of shear force is reached, the normal and tangential stiffness, tensile and shear bond strength, and shear expansion angle all contribute to an increase in the normal stress of the target surface.

The normal and tangential forces of the elastic contact at time $t + \Delta t$ are calculated by Eqs. (29) and (30):

$$F_{n}^{(t + \Delta t)} = k_{n} u_{n} A + \sigma_{n} A$$

(29)

$$F_{si}^{(t + \Delta t)} = F_{si}^{(t)} + k_{s} \Delta u_{si}^{(t + (1/2)\Delta t)} A + \sigma_{si} A$$

(30)

where $F_{n}^{(t + \Delta t)}$ and $F_{si}^{(t + \Delta t)}$ represent the normal force and tangential force at time $t + \Delta t$ respectively; $u_{n}$ and $\Delta u_{si}$ correspond to absolute normal penetration and relative shear displacement increment, respectively. $\sigma_{n}$ and $\sigma_{si}$ denote the normal stress and tangential stress of the stress initialization interface, respectively. $k_{n}$ and $k_{s}$ are normal and tangential stiffness respectively. $A$ represents the area of the associated area of the node.

For inelastic contact, FLAC3D provides multiple contact behaviors (Shan et al 2018). The first is bonded contact, where the interface is considered to be in a binding state when the interface force is less than the binding strength, and the binding contact breaks when the binding strength is exceeded. The second is sliding under binding conditions, that is, has normal binding behavior and allows tangential yield and relative sliding but doesn't allow contact surface separation. The third is unbond contact, where the contact surface behavior is determined by internal friction angle, cohesion force, and normal tangential stiffness. In this case, the interface cannot bear the tension, and the tangential force is zero when there is no normal extrusion at the interface. It seems that the third contact situation is more applicable for diamond beaded rope saw cutting cases.

The Coulomb shear strength criterion limits the shear force limit by the following formula:

$$F_{{\text{smax }}} = cA + \tan \phi \left( {F_{n} - pA} \right)$$

(31)

where $c$ represents the cohesion strength; $\phi$ is the internal friction angle; $p$ denotes the pore water pressure. Once $F_{s} > F_{{\text{smax }}}$ is satisfied, the contact surface slides. As the sliding process continues, the tangential displacement will lead to an increase in the effective normal stress at the node.:

$$\sigma_{n} : = \sigma_{n} + \frac{{\left| {F_{s} } \right|_{o} - F_{{{\text{smax}}}} }}{{Ak_{s} }}\tan \psi k_{n}$$

(32)

where $\psi$ is the shear swelling angle; $\left| {F_{s} } \right|_{o}$ represents the tangential stress before updating the normal stress.

To demonstrate the iterative calculation process of parameters involved in this model in the software, an example of a solid unit of a double-layer superimposed beam with contact surface was computed. A technical roadmap was created based on the details, as shown in Fig. 7.

Fig. 7

Force and displacement transfer process of solid unit and contact surface

2.3 Model verification

To compare with existing experimental data and verify the rationality of the calculation model, we refer to the indoor model test of diamond beaded rope saw slit conducted by Li et al. (2021), as illustrated in Fig. 8c. The model size is 2500 mm × 200 mm × 1800 mm, with a slit length of 1400 mm (yellow dotted line in Fig. 8c) and a diamond yarn diameter of 2.2 mm. Figure 8a displays the rope saw's location in the experimental model. Drill holes in the inlet and return air lane at the appropriate position first, then insert the rope saw through the hole, and wrap around the entire working face through the roadway, which forms a closed quadrilateral. Guide pulleys are set at the angle of the rope saw, and the end of the rope saw is wound around the tractor and pulled by the motor. Figure 8b shows the cut slit formed by the rope saw and the crack resulting from the cut.

Fig. 8

Laboratory experiment model of cutting seam with diamond beaded rope saw a device layout, b monitoring point arrangement

A numerical calculation model of the same size as the indoor tested one was constructed to compare its results with the testing data and demonstrate the reliability of the model calculation. The thickness and mechanical properties of rock strata are consistent with those presented by Li et al., as seen in Fig. 8d. In order to further promote the application of the model, we increased its size to 60 m × 50 m × 30 m and added complexity to account for the influence of roadway structure and support on calculation results. The green and blue parts in the figure depict the upper rock mass and the lower rock mass respectively. The gray part represents the coal seam, and the purple part represents the roadway support. The coal seam has a thickness of 2.5 m, the bottom section of the roadway has a width of 5 m, and the top and bottom have a height of 3.6 m, with the support having a thickness of 0.2 m, as shown in Fig. 9.

Fig. 9

Model verification schematic and grid division a Model ensemble, b front view c local zoom around the roadway

2.3.1 Reliability analysis

Figure 10a illustrates the relationship between the displacement of the model and the minimum principal stress during the process of slit advancement. As the slit distance increases, the subsidence area at the top of the model and the subsidence displacement both increase. Additionally, the relief area of the slit also expands with the increase in slit distance, leading to stress concentration at both ends of the slit. The distribution of vertical displacement and minimum principal stress is plotted in Fig. 10c and e. The subsidence of coal and rock above the slit follows a distribution law where it is larger in the middle and smaller on both sides, and it decreases with the increase of monitoring distance. The pressure relief amplitude in the center of the slot is greater than that on both ends. Additionally, the closer the slit position, the more significant the pressure relief effect becomes. Although the simulation results are not entirely consistent with the laboratory test data, the variation pattern of the data aligns with the experimental and calculation results of Li et al. (shown in Fig. 10b, d and f). This indicates the rationality of the simulation results to some extent.

Fig. 10

Comparison with laboratory experiment results and simulation results of Li et al.

2.3.2 Stress change during slotting advance

As per the construction procedure of seam cutting pressure relief, it can be categorized into two parts: roadway driving and seam cutting propulsion. The seam cutting propulsion process can be characterized by seam cutting distance. Figure 11a–d respectively show the slit position under different slit distances, where the red arrow in Fig. 11b indicates the slit's advancing direction. The slit advancing distance is defined as shown in Fig. 11c, which is calculated in four stages according to the slit distances of 5 m, 15 m, 25 m and 35 m.

Fig. 11

Slit propulsion process a 5 m, b 15 m, c 25 m, d 35 m

The stress distribution in the coal seam and upper and lower rock mass can be seen along with the process of slotting from Fig. 12. To more comprehensively reflect the stress distribution law in coal rock mass, three sections of y = 10 m, 25 m and 40 m were intercepted, and three stress contours of $\sigma_{1}$ = 1.0 MPa, 1.1 MPa and 1.2 MPa were selected to reflect the stress variation trend directly. When the slit length is 5 m (Fig. 12a), none of the sections are affected by the slot, hence the stress contours of the three sections do not change much compared to the initial state. The blue marks in the figure show the states of the three sections. With the slit length of 15 m (Fig. 12b), the y = 10 m section is affected, causing the stress contours of this section to move down indicating a stress reduction, as shown by the green arrow. However, the sections at y = 25 m and 40 m have not been affected, that is, remain in stress equilibrium state. As the slit length reaches 25 m (Fig. 12c), the slit leading edge is at y = 25 m. Here, due to the phenomenon of stress concentration at the slit tip, the stress in this section will increase, but the influence range is small and limited to the near field area of the tip. In addition, the stress in the area between the leading edge and the trailing edge is released, and the area outside the leading edge is in a state of stress equilibrium. When the slit length reaches 35 m (Fig. 12d), the influence range of the slit includes the first two sections but not the last one, causing the stress of these sections to show a decreasing trend while the stress of the third section still maintains equilibrium.

Fig. 12

The principal stress nephogram varies with the slit advanced distance

In order to quantitatively analyze the influence of slit length on the pressure relief effect of coal and rock mass, the principal stress of the propulsion direction model is monitored. According to the monitoring results shown in Fig. 13, the initial ground stress of the monitoring position is 1.0 MPa when no roadway is excavated. After the roadway is excavated, the principal stress of the monitoring position slightly increases to 1.05 MPa, and this stress state is considered as a reference point for subsequent analysis. The dashed line in the figure indicates the position of the leading edge of the slit. It is observed that when the slit length was 5 m, the stress in the range of 0–5 m is lower than the initial stress (1.05 MPa), with the lowest stress value being about 0.85 MPa, resulting in a pressure relief amplitude of 19.0%. However, within a certain range near the leading edge, the stress is greater than the initial stress, indicating that there is a phenomenon of stress concentration at the slit tip, and the range of the stress concentration zone shows a smooth downward trend, gradually transitioning to the stress equilibrium zone. The transition area is about 8–20 m, and the maximum stress is about 1.15 MPa, with an increase of 9.5%. When the slit length is 15 m, 25 m, or 35 m, the maximum pressure relief range is between 9.5 and 12.4%, and the stress transition zone is approximately symmetric about the slit leading edge. It can be concluded that with the increase of slit length, the area of pressure relief area gradually increases, the stress concentration area moves with the position of the slit front, and the stress in the unslit area basically maintains the initial state.

Fig. 13

Monitoring of principal stress above roadway at different advancing stages

2.3.3 Comparison with laboratory test data

To ensure a direct comparison with the test data, monitoring lines were established at locations 0.5 m, 1.5 m, 2.5 m and 3.5 m below the cut suture, The monitoring cross section was designated as y = 25 m, as demonstrated in Fig. 14.

Fig. 14

Position of monitoring lines above and below the roadway

The monitoring results of principal stress can be seen in Fig. 15. As shown in Fig. 15a, the stress changes of each monitoring line above the roadway are illustrated before and after the slit. The dashed line in the figure represents the principal stress value before slit, and the solid line represents the principal stress value when the slit advanced distance is 35 m. According to the figure, the stress at each monitoring position above the roadway decreases after the slit cutting. The minimum stress at 0.5 m above the roadway decreased from 1.06 to 0.99 MPa, while the minimum stress at 3.5 m above the roadway decreased from 0.99 to 0.90 MPa. Figure 15b shows that the monitoring value under the slit also decreased, and the reduction amplitude was not much different from that above. The stress distribution showed a law of small in the middle and large on both sides, which was basically consistent with the laboratory test results.

Fig. 15

Main stress monitoring results (slit distance 35 m) a above, b below

2.3.4 Slit position independence

In order to study the effect of seam position on the test results, three kinds of seam cutting conditions of upper, middle and lower coal seams were calculated. These conditions were calculated based on the bottom boundary of the coal seam, with the distance between the three slit positions and the base plane being 0.25 times, 0.5 times, and 0.75 times the thickness of the coal seam, respectively, as shown in Fig. 16a–d.

Fig. 16

Different seam position of coal seam a upper, b middle, c lower, d local amplification

The principal stress values of the monitoring line 0.5 m and 3.5 m above the slit are plotted in Fig. 17, where the black line represents the stress when the slit is not cut. It can be seen that there is minimal difference in the stress of the three different slit positions after slitting, and the monitoring values almost coincide. In the scope of the project, it can be considered that the position of the slit has little influence on the pressure relief of the slit and can be ignored.

Fig. 17

Influence of different seam locations on stress distribution (y = 25m)

3 Numerical simulation of diamond beaded rope saw cutting

3.1 Calculation model settings

3.1.1 Model size and parameter assignment

The physical model depicted in Fig. 18a was adopted to accurately represent the construction scene of diamond beaded rope saw cutting. The outer light gray area in the figure represents the outer rock mass, while the inner dark gray structure is the roadway. The presence of the roadway causes the coal body in the advancing direction of the working face to form a large-area "pillar" structure. The red part is the joint surface of coal rock formed after diamond beaded rope saw cutting. The coal rock on both sides can embed, separate and slide along the contact surface. The numerical calculation model shown in Fig. 18b–e has a size of 500 m × 500 m × 300 m. The height of the basic top of the coal seam (light blue part in the figure) and basic bottom (dark blue part in the figure) is 145 m, and the thickness of the direct top of the coal seam (light red part in the figure) and direct bottom (green part in the figure) is 4 m. The thickness of the coal seam (the gray and black part in the figure) is 2 m, and the roadway is located in the coal seam, with a section width of 3 m and a height of 2 m. The length of the working face is 200 m.

Fig. 18

Computational model size and meshing a physical model, b overall meshing, c roadway and working face, d division of rock strata and e roadway section

Due to the complex distribution of actual coal seam in the stratum, there are twists and turns, uneven thickness, unequal coal quality, which makes it unfavorable to the regularity study in the initial stage of technical demonstration. To simplify the problem, the homogeneity assumption of coal seam is made, assuming that the coal seam in the study area has the same thickness, uniform mechanical properties, and no natural defects. Similar assumptions are adopted for the top and bottom of coal seam. The mechanical properties and thickness of coal seam and roof and floor are different, reflecting the clamping effect of roof and floor on coal seam. It is divided into five layers from the top down: basic top, direct top, coal seam, direct bottom, and basic bottom. The lithologic parameters of coal seam and roof and floor in Table 1 are derived from the typical test parameters provided by the State Key Laboratory of China Pingmei Group.

Table 1 Lithology grouping and parameter assignment

3.1.2 Coal seam inclination and slit parameters

To investigate the impact of coal seam inclination on the pressure relief effect of the diamond beaded rope saw, the research scope was expanded beyond the common inclination range of 0–20°, with coal seam inclinations $\alpha$ of 0°, 15°, 30° and 45° selected for the study, as depicted in Fig. 19. The study also examined the stress distribution of the coal seam under different slit advancing distances $d_{s}$, namely 50 m, 100 m, 250 m, and 350 m. To maintain consistency, the angle between the seam surface and the horizontal plane is set to be consistent with the inclination angle of the coal seam. The position of the study was located in the center of the coal seam, with a vertical distance of 1 m from the upper and lower boundaries of the coal seam.

Fig. 19

Different coal seam dip angle and slot position

For the parameters of the contact surface, it's recommended to refer to the research of Li (2020). To replicate the tangential slip and normal separation of the contact surface, the internal friction angle is set to 0, while the tangential stiffness and tensile strength are assigned relatively small values. Additionally, the normal stiffness is assigned a significantly larger value to avoid excessive normal extrusion penetration of the contact surface. All parameters of the contact constitutive model are shown in Table 2.

Table 2 Contact surface parameter setting

Considering practical engineering requirements, the working faces with short, medium and long lengths ($L_{w}$ = 150 m, 200 m, 250 m) are selected for testing. Additionally, two control groups (Hard coal 1 and Hard coal 2) were set to consider the influence of coal rock hardness on the pressure relief effect on the basis of the original group (Soft coal). The hardness relationship is: Hard coal 2 > Hard coal 1 > Soft coal. Test group Settings can be find in Table 3.

Table 3 Test group setting

3.2 Analysis of factors affecting the pressure relief law

3.2.1 Influence of coal seam inclination angle

Figure 20a–d shows the stress distribution of coal seam under different coal seam inclination angles. It seems that slit cutting can significantly reduce the near-field stress in the cutting area because it damages the integrity of coal and rock mass, increases the displacement space of coal and rock mass, and helps the stress transfer to the depth. It can be observed that as the dip angle increases from 0° to 45°, the stress release effect caused by the slit becomes more and more obvious, indicating that the mutual sliding of coal and rock masses along the contact surface on both sides of the slit is the main cause of stress redistribution. The larger the dip angle, the larger the slip trend and the more obvious the pressure relief effect. Due to the tip effect, stress concentration occurs on one side of the slit tip area.

Fig. 20

Distribution of principal stress with coal seam inclination (y = 100 m) a 0°, b 15°, c 30° and d 45°

In order to better reflect the influence of the inclination angle on the stress distribution around the slot, a monitoring line was set at a position 0.5 m above the roadway, as shown by the dotted line in Fig. 20. The stress detection results are depicted in Fig. 21. It is observed that when $\alpha = 0^\circ$, the stress pressure relief amplitude is maintained at approximately 1.9%; As $\alpha$ increases to 15°, the pressure relief amplitude is about 6.8%; Similarly, when $\alpha$ = 30° and 45°, the pressure relief amplitude is about 12.8% and 18.2%, respectively, indicating that the pressure relief effect improves with an increase in the coal seam inclination. The stress concentration is observed at the slot tip, and it was found that the performance of stress concentration is related to the inclination angle. When the seam is horizontal, the monitoring line shows that the stress at both ends of the slot is symmetrical, and the stress increases first from the outside to the inside and then decreases, indicating that the coal-rock interaction on both sides of the seam surface is mainly normal behavior. However, when the coal seam has a certain inclination angle, the stress at both ends shows an opposite trend. In such a case, the stress at one end increases sharply, while the stress at the other end decreases. This happens because the coal-rock interaction on both sides of the joint surface is mainly tangential sliding, and the tip stress is distributed "windmill" about the center of the slit. As the monitoring line is arranged on one side of the joint surface, the peak value of the monitoring curve also shows central symmetry.

Fig. 21

Influence of coal seam dip angle on pressure relief amplitude

The experiment set up monitoring points at different positions above the roadway of the horizontal coal seam to eliminate their influence on the results. The distance of monitoring lines from the top of the roadway is 0.5 m, 10.5 m, 20.5 m, 30.5 m and 40.5 m, respectively. Figure 22 shows that the pressure relief amplitude is distributed in a way that conforms to the stress balance in the far field (in the green dashed line frame), stress concentration at the tip (in the red dashed line frame), and stress release in the middle (in the blue dashed line frame). The monitoring law remained consistent despite the different monitoring positions, with the tip effect more pronounced closer to the top of the roadway. The pressure relief amplitude reached 5.2% at the upper 0.5 m position, and about 2.1% at the 40.5 m position. However, the difference of pressure relief amplitude in the middle was not significant, with both positions showing about 2.0%.

Fig. 22

Pressure relief amplitude of different positions above the horizontal coal seam roadway

Figure 23 depicts how the inclination angle affects the pressure relief effect of coal seam. In the case of a horizontal coal seam, the direction of the principal stress is perpendicular to the direction of the coal seam. The red area in the figure represents the coal pillar located behind the working face, which mainly bears the pressure. The immediate area above and below the coal pillar (yellow area in Fig. 23) can be considered a "roof and floor" structure that transmits stress to the coal pillar. The “roof and floor” structure will bend and deform under the influence of ground stress. When the coal pillar is intact, the middle part of the coal pillar expands under pressure. However, the degree of deformation is limited due to the constraint of the complete coal rock, resulting in the accumulation of a large amount of strain energy in the coal pillar, as shown in Fig. 23a. When the slit is connected, the deformation space is generated in the middle of the coal pillar, and the strain energy of coal and rock is released. On the other hand, when the slit is connected, the deformation space is created in the middle of the coal pillar, which releases the strain energy of coal and rock. At this point, the main displacement is the mainly normal in coal, while a small part of the transverse shear displacement is also found (Fig. 23b).

Fig. 23

Difference of pressure relief mechanism between horizontal and inclined coal seams with diamond beaded rope saw

In the case of an inclined coal seam, there is a relative dislocation trend in the “roof and floor” structure due to the angle between the direction of the principal stress and the strike of the coal seam when the seam is not cut. In such a situation, the complete coal pillar will accumulate shear strain energy under the action of torque, including some compressive strain energy, as shown in Fig. 23c. After the slit is created, the coal pillars on both sides of the slit move relative to each other, which releases significant shear strain energy and compressive strain energy along with the normal relative displacement. Simultaneously, certain regions outside the roadway (shown in purple in the Fig. 23) experience shear displacement and accumulate shear strain energy, resulting in local stress concentration (Fig. 23d). In general, the pressure relief of inclined coal seams involves a more extensive potential release process of shear strain energy, which is the fundamental difference between the pressure relief mechanism of inclined and horizontal coal seams.

3.2.2 Influence of working face length

Figure 24a–c demonstrates how the pressure relief effect of the slit is affected by the length of the working face. Specifically, the length of the working face being 150 m, 200 m, or 250 m has a direct impact on the length of the slit of the parallel working face, which is visually manifested as an increase in the pressure relief range in the direction of the parallel working face since the slit runs through the entire working face.

Fig. 24

Distribution of principal stress with length of working face (y = 100 m) a 150 m, b 200 m and c 250 m

The influence of the length of the working face on the pressure relief amplitude is analyzed from a quantitative point of view. Figure 25 shows the monitoring curves of pressure relief at different slit lengths of working faces. It is observed that when the slit length $L_{w}$ = 150 m, the pressure relief zone of the parallel working face ranges from − 75 to 75 m. Similarly, this interval increases to − 100 to 100 m and − 125 to 125 m when $L_{w}$ is 200 m and 250 m, respectively. The minimum pressure relief amplitude is 2.26% when the length of the working face is 150 m, and this value is 1.92% and 1.73% at 200 m and 250 m, respectively. Therefore, an increase in the length of the working face results in a slight decrease in the pressure relief amplitude in the middle of the working face. However, considering the increase of the slit range, the negative effect of the reduced pressure relief amplitude is offset.

Fig. 25

Influence of working face length on pressure relief amplitude

3.2.3 Influence of coal seam hardness

The model is assigned regarding the mechanical parameters of hard and soft rock respectively to quantitatively analyze the influence of coal seam hardness. The initial coal rock parameters are "soft coal", and the parameters of "hard coal 1" and "hard coal 2" are shown in Table 4. The research object is the model of coal seam inclination of 15°, and the stress relief amplitude of the parallel working face section is monitored, as shown in Fig. 26. It is observed that the pressure relief amplitude in the middle of the slit decreases with the increase of the hardness of coal and rock. The pressure relief amplitude in soft coal was 6.9%, and that in hard coal 1 and hard coal 2 was 6.7% and 6.3%, respectively. Another influence of the hardness of coal and rock was reflected in the position of the slit tip, which reached 65.6% and 64.1% in "hard coal 1" and "hard coal 2. The reason is that the small elastic modulus and strong rheology of soft coal results in more significant deformation in the direction of unrestricted freedom after slit cutting compared to hard coal, making it more conducive to stress redistribution. The numerical simulation results are also consistent with practical engineering practice since soft coal is more likely to break during the cutting process, which further increasing the internal stress release rate.

Table 4 Soft and hard coal rock parameter difference

Fig. 26

Influence of soft and hard coal on pressure relief amplitude

3.2.4 Influence of slotting advance distance

To intuitively understand the stress evolution process of coal and rock mass in the process of advancing, slit length directly related to the process of seam advancing is selected as the research factor, and the principal stress cloud maps of coal seam advancing direction are drawn in Fig. 27a–f. The model boundary is represented by the boundary line of the cube, the location of the roadway is shown by the internal black line, the leading edge of the slit is represented by the red line segment, and the stress release area is in the oval box of the blue dotted line. In Fig. 27a, the stress distribution in the formation is uniform and conforms to the gradient distribution in the depth direction since the roadway has not yet been formed. When the roadway is driven, a stress disturbance area is formed in the vicinity of the roadway due to the roadway's pressure relief effect, as shown in Fig. 27b. Figure 27c shows the stress distribution when the slit distance is 50 m. It can be found that within the range of the slit leading edge, the stress contour appears a downward bending trend, indicating that the stress within the slit range is effectively reduced. As the slit distance continues to increase (150–350 m), the range of stress release zone increases and always remains between the leading edge and the trailing edge of the slit, as shown in d–e of Fig. 27.

Fig. 27

The principal stress in advancing direction of horizontal coal seam changes with advancing process a before excavation, b after excavation, c slot 50 m, d slot 150 m, e slot 250 m and f slot 350 m

Figure 28a–d displays the stress distribution of the $xoz$ cross section of different coal seam inclination models in various construction stages. The figures clearly demonstrate that seam cutting can lead to a significant reduction in stress in the seam zone, resulting in a noticeable "drop" in the stress monitoring curve. It is interesting to note that the stress reduction of coal seam with inclination angle is greater than that of horizontal coal seam. Furthermore, it is verified that the pressure relief of coal seam is mainly caused by the dislocation between coal seams.

Fig. 28

Monitoring of principal stress in parallel working face direction at different slotting angles (y = 250 m) a 0°, b 15°, c 30° and d 45°

The stress monitoring results of the horizontal coal seam and 30° inclination coal seam along the slit advance direction ($yoz$ cross-section) are shown in Fig. 29. It can be found from the figure that the initial stress at the monitoring position is approximately 15.2 MPa, and the sudden drop of stress occurs at the roadway, with the lowest value of about 8.0 MPa. With the advance of seam cutting, the average stress in the seam zone of the horizontal coal seam is about 14.9 MPa, while it is 13.5 MPa in the coal seam with a 30° inclination angle. Notably, the stress concentration occurs at the leading edge of the slit, and the maximum value in the horizontal seam and 30° seam is 15.8 MPa and 17.3 MPa, respectively. Figure 29 better shows the spatial and temporal distribution characteristics of the evolution of stress in coal and rock mass with the advancing process of the slit. It can be considered that rule "where the diamond beaded rope saw arrived, where the stress released" is determined to a certain extent by these findings.

Fig. 29

Horizontal and 30° inclination seam thrust direction principal stress monitoring (x = 0 m)

3.3 Pressure relief mechanism of diamond beaded rope saw cutting seam

Figure 30 illustrates the distribution of displacement vectors of both horizontal and inclined coal seams before and after the slits. It can be seen from the figure that for horizontal coal seams without slits, the stress distribution of coal and rock from top to bottom takes the shape of horizontal steps. Only a small range of displacement deflection exists around the roadway, and the internal stress distribution of coal and rock also follows the gradient distribution of the combined action of dead weight and the pressure of the upper layer. However, when the seam is cut, the extraction of part of the coal and rock debris causes a certain deformation space to be generated in the height direction of the seam. The coal and rock on the top of the seam form a structure similar to a "beam with simple supports at both ends". The "beam" rotates around the simple fulcrum at both ends, thereby resulting in downward deflection in the middle of the beam, and the whole forms a downward arch. The coal rock in the lower part of the slit arches upward due to the stress compression on both sides, and the deflection is smaller than that of the upper rock. The upper and lower rock masses come into contact through deflection, and normal embedding and tangential slip can occur along the contact surface. The extra displacement space generated by the slit leads to the stress release of the coal rock mass at the joint face, and the stress at the simple support end is transferred to the deep to maintain the static stability of the new structure.

Fig. 30

Displacement vector distribution before and after seam cutting of coal seam

It is worth noting that when dealing with inclined strata, the displacement distribution of the coal seam is different from that of horizontal coal seam. Due to the existence of a dip angle, the initial displacement vectors distribution of coal seam without slit are inclined towards the dip direction rather than being completely gradient along the vertical axis. However, if the displacement vectors are projected along the vertical direction, it still approximates the gradient distribution in the vertical direction, and the initial ground stress is the gradient distribution in the vertical direction. Furthermore, when the coal rock is cut and separated, the upper rock mass produces the sliding force along the seam surface under the action of self-weight, while the lower rock mass produces sliding along the seam surface under the push of the bottom and lateral ground stress. During this process, the normal and tangential deformation along the seam surface work together to relieve the pressure of the coal rock mass.

Further, the displacement at the local position of the slit was analyzed and the displacement vector distribution at the middle and tip of the horizontal seam was captured, as depicted in Fig. 31. It can be found that the coal rock in the middle of the slit has a large distance between two adjacent displacement gradients in the initial state, indicated by the dashed line in the figure. However, this distance decreases significantly after the slit, indicating that the two sides of the slit surface move in the opposite direction and embed each other. At the slit tip, due to the influence of roadway deformation, the displacement contours of two adjacent gradients bend to one side of the roadway, and the displacements on both sides of the roadway are symmetrically distributed. After slitting, the linear distance of the two adjacent gradient displacements shrinks due to the deformation of coal and rock along the normal direction in the inner side of the roadway. This forms a smooth transition of both sides of the roadway, as shown by the red arrow in the figure. It is also observed that apart from the horizontal compression, a stress concentration area tends to form at the outer corner of the roadway.

Fig. 31

Displacement vector distribution in the middle and tip of horizontal seam

Figure 32 shows the distribution of displacement field before and after seam cutting of inclined coal seam. Due to the existence of dip angle, the displacement distribution at both ends of the slot is no longer axially symmetrical. As a result, the distribution is divided into three parts: the upper tip, middle tip, and lower tip. Before cutting, the displacement vectors of the upper and lower rock mass in the lower tip are in the lower right direction (red oval dotted line frame in the figure). After the slit is cut, the displacement vectors of the upper rock mass are more inclined, while the lower rock mass is pushed to produce a reverse displacement trend. This generates a stress concentration area on the outside of the roadway, extending in the downward counterclockwise direction. In the middle of the seam, the direction of the coal and rock displacement vectors are the same in the upper and lower parts of the seam before slitting, and after cutting, the rock mass below the slot has a tendency to move up to the left along the seam surface. The cheaper angle of the displacement vector closer to the seam surface is slightly smaller than that at the deep part, indicating that the seam surface friction has a clamping effect on the displacement of the coal and rock mass. Although this clamping effect exists, the fracture is beneficial to the coal seam pressure relief at this location when compared with the deformation of rock mass in the initial state. For the upper tip, the displacement vectors of the lower coal and rock mass after the slit deflected to the upper right and turned obviously at the approach of the tip. At this time, the coal and rock mass at the upper right of the roadway were squeezed, so the stress concentration area outside the roadway extended counterclockwise to the upper right.

Fig. 32

Displacement vector distribution in the middle and tip of seam of inclined seam

4 Discussion

In order to evaluate the similarities and differences with related research work, we referred to Tang's paper (2021). This paper focuses on the study of horizontal coal seams, where the advancing process of rope saw cutting coal seam is divided into 7 times, each advancing distance being 270 mm, and the next advancing is carried out after the state of the previous coal seam is stable, with a total of 1890 mm. The boundary condition type is the same as in this article (values are different). The test results show that in the early stage of the advance of the ropesaw slotting face, when the ropesaw slotting face did not exceed the position of the sensor on the stress monitoring line, the stress in the coal above and below the slot where the measurement point was located increased to different degrees (that is, after the first advance of the ropesaw slotting seam, the internal stress in the coal body at 0.5 m below the slot, 0.5 m above and 1 m above the slot increased). When the advancing position of the rope saw slit exceeds the position of the sensor on the stress monitoring line, there are different degrees of stress reduction in the coal body above and below the slot where the measurement point is located (the internal stress at the corresponding position is reduced), which is consistent with the calculation results in Sect. 3.2 of this paper.

The results of Tang's test data indicate that the internal stress at the corresponding position decreases from 18%, 22%, and 2% in the second advance to 43%, 55%, and 32% in the seventh (Fig. 33). This is higher than the calculated results in this paper, which could be due to the impact of the slit height of the indoor model test on the results. The reference paper notes that the bending deformation space of the upper coal rock is ample, resulting in different pressure relief amplitudes.

Fig. 33

Laboratory test stress monitoring a cutting start position, b model center

In fact, a phenomenon called the gas lock effect is observed in low-permeability coal seams, as depicted in Fig. 34a. Due to high gas stress, the coal and rock particles on either side of the potentially weak surface get closely occluded like a "sawtooth", making it difficult for them to slide towards each other, with no space for stress release inside the coal and rock. However, after cutting with the diamond beaded rope saw, a gas seepage channel is formed inside the coal and rock, as illustrated in Fig. 34b. This greatly reduces the gas pressure near the joint surface, and the pore pressure inside coal and rock as well as the biting force of the contact surface drop sharply, which is more conducive to the stress transfer to the depth of coal seam. Therefore, this method of pressure relief may yield better results in actual coal seams than in laboratory tests or numerical simulations.

Fig. 34

Influence of gas locking effect and gas release on coal seam pressure relief a before slitting, b after slitting

In terms of numerical simulation results, we referred to the calculation methods of Tang (2021) and Zhu (2022). FLAC3D and UDEC were utilized to examine the stress distribution of diamond beaded rope saws cutting. The analysis revealed a conclusion consistent with Sect. 3.2 of this paper. The authors believe that when the cutting advance length is small, a pressure relief zone is formed in the coal strata above and below the slot. With the cutting horizontal plane of the rope saw as the symmetry center, the pressure relief zone presents a "U-shaped" symmetrical distribution (Fig. 35). With the increase of the advancing distance, the scope of the pressure relief zone of the coal seam around the slot increases significantly, and the pressure relief effect at both ends of the slit is better than that in the middle. The calculation results showed a small range of stress recovery zone is formed in the middle of the pressure relief zone because of the joint and slot top plate contact with the bottom plate. However, such a stress recovery zone was not found in this paper, and the existence of stress recovery zone was not confirmed in the test. In contrast, the results of this paper show that the stress of the bottom part is smoothly transitioning with the advance of the slit, and the pressure relief amplitude is basically stable. The reason may be that the contact surface is used in the calculation model in this paper, and the grid nodes on both sides of the joint surface are independent (there is no common nodes), and direct stress conduction does not occur, so there is no phenomenon of stress concentration at the common nodes. Our results also correspond with the experimental results, strongly showing the superiority of the contact surface model in calculating this kind of problem.

Fig. 35

Location of stress recovery zone a by FLAC3D and b by UDEC

To summarize, it is suggested that future numerical simulations should combine the benefits of the reference paper and this paper. On one hand, the impact of seam height direction size should be taken into account to ensure that the pressure relief amplitude is as close to the laboratory test data as possible. On the other hand, establishing contact surfaces on both sides of the slot has prevented the occurrence of common nodes in the grid division process, which can compromise the accuracy of the numerical simulation.

5 Conclusion

The main conclusions of this paper are as follows:

• 1. The method based on superposition beam theory and contact surface model has good applicability in numerical calculation of stress distribution in coal seam with diamond beaded rope saw. The results are consistent with the results of similar indoor model tests.

• 2. Diamond beaded rope saws can effectively relieve pressure in low permeability coal seams. The stress distribution of each monitoring position in the parallel slit direction is small in the middle and large on both ends. The amplitude of stress drop increases with the monitoring distance.

• 3. The mechanism of diamond beaded rope saw cutting slit pressure relief involves cutting a coal rock which is held together by shear and cohesion forces, resulting in two coal rocks held together by friction. This increases the flexibility of the coal rock and reduces dislocation resistance, leading to a redistribution of internal stress. Therefore, the pressure relief of the diamond beaded rope saw is improved by increasing the inclination of the coal seam in the range between 0° and 45°. In addition, soft coal is also found to have a better pressure-relief effect than hard coal.

• 4. The influence of the length of the working face and the advancing distance of the cutting seam on the pressure relief effect of the coal seam is reflected in the direction along the working face and the advancing direction, respectively. With the advance of slotting, the stress in the coverage area of slotting tends to decrease. However, there is a local stress concentration in the front of slotting, which causes the stress in that area to shift to the two sides of the roadway and the deep behind the working face.

Appendix

The coefficients of Eqs. (9)–(12) in Sect. 2.1.1 are shown in Table 

Table 5 Double layer laminated beam coefficient

5.

The geometric relation conversion formulas of each Angle in Sect. 2.1.2 are shown in Table 

Table 6 Conversion of angular geometric relations

6.