Introduction

China is rich in coal resources, but due to its location in the combination of the Eurasian plate, the geological conditions of coal seam endowment are complicated, especially in Guizhou in the southwest region, where the geological structure is complex, with many fault formations in the mining area, and there are many coal seams with high gas and coal and gas protrusion, making it difficult to mine the coal seams1,2,3,4,5,6. The existence of faults cuts the integrity of coal seams, and the superposition of mining stress and tectonic stress in the process of coal seam mining disrupts the original stress distribution law of coal and rock seams, especially the fault activation caused by mining and the tectonic coal gas endowment and other multi-physical factors coupled to increase the difficulty of mining coal seams7,8,9,10,11,12. In the process of mining coal seams endowed with faults, as mining enters the area affected by faults, the mining stress field and the fault tectonic stress field are coupled and superimposed on each other, which disturbs the normal distribution of the roadway rock stress and induces a variety of hidden hazards such as abnormal mine pressure, abnormal gas outflow and so on, which increases the risk of accidents in coal mining in the area of faults, and has an important impact on the safety of coal mine mining.

It can be seen that the fault structure is a disaster-causing factor that cannot be ignored in the mining and extracting activities, and many scholars at home and abroad have carried out in-depth studies on the stress distribution law near the fault. Gunaydin13,14 and others mainly based on the pre-consolidation method to get the in-situ stress distribution of the fault and combined it with the GNSS technique to analyze the displacement of the fault. Tan et al.15 identified ground stress anomalies at several locations near faults through hydraulic fracturing tests and verified their accumulation mechanisms, revealing and quantifying the stresses at the upper disc of the fault, the lower disc, the inter-fault, the end of the fault, the fault junction, and the far field of the fault. Li et al.16 analyzed the fault stability through the ratio of horizontal stress to vertical stress at the fault and obtained the possibility of rock bursts in different spatial regions of the fault zone after studying the spatiotemporal evolution law of rock stress in the fault zone. Lan et al.17 and others determined the distribution characteristics of tectonic stress in the mining area under the dual action of fault activation and original rock stress through quantitative research and analysis, revealing the significant influence of different fault activation characteristics and different tectonic stress zones on the stability of the roadway enclosure; And based on the Mohr–Coulomb intensity criterion, the fault activation mechanism was investigated and a mathematical model for fuzzy comprehensive evaluation was established. Wang et al.18 concluded that reserving coal pillars can reduce the chance of rock burst disasters induced by mining activities near faults, established numerical models and rock burst-induced rheological models, and analyzed the effects of coal pillars with different residual faults on rockburst-induced rock bursts. Wu et al.19 took the effect of fault dip on fault stability as a research direction and concluded that high dip faults are more likely to induce dynamic hazards; Wang et al.20, to deeply understand the mechanism of coal explosion during underground coal seam mining, proposed a mechanical model considering mining stress, which was used to calculate the stress distribution on the surface of the fault and illustrate the sliding characteristics of the fault, and analyzed the mechanism of the formation of positive and negative faults when the lateral pressure coefficient is greater than 1.0 and less than 1.0 through experimental results. Su et al.21 analyzed the near-field stresses in the strike-slip fault model and classified the fault development stages into nucleation, stable growth and unstable growth stages based on the stress–strain relationship. Shi et al.22 proposed three criteria, fault dislocation trend, fault strike dislocation trend, and dip dislocation trend, based on the mechanical relationship between the direction of the ground stress and the occurrence of faults, and inferred the fault sliding and sliding type based on the criteria. Li et al.23 studied the stress evolution and fault-sliding behavior of normal faults with different dips through numerical simulation and engineering practice and established a fault model to derive the necessary conditions for fault sliding. It can be seen that the fault is a complex geological unit with a variety of mechanical relationships and is an influential factor that must be taken into account in underground engineering activities.

The presence of faults disrupts the continuity of coal seams, and the tectonic stress effect of faults is an important factor in the frequency of mine accidents near faults. Therefore, the fault tectonic region has been the focus of mine safety mining research. Under the superimposed effect of fault tectonic stress and mining stress, the safe mining of coal seam group in fault areas is facing greater challenges, while the research on the influence range of faults on coal seam mining is still less, and the mastery of the influence range of faults can provide a basis for the comprehensive prevention and control of disasters near faults, such as intensive gas extraction at faults, rock support in fault areas and fault tectonic solidification during coal seam mining. This paper analyses the influence range of faults under the repeated mining action of coal seams quantitatively by establishing the slip-convex body mechanics model of the rock body in the fault zone and the fractal evolution law of the overburden fracture network, to provide certain reference for the safe mining of the coal seam group endowed with faults.

Fault zone rock slip-convexity mechanics model

In the actual mining work, after the coal rock’s original stress balance is destroyed, some fault structure movement patterns are obvious, and fault movement patterns are not easy to detect, which is greatly related to the friction nature of the fault. When the Coulomb stress on the fault surface reaches the maximum shear strength S of the contact surface, relative frictional misalignment of the fault will occur24,25,26,27,28, especially when the top plate collapses to form a ‘masonry beam’ structure, the articulated rock mass on the fault contact surface, under the action of compaction by the upper load, is subject to transmission of forces to the fault plane, which in turn exacerbates the complexity of Coulomb stress at the fault structure, while most of the fault plane tends to be rugged, some scholars, after taking into account this state of contact, obstacle body and concave-convex body models are proposed to describe the physics of faults, and both toothed contacts on the fault surface and Coulomb stresses on the fault surface should be considered in the study of specific fault kinematic states29,30, as shown in Fig. 1.

Fig. 1
Fig. 1
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Fault plane occlusal contact and adjacent rock block structure micro-element stress analysis schematic diagram.

A concave-convex body is a specific region of the unit fault that is stronger than other surrounding regions, and a loaded Coulomb stress that varies linearly with time is considered for:

$$\sigma_{0} = \sigma_{00} + \alpha t$$
(1)

where \(t\) is time, \(\sigma_{00}\) and \(\alpha\) are constants. When the Coulomb stress at a lattice point exceeds the strength of the miniature fault at this location, the miniature fault ruptures and the Coulomb stress at this location drops to zero, and the loading Coulomb stress \(\sigma_{0}\) is then uniformly borne by the rest of the small fault blocks, so that under this assumption the Coulomb stress on the small fault block at point \((i,j)\) is:

$$\sigma \left( {i,j} \right) = \sigma_{0} /[1 - (l/N)]$$
(2)

where \(l\) is the number of small fault blocks ruptured and \(N\) is the total number of fault blocks within the unit fault, from Eq. (2), it can be seen that when the number of ruptured small fault blocks is infinitely close to the total number of fault blocks within the unit fault, the Coulomb stress at the fault surface is infinitely large, which is physically implausible, since the unit fault studied above is not an isolated system, most of its rupture results will cause some of the loading stresses to be withstood by fault zones in the vicinity of the unit fault, optimizing Eq. (2):

$$\overline{\sigma }\left( {i,j} \right) = {{\sigma (i,j)} \mathord{\left/ {\vphantom {{\sigma (i,j)} {\left[ {1 + C\left( {\frac{l/N}{{1 - l/N}}} \right)} \right]}}} \right. \kern-0pt} {\left[ {1 + C\left( {\frac{l/N}{{1 - l/N}}} \right)} \right]}}$$
(3)

Taking the ruptured rock mass to have a horizontally acting positive stress \(\sigma_{x}\) and corresponding shear stress \(\tau_{xy}\) on the structural unit of the fault plane, and a vertically acting stress \(\sigma_{y}\) and corresponding shear stress \(\tau_{yx}\), the positive stress acting on the fault plane is \(\sigma_{n}\), and the shear stress is \(\tau_{n}\), combined with the distribution characteristics of the fault concave-convex body and the quantification process, the Coulomb stress on the fault surface needs to be satisfied if the fault surface is allowed to slip:

$$f\left( {\tau_{n} ,\sigma_{n} } \right) = {{\left( {\left| {\tau_{n} } \right| - \mu \sigma_{n} } \right)} \mathord{\left/ {\vphantom {{\left( {\left| {\tau_{n} } \right| - \mu \sigma_{n} } \right)} {\left[ {1 + C\left( {\frac{l/N}{{1 - l/N}}} \right)} \right] > S}}} \right. \kern-0pt} {\left[ {1 + C\left( {\frac{l/N}{{1 - l/N}}} \right)} \right] > S}}$$
(4)

where \(C\) is a constant value, expressed by the compression wave velocity \(V\), shear wave velocity \(\beta\) and rupture velocity \(v\) as:

$$C = 4\left( {\beta /v} \right)^{2} \left( {1 - v^{2} /V^{2} } \right)^{\frac{1}{2}} \left[ {\left( {1 - v^{2} /\beta^{2} } \right)^{\frac{1}{2}} - \left( {1 - v^{2} /2\beta^{2} } \right)^{2} } \right]$$
(5)

From the mechanical equilibrium relationship, \(\sigma_{n}\), \(\tau_{n}\) can be expressed as:

$$\left\{ {\begin{array}{l} {\sigma_{n} = \sigma_{x} \sin^{2} \theta + \sigma_{y} \cos^{2} \theta + 2\tau_{xy} \sin \theta \cos \theta } \hfill \\ {\tau_{n} = \left( {\sigma_{x} - \sigma_{y} } \right)\sin \theta \cos \theta + \tau_{xy} \left( {\cos^{2} \theta - \sin^{2} \theta } \right)} \hfill \\ \end{array} } \right.$$
(6)

Taking \(\tau_{xy} = 0\) from Eq. (6) and bringing it into (4) gives the collation:

$$f\left( {\tau_{n} ,\sigma_{n} } \right) = \left\{ {\begin{array}{l} {{{\left[ {\sigma_{x} \left( {\sin \theta \cos \theta - \mu \sin^{2} \theta } \right) - \sigma_{y} \left( {\sin \theta \cos \theta + \mu \cos^{2} \theta } \right)} \right]} \mathord{\left/ {\vphantom {{\left[ {\sigma_{x} \left( {\sin \theta \cos \theta - \mu \sin^{2} \theta } \right) - \sigma_{y} \left( {\sin \theta \cos \theta + \mu \cos^{2} \theta } \right)} \right]} {\left[ {1 + C\left( {\frac{l/N}{{1 - l/N}}} \right)} \right]\sigma_{y} \le \sigma_{x} }}} \right. \kern-0pt} {\left[ {1 + C\left( {\frac{l/N}{{1 - l/N}}} \right)} \right]\sigma_{y} \le \sigma_{x} }}} \hfill \\ {{{\left[ {\sigma_{y} \left( {\sin \theta \cos \theta - \mu \cos^{2} \theta } \right) - \sigma_{x} \left( {\sin \theta \cos \theta + \mu \sin^{2} \theta } \right)} \right]} \mathord{\left/ {\vphantom {{\left[ {\sigma_{y} \left( {\sin \theta \cos \theta - \mu \cos^{2} \theta } \right) - \sigma_{x} \left( {\sin \theta \cos \theta + \mu \sin^{2} \theta } \right)} \right]} {\left[ {1 + C\left( {\frac{l/N}{{1 - l/N}}} \right)} \right]\sigma_{x} < \sigma_{y} }}} \right. \kern-0pt} {\left[ {1 + C\left( {\frac{l/N}{{1 - l/N}}} \right)} \right]\sigma_{x} < \sigma_{y} }}} \hfill \\ \end{array} } \right.$$
(7)

From Eq. (7), it can be seen that the positive stresses \(\sigma_{n}\) and tangential stresses \(\tau_{n}\) in different directions concerning the given parameters \(\mu\), \(C\) and \(l/N\), this can be determined by a combination of \(\sigma_{x}\), \(\sigma_{y}\), \(\tau_{xy}\) (equal to \(\tau_{yx}\)), fault dip \(\theta\), fault friction factor \(\mu\) and the ratio of ruptured small fault blocks to fault blocks within unit faults \(l/N\) that characterize the mining disturbance. Taking the derivative of Eq. (7) concerning θ and taking zero, and \({\text{df}}/{\text{d}}\uptheta = 0\), the collation yields:

$$\tan 2\theta = \left\{ {\begin{array}{l} {1/\mu \sigma_{y} \le \sigma_{x} } \hfill \\ { - 1/\mu \sigma_{x} < \sigma_{y} } \hfill \\ \end{array} } \right.$$
(8)

When the dip angle of the fault satisfies Eq. (8), the Coulomb stress on the fault surface takes the maximum value, and at this time, the risk of relative misalignment slip on the fault surface is the greatest, from Eq. (7), it can be seen that the main factors affecting the model are the ratio of horizontal to vertical stress in the rock mass of the fault zone \(\lambda\), the fault dip \(\theta\), the fault friction factor \(\mu\), and the ratio of ruptured minor fault blocks to fault blocks within the unit fault \(l/N\).

Establishment of numerical model and fractal dimension of overburden fractures

Establishment of UDEC numerical simulation

The numerical model established by UDEC Numerical Software is based on the actual conditions of a coal mining face at a mine in Guizhou, China. This face is located in the Shuicheng Mining Area in western Guizhou. The area lies in the transitional terrain zone of the central Yungui Plateau. The strata belong to the Longtan Formation of the Upper Permian System. The geological characteristics of this area are unique. Its most distinctive feature is the complex and variable geological structures, particularly the highly developed structural coal deposits. Fault structures are widely distributed throughout the area, primarily consisting of small faults. Some regions exhibit a dense concentration of small faults. This creates a complex coal deposit environment. Exploitable coal seams are primarily distributed along the axial or wing sections of anticlines. The study area is primarily characterized by normal fault structures. The average dip angle is 55°–65°, with a maximum displacement of approximately 4.9 m. The exploitable coal seams are the 1#, 2#, and 3# coal seams. Since the overlying strata of the coal mining face are abandoned mine areas, there is repeated unloading and mining impact. To better observe the development of fractures in the overlying strata, a repeated mining impact model was established to analyze the fracture field and stress spatiotemporal evolution of the coal seam mining overlying strata under reverse faulting.

The numerical model of reverse fault mining is shown in Fig. 2. According to the relationship between the location of coal seam mining and the fault, the coal seam is 66 m away from the center of the fault from the left to the right, and the fault distance from the upper plate of the 3# and 2# coal seams is 16.5 m and 29.5 m respectively, and the inclination angle between the fault and the upper plate of the coal seam is 112°, and the size of the simulation model is designed to be 140 × 128 m (length × width), and the thickness of the 2# coal seam and 3# coal seam are 1.2 m and 2.3 m respectively, and 9 measuring points are arranged in the rock body of the fault zone to monitor the fault stress changes. To eliminate the influence of the boundary, 15 m protective coal pillars are left on the left and right sides of the numerical simulation. Based on the actual coal seam mining sequence of the mine, the numerical simulation excavates the 3# and 2# coal seams, and the excavation sequence starts from the lower disc of the fault of the 3# coal seam.

Fig. 2
Fig. 2
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Summary of numerical model.

In the numerical simulation calculation model, the constitutive relationship of the coal rock layer is based on the Mohr–Coulomb criterion, and the joint surfaces are modeled using the joint surface contact-Coulomb slip criterion. The bottom boundary of the model restricts vertical displacement as a displacement boundary; the left and right boundaries restrict horizontal displacement as displacement boundaries; and the upper boundary is set as a free boundary. A uniform load of 6.34 MPa is applied to the top of the model. Based on the data provided by the coal mine, a geological columnar diagram of the coal mine and the physical and mechanical parameters of the rock layers are plotted, as shown in Fig. 3.

Fig. 3
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Coal and rock mechanics parameter table.

Fractal dimension of fracture in mining overburden rock

Fractal theory mainly studies a large number of complex phenomena with scale invariance, randomness and other properties under certain conditions. The fractal dimension is one of the important concepts of fractal theory, and its fractal dimension index can reasonably and accurately reflect the complexity of the overlying rock fracture network31,32,33,34,35,36. In the study of overburden rock fissure evolution law and quantitative analysis of rock body fissure, the analytical dimension has been well applied37,38,39,40, in the coal seam over fault mining, when the analytical dimension appears mutation point, it indicates that the overburden rock fissure network develops more rapidly in this stage, and then, according to the study of fault tectonics of mechanism of formation and destabilization, the degree of overburden rock fissure network development is characterized by the use of the fractal dimension, and it is possible to discuss and determine whether the occurrence of fractal dimension mutation point during the mining process can be indicated as entering the influence range of the fault.

In this study, the fractal dimension of the fracture network of the mining overburden rock in this working face is calculated using the FracLab toolbox in Matlab software, specifically using the Box-counting dimension calculation method. The calculation steps are divided into the following 2 stages:

  1. (1)

    Data pre-processing stage: this stage is mainly two-dimensional color image data into grey-scale data, binary data, the use of Photoshop in the grey threshold function, through the threshold segmentation method to set a grey threshold to the calculation of the region into a black and white bitmap, white areas are 1 and black areas are 0. Image features are characterized by black curves, and points with a value of 1 after binarisation corresponds to the background. In this paper, the black area is the development characteristics and distribution pattern of the mining overburden fissures, and the white area is the undamaged overburden, as shown in Fig. 3b.

  2. (2)

    Fractal dimension calculation stage: the processed 2D digital image is transferred into FracLab fractal calculation software, and the box dimension algorithm is used to calculate its fractal dimension, which consists of the number of line segments required to cover one unit length of a usual regular object \(N\left( r \right) = 1/r,\) the number required to cover a square of unit side length \(N\left( r \right) = \left( {1/r} \right)^{2}\), the number required to cover a cube of unit side length \(N\left( r \right) = \left( {1/r} \right)^{3}\), the area bounded by the return line is finite by continuing the overburden fissures in such an infinite manner from large to small, according to the square of unit side length, therefore, the space occupied by the overburden fissure squeezed in a finite area with infinite length, i.e., between 1 and 2 dimensions, with the number of dimensions, i.e., fractions, as in Fig. 3c. The calculation formula is shown in Eq. (9):

    $${\text{D}} = \mathop {\lim }\limits_{{{\text{r}} \to 0}} \ln {\text{N}}\left( {\text{r}} \right)/\ln \frac{1}{{\text{r}}}$$
    (9)

    where r—is the side length of the square; N(r)—is the number of boxes; D—is the fractal dimension of the fracture of the mining overburden.

Analysis of the influence range of rock fissures

According to the discrete element simulation results of coal seam mining overburden rock fissure evolution, as shown in Fig. 4. The features of mining overburden rock fissure development are extracted, and the fractal dimension of the working face over fault mining overburden rock fissure development is calculated by applying Fraclab software, and the calculation results are shown in Table 1, It can be seen from Table 1: the fractal dimension D of the coal seam group over fault mining fissure development under the reverse fault structure is between 0.754 and 1.523, and with the increase of the working face advancement distance, the fractal dimension value shows a dynamic growth trend.

Fig. 4
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Fractal dimension calculation process diagram.

Table 1 Fractal dimension calculation table.
Full size table

The evolution of fractal dimension with the number of mining is shown in Fig. 5, and it can be seen from Fig. 5 and Table 1: with the increase of mining times, the fractal dimension shows a gradual increase in the overall trend, and the evolution of fractal dimension of the overburden fracture during the whole process of mining can be divided into three phases: ascending, descending and changing dimension, and there are two points of sudden increase and two points of sudden decrease in the total number of mining phases.

Fig. 5
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The relationship between fractal dimension and mining times in the whole mining process.

Stage 1: ascending dimension stage, this stage is in the 3# coal seam to open the cutting eye to the working face to advance to 80 m, in the mining to 50 m fractal dimension value appeared suddenly increase point, its value from 1.165 to 1.301, the reason is due to the advancement of the process by the influence of the mining is gradually aggravated, along with the working face to the direction of the fault to promote the fault zone rock body by the influence of the mining crack expansion effect, the fault zone rock body by the influence of mining, therefore, it is considered that the work face enters the fault influence range when the 3# coal seam advances 50 m, and as the work face continues to advance, the overburden rock fissure network continues to develop, and the fractal dimension value increases to 1.396. Stage 2: the stage of decreasing dimension, this stage is in the 3# coal seam working face advancing 90 m to 2# coal seam working face advancing 30 m, in this stage of the coal seam mining process, 3# coal seam mining end of the fissure of the mining airspace area is gradually compacted, the overburden rock fissure network development degree gradually reduced, the working face away from the fault, the value of the fractal dimension from 1.382 down to 1.321, that when the 3# coal seam advancing 90 m It is believed that the working face is far away from the influence range of the fault. In 2# coal seam excavation 20 m, at this time 3# coal seam overburden rock has been compacted fissure network under the influence of repetitive mining fissure network produces secondary development, the formation of the fault crushed area continues to produce new damage, the fractal dimension of the fractal appears to be a point of sudden increase, its value from 1.357 to 1.479, that the 2# coal seam working face advances 20 m into the scope of the influence of the fault. Stage 3: variable dimension stage, this stage is in the 2# coal seam working face advancing 20 m to the end of mining, the development of the fracture network in this stage is largely formalized, and the fractal dimension value is maintained at a higher value, and the fractal dimension peak of the whole process mining stage is 1.523, the development of overburden rock fissure network shows cyclic opening-closing, and the fractal dimension value is in the state of variable dimension, and the fractal dimension value is in the state of sudden drop point when the working face advances 80 m, and its value drops from 1.517 to 1.435, and it is considered that the working face is far away from the influence range of fault.

The above analyses show that, based on the fractal dimension to characterize the degree of development of the overburdened rock fracture network, when the fractal dimension value appears to have a surge point and a drop point, then it is considered that the range of the intermediate stage between the surge point and the drop point is the scope of influence of the fault, according to the fractal dimension judgment method, it is initially believed that it enters the fault influence when mining 50 m in 3# coal seam, and detaches from the fault influence after 90 m, and the fault influence range is between 50 and 90 m and the fault influence range is around 40 m in the mining stage of 3# coal seam; it enters the fault influence when mining 20 m in 2# coal seam, and detaches from the fault influence after 80 m, and the fault influence range is between 20 and 80 m and the fault influence range is around 60 m in the mining stage of 2# coal seam.

Discrimination of rock-slip-convex body mechanics models in fault zones

The fractal dimension of the mining overburden fracture characterizes the fracture network as a whole and in stages and does not address the dynamics of the fault after it enters the Influence phase and the fault undergoes motion, therefore, according to the slip-concavity stress model of the rock body in the fault zone in the study method of fault influence range discrimination, the relative frictional dislocation of the fault will occur when the Coulomb stress on the fault surface reaches the maximum shear strength S of the contact surface, which can qualitatively describe the dynamics of the fault when the frictional dislocation occurs, an attempt can be made to derive Coulomb stresses at the fault plane during mining based on the vertical stresses, horizontal stresses and rock mechanical parameters applied to the rock mass in the fault zone, and solve the strain or stress distribution inside and on the surface of the object when the displacement occurs on both sides of the dislocation surface based on the Coulomb stress, and judge the points where the faults are prone to live in the process of advancing of the working face, and then judge the scope of influence of the faults.

Based on this, this study adopts the fault zone rock slip concave-convex body mechanics model to identify the influence range of faults, and firstly, the UDEC numerical simulation software is used to derive the values of the stress data at each measurement point in different mining stages, then the Coulomb stress value at the fault plane is found by Eq. (7), which puts the fault zone rock \({\tau }_{xy}\)=\({\tau }_{yx}\)=0, μ = 0.15, \(C\)=0.312 (where, \(V\)=6.3 km/s, \(\beta\)=3.16 km/s, \(v\)=5.48 km/s), \(l/N\)=0.1, \(\theta\)=68°, and \({\sigma }_{y}\), \({\sigma }_{x}\) values are the values of the measurement points. Figures 5 and 6 show the change rule of Coulomb stress at the fault surface under different excavation distances of 3# and 2# coal seams, respectively.

Fig. 6
Fig. 6
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Reverse fault structure under the 3# coal seam excavation times and Coulomb stress relationship.

In the UDEC simulation, the stress value is expressed as ‘tension positive pressure negative’, that is, when the stress value is positive, it means that it is subjected to the pulling effect, and when the stress value is negative, it means that it is subjected to pressure. The Coulomb stress values of the fault face with different excavation times in the simulation process were calculated and called, and the spatial and temporal distribution of the Coulomb stress at the 9 measurement points at the fault in different excavation stages in the excavation of the 3# coal seam is shown in Fig. 6, from Fig. 6 can be seen in the first 4 steps of excavation stage, the fault surface at the measurement point Cullen stress value is negative mainly affected by compressive stress, continue to excavate 10 m after the mining effect on the fault zone rock body influence gradually increased, the measurement point Cullen stress value changes more obvious complex, measurement point 3, 4, 5, 9 become tensile stress, based on the fault zone rock body stress changes, judge this time the working face advances to the fault influence stage. When advancing 60 m or so, the 3# coal seam is in the stage of over-fault excavation, and the value of Coulomb stress at measuring points 9 and 7 exceeds the maximum shear strength of the rock body in the fault zone, which increases the risk of fault activation for the location of the measuring point that is prone to slip phenomenon along the fissure surface. After advancing another 10 m, the coal rock body of the base plate is in an expansion state, so that the fault measuring points 4 and 5 at the base plate of 3# coal seam tends to be activated, and the difference between vertical stress and horizontal stress produced by the overlying rock structure after the fault position is too large, so that the value of Coulomb stress at the measuring point 8 and 9 is also close to the maximum shear strength of the rock body of the fault zone, and the value of Coulomb stress at the upper and lower measuring points of the rock body of the fault zone is in the state of tensile stress in this stage, and the fault is more prone to cause mine pressure disaster after activation phenomenon occurs. After 80 m of excavation, the Coulomb stress value at fault measuring point 7 again exceeds the maximum shear strength of the rock body in the fault zone, and a secondary activation phenomenon occurs at this position. The reason for the analysis is that the weak structural body stress transfer phenomenon of the coal and rock body appearing fissure occurs at this stage, which produces a horizontal extrusion effect on the local rock body of the fault in the region, so that the difference between the horizontal stress and the overburden rock stress is too large, and the values of Coulomb stress at the rest of the measurement points are smaller than the maximum shear strength of the rock body in the fault zone. After 90 m of excavation, the rock body in the fault zone of the top and bottom plates is always in the stage of ‘pressurization-depressurization-recovery’ in the normal mining stage, and it repeats itself as the working face advances, and the rock body at the measuring points of faults 4, 5 and 6 are located in the depressurize zone and subject to small vertical stress, which makes the difference between the horizontal stress value and vertical stress value too large under the influence of the stress transfer, the Coulomb stress values at points 4, 5, and 6 are all around the maximum shear strength of the rock mass in the fault zone; in the subsequent mining stage, the change of Coulomb stress at each measuring point of the fault tends to be flat and the value is lower than the maximum shear strength of the rock body in the fault zone, so the risk of fault activation is small, and according to the change of Coulomb stress, it is judged that at this time, the advancement distance of the working face is more than the range of the fault influence. According to the analysis of Coulomb stress change at different measuring points of the fault, it is initially believed that when mining 40 m of the 3# coal seam, it enters into the influence range of the fault, and after 100 m, it leaves the influence of the fault, and the influence range of the fault in the mining stage of the 3# coal seam is between 40 and 100 m.

During the excavation of the 2# coal seam over the fault, the measuring point 3 is located in the excavated rock body, so the Coulomb stress value at the measuring point 3 is not calculated, and the Coulomb stress value of the remaining measuring points at the fault is calculated to obtain the relationship between the number of times of excavation of the coal seam and Coulomb stress as shown in Fig. 7. It can be seen from Fig. 7: when mining back under repetitive mining, there are positive and negative values of Coulomb stress at the fault surface, after mining 30 m, according to the change of Coulomb stress value at each measurement point, it is judged that at this time, the working face advances to the stage of fault influence, and compared with the mining of the 3# seam, under the influence of repetitive mining and pressure relief, the fault influences the scope of the 2# seam 2 steps in advance. When the working face advanced 50 m, the Coulomb stress value at the measurement point 4 exceeded the maximum shear strength of the rock body in the fault zone, and the activation stage of the mining fault was advanced relative to that of the 3# coal seam, and after advancing another 10 m, the working face of No. 2 coal seam is in the stage of over-fault mining, the Coulomb stress value at the measuring point 4 is still greater than its maximum shear strength, the Coulomb stress value of the rest of the measuring points is less than the maximum shear strength, compared with the stage of over-fault mining of No. 3 coal seam, the fault is prone to activation of the measuring points are less, analyze the reason may be due to the upper plate of the fault 3# coal seam mining gap is gradually compaction is conducive to the propagation of stress, the fault zone rock body to become loaded rock layer of the compressive stress increased; In the subsequent mining process, measurement points 2, 5 and 6 respectively in the 70 m, 80 m and 90 m mining stage of the fault activation phenomenon, in the 100 m and 110 m fault each measurement point at the Coulomb stress situation tends to flatten, at this time that the working face is located in the fault outside the scope of influence. Analyzing the change of Coulomb stress at different measuring points of the fault, it is initially believed that the fault influence enters into the fault when 20 m of the 2# coal seam is mined, and detaches from the fault influence after 100 m, and the scope of the fault influence in the mining stage of the 2# coal seam ranges from 20 to 100 m.

Fig. 7
Fig. 7
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Reverse fault structure under the 2# coal seam excavation times and Coulomb stress relationship.

From the perspective of analyzing the coal seam over the fault to prevent roofing, top rock damage and gas protrusion, it can be seen that, through the fractal dimension evolution law and the fault zone rock slip mechanics model, it is finally determined that the influence range of the fault of the 3# coal seam is between 40 and 100 m, and the influence range of the fault is about 60 m, and the influence range of the fault of the 2# coal seam is between 20 and 100 m, and the influence range of the fault is about 80 m. When the coal seam is mined over a fault, it is necessary to reduce the vertical displacement of different coal and rock bodies and strengthen the support for the roof plate and the fault to withstand the load capacity when it enters the influence range of the fault, and at this time, it is necessary to increase the gas extraction boreholes of the drilling site in the area of the drilling site of the tunnel gangway in the return wind lane as part of the regional anti-surge measures.

Engineering applications

Gas extraction drilling program

Based on prior research findings and considering the distribution characteristics of overburden fracture evolution zones during the mining of 3# Coal Seam, a detailed drilling layout plan was developed using CorelDraw (Version:2024; https://www.coreldraw.com/cn/) software to create the drill site layout diagram. The specific spatial arrangement is shown in Fig. 8. Each set of boreholes consists of five holes, with a single hole designed to be 15 m in length and drilled at an angle of 15° concerning the vertical top plate (i.e. the Z-axis). The No.1 borehole is 0.5 m from the coal wall, 1.6 m from the back of the goaf, and the spacing between the boreholes is 0.8 m. The projection of borehole 1 on the XOY plane is at an angle of 45° to the working plane (i.e. the X-axis), whereas the projection angle of boreholes 2–5 decreases in turn, by 5° between the neighborhood of each borehole. Detailed layout parameters for each borehole are shown in Table 2. At the same time, according to the limit collapse distance of the working face roof, a new set of extraction drilling holes was designed to be set up after the working face advances 18 m, and the schematic layout of the extraction lane of the working face is shown in detail in Fig. 8.

Fig. 8
Fig. 8
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Layout of fight-level borehole yard.

Table 2 Drill hole layout parameters.
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Analysis of gas extraction

To further verify the effectiveness of this drilling arrangement on the gas extraction effect, on-site monitoring work was carried out, the amount of gas extraction and the change of gas concentration in the return airway and the upper corner were monitored during the extraction of the working face. Based on the actual monitoring data, the curve graph of gas extraction with time was obtained, as shown in Fig. 9, as well as the real-time change curve of gas concentration in the return alley and the upper corner, as shown in Fig. 10.

Fig. 9
Fig. 9
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Variation curve of gas extraction from working face.

Fig. 10
Fig. 10
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Change curve of gas concentration monitoring in the return airway and upper corner.

As can be seen from Figs. 8 and 9, when the working face has not yet encountered a fault, the mix of gas extraction remains between 70 and 80 m3/min, which is overall more stable. When the working face advances to the fault position, the extraction borehole can effectively extract the unloaded gas from the neighboring coal seam, and at this time, the mixed volume of gas extraction from the borehole reaches the maximum value of 93 m3/min. From Fig. 9, it can be further learned that the gas concentration in the return airway is maintained between 0.05 and 0.39%, while the gas concentration in the upper corner is controlled within the range of 0.19–0.77%, which are all in line with the standard requirements for safe production in coal mines. This shows that after the directional gas extraction technology is adopted, the risk of gas accumulation in the upper corner can be effectively eliminated when the working face encounters a fault, which ensures the efficient and safe production of the fully mechanized mining face.

Conclusion

  1. (1)

    Mechanical modeling of concave-convex rock bodies in fault zones established, and the main factors affecting the model are the ratio of horizontal stress to vertical stress in the rock body of the fault zone \(\lambda\), the dip angle of the fault \(\theta\), the friction factor of the fault \(\mu\), and the ratio of the ruptured small fault blocks to the fault blocks within the unit fault \(l/N\).

  2. (2)

    Through the MATLAB software to calculate and analyze the fractal dimension of the whole process of coal seam mining under the reverse fault structure, we obtained that the fractal dimension D of the overlying rock fissure is between 0.754 and 1.523, and the evolution law of fractal dimension D can be specifically divided into three stages: ascending, descending, and changing dimensional stage.

  3. (3)

    From the perspective of analyzing coal seam passing through faults to prevent roof fall, top rock mass failure and gas outburst, it can be seen that through the evolution law of fractal dimension and the slip mechanics model of rock mass in fault zone, it is finally determined that the influence range of faults in 3 # coal seam is between 40 and 100 m, and the influence range of faults is about 60 m. The influence range of faults in 2# coal seam is between 20 and 100 m, and the influence range of faults is about 80 m.

  4. (4)

    On-site monitoring of the amount of gas extracted from the working face during the mining period when it meets the fault, and the change of gas concentration in the return-air lane and the upper corner, shows that when the working face advances to the influence range of the fault, the extraction drill holes can extract the unloaded gas from the neighboring coal seams effectively, and can eliminate the risk of gas gathering in the upper corner, thus guaranteeing the high efficiency and safe production of the comprehensive mining face.