A new method for layout layer optimization of long horizontal boreholes for gas extraction in overlying strata: A case study in Guhanshan coal mine, China

The gases released by underground coal mining pose a threat to mine safety, lead to resource wastage, and contribute to environmental pollution. Employing long horizontal boreholes (LHB) for gas extraction proves to be an effective solution. However, accurately determining the LHB's position within the overlying rock strata is challenging due to complex mining and geological conditions. This study introduces a novel “zone‐position” method for identifying the optimal LHB placement, utilizing both physical simulation tests and theoretical analysis. The approach comprises two steps. Initially, it identifies the appropriate LHB layout zone within the overlying strata. It delineates four subzones within the fractured zone, among which the stable fractured subzone (SFSZ) is identified as the most favorable for LHB placement. The boundaries of the SFSZ are also defined. Subsequently, the method focuses on pinpointing the LHB's precise location within the SFSZ, proposing a criterion that considers gas accumulation, strata permeability, and LHB stability. Application of this method in engineering projects demonstrates that the gas extracted by LHBs accounts for about 60% of the total gas emission. Furthermore, the volume of gas extracted at the optimal LHB location reaches up to 5.52 m3 min−1, triple that of other locations.


| INTRODUCTION
Typically, the strata overlying areas affected by underground mining are categorized into three zones based on the distribution of fractures in various strata layers: the caved zone, the fractured zone, and the bending zone.2][3] As fractures develop within these zones, the permeability of the strata significantly increases.Concurrently, coal seam mining releases a substantial volume of gas (primarily methane, CH 4 ) known as pressure-relief gas.This gas accumulates in the working face and gob, [4][5][6] presenting a critical safety risk to mining operations. 7,8However, this gas also represents a valuable clean energy resource.0][11] Therefore, effectively extracting this gas is crucial for achieving safe and sustainable mining practices.
3][14][15][16] Presently, coal mines in China predominantly employ the LHB technique due to its cost-effectiveness and high construction efficiency (Figure 1). 17,18s depicted in Figure 1, LHBs are drilled at an inclined angle toward the targeted strata layers, extending horizontally before panel excavation.The horizontal section of the LHB, situated within the overlying strata, is surrounded by fractures induced by mining, serving as primary pathways for the diffusion, seepage, and extraction of pressure-relief gas.The total length of LHBs varies from 100 to 1000 m, depending on specific geological conditions and the intended scale of gas extraction from panels. 16,18,19xtracting pressure-relief gas through LHBs involves two steps.1][22] The concept of an "O-shape circle" with a 34 m width above the mined-out panel in the overlying strata was proposed, drawing on the key-stratum theory. 23,24Subsequently, the annular fractured ring theory was developed to delineate the area for efficient gas extraction, which varies in size from 75 to 115 m. 25,26 Furthermore, a conceptual model of three zones in the overlying strata was introduced, indicating that the height of the fractured gas-flow zone is approximately 7−10 times the mining height. 27,28Additionally, the gas flow area in abandoned mine gobs was segmented into four zones, from bottom to top: the gas highconcentration zone, the gas transition zone, the gas enrichment zone, and the gas no-stream zone, with the boundaries of the gas enrichment zone forming a V-shape at a height of 30 m. 29 The results from these studies, identifying gas locations and flow channels extending from several meters to over 100 m, are challenging to directly apply in coal mines for gas extraction due to the imprecise positioning of LHBs, which have diameters ranging from 80 to 200 mm and extraction radii of about 5 m. 16,17,30he second step involves assessing the stability of LHBs.2][33][34] These studies provide a fundamental theoretical framework for maintaining LHB stability during drilling before the strata are affected by underground mining.Postdrilling, LHB stability is influenced by the development of fractures within the overlying strata due to mining activities.Nevertheless, research on this aspect remains scarce.
Therefore, there are two primary challenges in extracting pressure-relief gas through LHBs in the overlying strata, based on existing research: (1) the inaccurate positioning of LHBs for extraction and (2) a lack of dynamic analysis of LHB stability during underground mining operations.To address these issues, this study introduces a "zone-position" method for precisely locating LHBs in the overlying strata to ensure stable and efficient gas extraction.This approach is validated through physical simulation tests and theoretical analysis, and its efficacy is demonstrated via an engineering case study.

| Study site
The Guhanshan coal mine is located in the northeast of the Jiaozuo coalfield in Henan Province, China, as illustrated in Figure 2.This coalfield is characterized by a monoclinal structure that gently dips to the southeast, situated between the Guhanshan and Youfangjiang faults.The predominant structural feature within this field is the presence of faults, with minor folds appearing locally.The No. 2 −1 coal seam, found in the lower part of the Shanxi formation, serves as the primary seam for mining operations at this site, boasting an average thickness of 5 m.The roof and floor of the No. 2 −1 coal seam consist mainly of mudstone and sandy mudstone, respectively, both of which exhibit poor permeability.This characteristic facilitates the preservation of gas within the coal seam.The minefield holds geological gas reserves estimated at 4539.83 Mm 3 .The original gas F I G U R E 2 Location and gas geological map of Guhanshan coal mine.

GUO ET AL.
| 2437 content of the coal seam ranges from 4.01 to 28.88 m 3 t −1 , generally increasing with depth from shallow to deep layers.Statistical analysis of the coal seam gas content (y) in relation to the corresponding coal seam floor elevation (x) reveals a fitting relationship expressed as y = 0.49 − 0.05x (Figure 2).The intricate geological structure, combined with the extraction of coal seams rich in gas, predisposes the mine to gas accidents, with 12 such incidents reported to date.
The No. 16031 strike longwall panel, situated in a deeper part of the coal mine, served as the representative site for this study.The average depth is 650 m.The partial geological column and lithology parameters of the overlying strata are depicted in Figure 3.The strike length of the panel is 600 m, the dip length is 155 m, and the mining thickness is 3 m.The geological structure comprises a monoclinal structure with a 12°dip angle, higher in the west and lower in the east.The original gas content of the coal seam is approximately 28.08 m 3 t −1 .Before mining, ordinary boreholes are drilled in the coal seam floor roadway, the intake airway, the return airway, and the setup room to extract the coal seam gas.However, the measured residual gas content in the coal seam remains significant, reaching up to 5.98 m 3 t −1 .The coal mining amount of the panel is 1488 t day −1 , and the pressure-relief gas emission can reach up to 8898.24 m 3 day −1 , corresponding to 6.18 m 3 min −1 .Additionally, the unmined coal and coal pillars in the gob continue to release gas.The presence of a large amount of pressurerelief gas can easily lead to gas accidents at the working face, posing a serious threat to safe production.Therefore, the extraction and control of the pressurerelief gas are urgent.

| Physical simulation test procedures
Notably, the gob becomes inaccessible after its closure, which challenges further in-situ studies and additional measurements. 35Consequently, physical model simulations have been widely applied in mining engineering research. 36,37A physical model of a rock mass was constructed based on the geological and mining conditions of panel 16031 at a specified scale using materials with mechanical properties similar to those of underground rock masses to simulate actual mining.Its aims are to simulate the distribution characteristics of the fracture channels for gas migration in overlying strata and analyze the stability of the LHB in different strata layers.The experiment was conducted using a twodimensional plane simulation test bench at the State and Local Joint Engineering Laboratory for Gas Extraction and Ground Control of Deep Mines at Henan Polytechnic University.
F I G U R E 3 Geological column and lithology parameters of the partial overlying strata.
Based on the laboratory's test platform and the mining situation of panel 16031, it was determined to complete the test on a simulation platform with dimensions of 2.5 m in length, 0.2 m in width, and 1.3 m in height.The similarity constant, consistent with actual mining, was calculated based on the existing similarity criteria.
Geometric similarity constant C L : where L m is the simulated mining length of the platform; L p is the actual mining length.
Poisson's ratio similarity constant C μ : where μ m is the Poisson's ratio of the simulated material; μ p is the actual Poisson's ratio of rock strata.Bulk density similarity constant C r where γ m is the bulk density of simulated material; γ p is the bulk density of rock strata.
where E m is the strength of the simulated material; E p is the strength of rock strata.
where σ m is the mining stress of the model; σ p is the actual mining stress.
where t m is the simulated mining time; t p is the actual mining time.

| Similar construction of strata
Gypsum, light calcium carbonate, and cement were selected as cementing agents, with sand used as the skeleton in the model.Similar materials were mixed in varying proportions to simulate different lithologies of rock strata with varying strengths. 38Furthermore, to ensure the accuracy of rock stratum failure and fracture development, each rock stratum was separated from the others by uniformly spreading mica powder on their surfaces.The test simulated strata No. 10-20 (as shown in Figure 3).Based on the distribution of the prototype strata and the obtained similarity constants, the required mechanical properties of the strata and the proportion of similar materials in the model were calculated, as listed in Table 1.

| Model loading
The model could not simulate all the rock layers above the coal seam.Therefore, loading was applied at the top of the model, and a medium layer with moderate stiffness was placed between the loading body and the model to generate a pressure distribution consistent with the actual situation.
The simulated loading stress is as follows: where q m is the external stress applied at the top of the model; q p is the self-weight stress of the rock strata that have not been simulated; γ p is the rock strata bulk density, 26,000 kN/m 3 ; H p is the height from coal seam to the surface on-site, 650 m; H m is the height from coal seam to the top of the model, 51 m.

| Layout of LHB
The LHB was constructed using special semicircular wood strips.During the model construction, five strips positioned 60, 300, 500, 700, and 900 mm away from the coal seam were set along the model's entire length, respectively.After the model baffle was dismantled, the wood strips were removed to form the LHB.

| Observation rows
The test consisted of nine observation rows, numbered 1-9 from bottom to top.Each observation row contained 25 observation points with a spacing of 10 cm, and the outermost point was 5 cm from the boundary of the model shelf.A row of points was arranged 1 cm above each LHB, followed by another row 10 cm above it.

| Mining simulation
The completed model, illustrated in Figure 4, comprises three main components: a main device, a hydraulic loading system, and a monitoring system.
To facilitate observation and analysis, the model's surface was painted white, while the LHB was colored differently.The test simulated a mining length of 1700 mm, equivalent to an actual mining length of 85 m.Coal pillars, each 400 mm in length corresponding to an actual size of 20 m, were preserved on both sides of the panel to minimize the boundary effect.The working face advancement was set at 40 and 60 mm per step alternately, mirroring the actual mining progression of 2 and 3 m per step, respectively.This alternation aimed to replicate the full actual mining process in the field.During the physical simulation, the coal seam was subject to a uniform load.The on-site and indoor experimental parameters of the simulation test are detailed in Table 2.

| Determination of the LHB layout zone
This section considers two primary factors to determine the suitable zone for the LHB layout: the distribution of fracture channels for gas migration and the stability of the LHB.Subsequent sections will analyze the appropriate zone for the LHB layout in both vertical and horizontal directions.

| Along the vertical direction
Distribution of fracture channels Mining induces two types of strata fractures 39 : throughlayer fractures, penetrating a specific rock layer, and separated layer fractures, occurring between two rock layers.Analyzing the evolutionary characteristics of these fractures in the simulation test enables the identification of the vertical height ranges of the caved, fractured, and bending zones (Figure 5A).Utilizing these height ranges, the subsidence values of observation rows in each zone were recorded, and the separation fracture rate for each zone was calculated (Figure 5B).The separation fracture rate, indicating the degree of mining strata separation, is determined by the formula presented: where S f is the separation fracture rate; d o is the spacing between observation rows affected by mining; d m is the original spacing between observation rows.Figure 5A reveals that separation fractures develop first during the excavation process.Following the collapse of the immediate roof, through-layer fractures begin to form.The development height of separation fractures consistently exceeds that of through-layer fractures.In the simulation test, the caved zone's height is 8.5 m above the coal seam.As the working face advances, the first occurrence of roof breaking, or the first weighting, leads to the upward development of through-layer fractures, transitioning into the fractured zone.The main roof then undergoes periodic breaking, known as periodic weighting, with through-layer fractures extending upward until a certain height is reached, beyond which through-layer fractures cease to develop.However, separation fractures continue to extend upward, breaking the rock stratum into the bending zone.The fractured zone extends from the top boundary of the caved zone to a height of 36.4 m from the coal seam level, with the bending zone situated above it.
Figure 5B highlights the significant development of separation fractures within the caved zone, with the maximum separation fracture rate reaching 313.4 mm m −1 according to Equation (8).The separation fracture rate exhibits considerable fluctuations due to unstable fracture development, with rates up to 129.5 and 86.6 mm m −1 for rock strata on either side of the fractured zone.The fracture development within this zone is relatively stable, spanning a width of 25-30 m.Toward the middle of the fractured zone, the separation fracture rate markedly decreases.In the bending zone, the separation fracture rate of rock strata is minimal, less than 10 mm m −1 .Thus, considering the distribution of fracture channels, the caved and fractured zones are identified as suitable areas for LHB layout for gas extraction.

LHB stability
Coal mining causes the movement and deformation of the overlying strata, which can lead to borehole failure due to tensile and shear forces. 32The deformation and failure characteristics of the LHB in each zone during the mining process are depicted in Figure 6.
Figure 6A illustrates the failure characteristics of the LHB in the caved zone.The LHB breaks and collapses with the rock stratum, and obvious shear dislocation occurs on the LHB (mining 30 m).As excavation progresses, regular collapse and dislocation occur on the LHB, leading to its complete destruction.In the fractured zone (Figure 6B), tensile-shear fracture occurs on the LHB (mining 40 m).As excavation continues, regular fractures occur on the LHB, but it manages to maintain its integrity overall.The LHB in this zone is affected but remains relatively stable.In the bending zone (Figure 6C), the LHB is not significantly deformed (mining 60 m), but there is a large separation area below the LHB.Then, the separation area is transmitted upward, and the LHB bends and deforms with the rock stratum (mining 70 m).This zone does not exhibit fractures along the LHB.Therefore, from the perspective of LHB stability, the fractured and bending zones are suitable for the LHB layout.In summary, the fractured zone is the most suitable for the LHB layout based on the analysis of fracture channel distribution and LHB stability.

| Along the horizontal direction
Considering the different fracture distribution characteristics in the fractured zone, it is necessary to analyze this zone horizontally to further specify the LHB layout zone.
There are six observation rows in the fractured zone, numbered from bottom to top (from the second row to the seventh row).Taking the third and fifth rows as standard lines, the strata of the fractured zone are divided into upper, middle, and lower layers (Figure 7B).Referring to Equation ( 8), the separation fracture rate of the upper, middle, and lower strata can be calculated from the subsidence of the corresponding row.By analyzing the separation fracture rate, the fractured zone is divided into four subzones horizontally, as shown in Figure 7A.The distribution of the four subzones in the test is depicted in Figure 7B.
From Figure 7A, these four subzones are characterized as follows: separation fracture rate curves of the upper, middle, and lower strata, it is evident that subzone III maintains a certain width and gradually inclines toward the middle of the model.Moreover, subzone III uses the strata breaking line as its outer boundary, with a width of approximately 25 m.
Comparing the fracture characteristics of the four subzones, the fractures in subzone Ⅲ are notably developed.Therefore, along the horizontal direction, subzone Ⅲ (SFSZ) is the most suitable zone for LHB layout in the fractured zone.

| Boundaries of the LHB layout zone
The SFSZ (Subzone Ⅲ) is a circular zone within the threedimensional stope.Based on the migration characteristics of pressure-relief gas, 26 this gas will gradually migrate to the uphill side of the SFSZ through diffusion, uplift, and permeability.To clearly illustrate the SFSZ and the LHB, their diagrams in both two-dimensional and three-dimensional formats are presented in Figure 8.
The boundaries of the SFSZ, as depicted in Figure 8A, are defined vertically and horizontally.Vertically, the boundaries are the vertical distance from the coal seam level, comprising the bottom boundary (B b ) and the top boundary (B t ), which also demarcate the fractured zone's limits.Horizontally, the boundaries are the horizontal distance from the adjacent coal pillar, including the outside boundary (B o ) and the inside boundary (B i ).In threedimensional terms, the SFSZ appears annular, as shown in Figure 8b, necessitating the definition of the outside and inside boundaries along the strike and dip directions, respectively.These are denoted as B o s and B i s in the strike direction, and B od and B id in the dip direction.

| Bottom boundary of SFSZ
Based on the characteristics of the SFSZ, the first broken stratum, forming a voussoir beam structure above the caved zone, serves as the SFSZ's bottom boundary (B b ).This boundary is influenced by various factors, such as mining height, caved strata expansion rate, and the sliding and rotary instability characteristics of the voussoir beam structure.The rock blocks composing the voussoir beam structure are determined using Equation (9). 40


where h r is the thickness of each layer of the main roof r from bottom to top; M is mining height; k r is the broken expansion rate of main roof r and its load strata, in the range of 1.15-1.33;∑h is the immediate roof thickness; k z is the expansion rate of immediate roof, in the range of 1.33-1.5;l r is the length of the broken rock block of main roof r.
Combined with Equation ( 9), the bottom boundary (B b ) can be obtained as follows:

| Top boundary of SFSZ
Within the SFSZ, the broken stratum develops upward in the form of a voussoir beam structure until the strata cease to break under the support of the underlying broken rock blocks.The level of the highest broken strata marks the top boundary (B t ) of the SFSZ.Hence, the state of the stratum, broken or not, acts as a criterion for identifying the SFSZ's top boundary.
The failure of a rock stratum typically requires two concurrent conditions: the span of the rock stratum must exceed its critical span, and the bending subsidence value of the rock stratum under this critical span must be less than the free space beneath it. 41In the case of strike longwall mining panels, the strike length exceeds the dip length.The broken height of the strata correlates with the panel's dip length.Therefore, following mining, the span of stratum i can be determined by the panel's dip length and the breaking angle of strata below stratum i, with the breaking angle being the angle between the breaking line of strata affected by mining and the horizontal line.The span of stratum i (l si ) after coal mining can be expressed as: where L is the dip length of the panel; h i is the thickness of stratum i; β d1 and β d2 represent the breaking angles of strata at the side of the return and intake airway of the panel, respectively.The unbroken stratum i is modeled as a fixed beam structure bearing a uniform load (q i ), allowing for the expression of stratum i's critical span (l maxsi ) as follows: where where R T is the ultimate tensile strength of stratum i; E i is the elastic modulus of stratum i; γ i is the bulk density of stratum i.
Thereafter, the first condition of the stratum i failure is l si ＞ l maxsi .
Upon the upward development of failure to stratum i, assuming the supporting foundation adheres to the Winkler foundation assumption (Figure 9), stratum i's maximum bending subsidence (y i ) can be articulated as follows 23 : where I i is the moment of inertia of stratum i; l h is half of the span of stratum i, given by l h = l si /2; ω is coefficient and can be calculated by using ω = (p/E i I i ) 1/4 , where p is elastic foundation coefficient, given by p = (E 0 /d 0 ) 1/2 and E 0 is elastic modulus of foundation supporting stratum i, d 0 is strata cushion thickness; α is coefficient and can be calculated by using the following relationship: As the broken stratum expands upward, the gap between it and the intact stratum above gradually narrows.The space beneath stratum i (Δ i ) is quantified as follows: where k si is the residual expansion rate of the pressurebearing broken rock stratum under the stratum i.
Thus, the failure of stratum i meets the condition y i < Δ i .Together with the initial condition, the failure of stratum i must satisfy two criteria: Consequently, when stratum i breaks and the stratum above it remains intact, the top boundary (B t ) of the SFSZ can be identified using Equation ( 17) as follows: (17)

| Outside boundary of SFSZ
Affected by mining, the breaking angle of a certain stratum can be obtained using Equation ( 18) as follows 42 : where φ is the internal friction angle of the stratum; η is the coefficient of breaking span, which is 9/2 for the first broken of the stratum and 3 for the periodic broken.
According to the key stratum theory, 23 the key stratum and its overlying strata (load layers) can be considered as a whole.The breaking of the key stratum controls the breaking of the load layers.Therefore, the combined breaking angle of the key stratum and its load layers can be approximated by the breaking angle of the key stratum alone.Consequently, along the strike direction, the strata breaking angle (β s ) can be obtained using Equation (19) as follows: where m is the number of immediate roof stratum below the first key stratum; h j is the thickness of the stratum j; β j is the breaking angle of the stratum j; n is the key stratum number within the range from coal seam to the top boundary of the SFSZ; h k is the total thickness of the key stratum k and its load layers; β k is the combined breaking angle of the key stratum k and its load layers.
Along the dip direction, the dip angle of strata is denoted as δ.Based on the characteristics of strata movement and deformation, the breaking angle of the strata should be corrected based on the strike-breaking angle.The breaking angle of strata along the dip direction (β d ) can be obtained using Equation (20) as follows: where f is the coefficient related to lithology, of which the negative value is taken on the uphill side, and the positive value is taken on the downhill side, usually ranges from ±0.3 to ±0.8.Assuming that strata failure develops upward to stratum i, the outer boundary of the SFSZ is defined as the horizontal distance from the adjacent coal pillar.The outer boundary along the strike and dip directions (B os and B od ) of the SFSZ can be expressed as follows: where H i is the normal distance from stratum i to coal seam; δ is the dip angle of strata, the positive value is taken on the uphill side, and the negative value is taken on the downhill side.

| Inside boundary of SFSZ
In the fractured zone, strata break to form the voussoir beam structure.The lowest stratum in the fractured zone is analyzed, as shown in Figure 10.It is assumed that the lengths of the broken blocks of the stratum are equal, that is, The rotation angles of the broken blocks of the stratum are expressed as From the stability analysis of broken block "S-R," 43 combined with Equation ( 9), the rotation angle of broken block 1 can be expressed as follows: where l is the length of the broken block of the stratum, given by l h R q = 2 / T .According to the displacement characteristics of the entire voussoir beam structure, the rotation angle of a broken block satisfies the following equation: .
As shown in Figure 10, fractures between the broken blocks in the bending section of the structure are clearly developed, whereas fractures in the flattening section are gradually closed.Research statistics 18 indicate that a separation fracture rate of 3‰ can serve as the critical value for fracture closure in the voussoir beam structure.
Therefore, using a separation fracture rate of 3‰ as the boundary, the width of the SFSZ refers to the range where the separation fracture rate in the voussoir beam structure exceeds 3‰.Setting θ n at 3‰ and substituting it into Equation ( 23) yields: Hence, the width of the SFSZ (W s ) can be defined as follows: Combining Equations ( 22), (24), and ( 25), the width of the SFSZ (W s ) can be determined.Then, based on the determination of the SFSZ's outer boundary (B os and B od ), the inner boundary (B is and B id ) can be expressed as follows:

| Layout position of the LHB
The section above determined that the SFSZ is the suitable zone for the LHB layout, and the boundaries of the zone were defined.The layout range of the LHB in mining overlying strata is obtained, but the position of the LHB still requires further analysis.

| Position criterion of the LHB
Given the characteristics of the LHB's small diameter, horizontal layout, and small extraction radius, its position in the mining overlying strata must satisfy the following conditions: (1) a high degree of gas accumulation around the LHB; (2) high permeability of mining strata nearby the LHB; (3) stability of the LHB affected by The stratum breaks to form the voussoir beam structure.SFSZ, stable fractured subzone.
mining.Therefore, to determine the position of the LHB, a position criterion (C p ) is proposed, which can be decomposed into three-factor indices: the degree of gas accumulation (R a ), the permeability of mining strata (R p ), and the stability of the LHB affected by mining (R s ).
The formula can be expressed as: Relevant research 16,17 shows that the extraction radius of the LHB in the mining overlying strata is about 5 m.To reduce the interaction between LHBs and improve extraction efficiency, the spacing of the LHBs should be twice the extraction radius, about 10 m.According to similar simulation results, the width of the SFSZ is about 25 m, and its height is 27.9 m.Therefore, in accordance with the LHB spacing, the SFSZ in the test can be divided into nine parts, namely, the upper-outer, upper-middle, upper-inner, middleouter, middle-middle, middle-inner, lower-outer, lowermiddle, and lower-inner parts (Figure 11).Due to the width and height of each part are about 10 m, setting the LHB position at the center of each part can meet the spacing requirements for LHB arrangement.In conjunction with the physical simulation test, this discussion quantitatively addresses the three conditions for the LHB position.

| Degree of gas accumulation
The gas concentration in the fractured zone (ρ) increases with the distance to the gob bottom (d) as follows: where a denotes a constant; λ is a coefficient considering the molecular diffusion and pressure diffusion of gas in fracture channels, which can be taken as 0.019. 29Moreover, Equation ( 28) has been verified by Li et al. 44 In the test, the mining height is 3 m, the height of the caved zone is 8.5 m, and the fractured zone is 27.9 m.The average heights of the upper, middle, and lower strata in the SFSZ (Figure 11), measured from the gob bottom, are 16.15, 25.45, and 34.75 m, respectively.Thus, the gas concentration at the LHB's corresponding positions in the SFSZ can be calculated using Equation (29).According to Equation ( 29)'s results and the normalization method, the overall gas accumulation degree (R a ) of the SFSZ is set to 1, and the relative values of R a for each part after normalization are listed in Table 3.

| Permeability of mining strata
The exponential function fits the separation fracture rate of the observation points in the SFSZ.This yields the fitting curves for the upper, middle, and lower strata in the SFSZ (Figure 12).The layers of the upper, middle, and lower strata in the SFSZ are shown in Figure 11. Figure 12 illustrates that by integrating the three fitting curves, respectively, the integral areas of the separation fracture rate for the outer, middle, and inner strata are obtained.Then, the average separation fracture rates for each part are calculated, as listed in Table 4. Additionally, previous experimental data indicates that the equation for mining strata permeability (K) and the fracture rate of fractured strata (ϕ p ) is as follows 45 : where μ is the dynamic viscosity coefficient of air at 25°C, μ = 1.834 × 10 −5 Pa s.By substituting the average separation fracture rates from Table 4 into Equation (30), the permeability of each part is determined.The overall mining strata permeability (R p ) of the SFSZ is set to 1, and the relative values of R p for each part after normalization are listed in Table 4. T A B L E 3 Relative value of gas accumulation degree (R a ) of each part in the SFSZ.

Gas concentration
Relative value of gas accumulation degree (R a ) The stability of the LHB arranged in the fractured zone is influenced by rock stratum fractures.The number of fractures in each part of the SFSZ within the fractured zone is statistically analyzed, as depicted in Figure 13.
Figure 13 shows the number of fractures in each part that impact the LHB's stability.The values are calculated using the reciprocal method and are provided in Table 5.These values represent the relative stability of the LHB layout in each part of the SFSZ.The overall stability of the LHB (R s ) in the SFSZ is set to 1, and the relative values of R s for each part after normalization are listed in Table 5.

| Position determination of the LHB
By substituting the three-factor values from Tables 3-5 into Equation ( 27), the position criterion value of the LHB in each part is calculated.Similarly, the overall position criterion (C p ) of the LHB in the SFSZ is set to 1, and the values of C p for each part after normalization are shown in Figure 14.

| Method procedure of the LHB layout
Based on the analysis, a "zone-position" method for determining the LHB position in the overlying strata is proposed, with its procedure illustrated in Figure 15.
From Figure 15, the zone suitable for the LHB layout is first defined based on the mining method, panel parameters, and the lithology sequence of the overlying strata.The identified zone is then divided into several parts according to the LHB extraction spacing.Three factors affecting the LHB's position are analyzed to establish the position criterion for the LHB in each part.Finally, the LHB layout's position sequence is determined.

| Layout zone
The boundaries of the SFSZ (uphill side) are defined by theoretical formulas in Section 4, with the results listed in Table 6.The lithology parameters of the overlying strata used in the calculations are shown in Figure 3.

| Layout position
Thereafter, the defined SFSZ (uphill side) is divided into nine parts.Three LHBs with a diameter of 96 mm each are drilled along the strike in the overlying strata.Borehole 1# is located at position I, with a length of 291 m.Borehole 2# is located at position II, with a length of 336 m.Borehole 3# is located at position III, with a length of 264 m.The spacing of the LHBs is about 10 m, as shown in Figure 16.

| Gas extraction of the LHB
During the excavation of the panel, the extraction data of the three LHBs are statistically analyzed, as shown in Figure 17.
Figure 17 shows that the gas extraction volume starts to increase when boreholes 1-3# are 18, 14, and 7 m away from the working face, respectively.However, the gas extraction volume is very small, and the average pure volume of gas extracted through the three boreholes is 0.04, 0.06, and 0.24 m 3 min −1 , respectively.At this time, there is no obvious fracture development inside the overlying strata around the boreholes.When the working face passes 11, 11, and 9 m from the ends of boreholes 1-3#, respectively, the pure volume of gas extracted increases significantly to 0.75, 0.13, and 0.36 m 3 min −1 , respectively, and then continues to increase and maintain stable extraction.This indicates that the fractures around the boreholes have developed, and the boreholes are in the SFSZ.
The above LHB extraction data shows that: (1) The layout zone of LHB.When the LHBs are in the SFSZ, the extraction volume increases rapidly and maintains a high value with the advance of the working face.During the mining of the working face, the gas emission is 6.08 m³/min.Affected by the gas extracted through the LHBs in the SFSZ, the gas concentration in the return airway fluctuates in the range of 0.17%-0.46%.The gas drainage by ventilation fluctuates in the range of 1.44-3.90m 3 min −1 , as shown in Figure 18.As the LHBs successively enter the SFSZ for gas extraction (around September 21), the proportion of gas drainage by ventilation is only about 40%, indicating that the gas extraction effect of the LHBs is significant.It also verifies that the SFSZ is a suitable zone for LHB layout and gas extraction.

| CONCLUSIONS
Efficient gas extraction from overlying strata presents a complex challenge, necessitating a multifaceted understanding of geology, rock mechanics, fluid mechanics, and fracture mechanics.This research concentrates on pressure-relief gas extraction prompted by underground mining, introducing a novel method to identify the optimal LHB position for effective gas extraction.This method has been corroborated by an engineering case.The findings are summarized in three main conclusions: (1) The fractured zone is divided into four subzones based on fracture development characteristics: the From Equations ( 22) and ( 24  initial fissure subzone, the tensile fractured subzone, the SFSZ, and the compaction-fractured subzone. After evaluating fracture distribution and LHB stability, the SFSZ is identified as the most appropriate area for LHB placement.Its spatial boundaries are theoretically delineated.(2) An LHB position criterion is proposed considering the gas accumulation degree, mining strata permeability, and LHB mining-affected stability.The SFSZ is divided into nine parts to further determine the LHB-specific position.The three factors of each part are analyzed quantitatively.Additionally, the position sequence of the LHB is obtained, and then the best position of the LHB in overlying strata is determined accordingly.Therefore, a "zoneposition" method for determining the best position of the LHB in overlying strata is proposed.(3) The effectiveness of the proposed method is validated through an engineering case, demonstrating that gas extraction via LHB constitutes approximately 60% of total gas emissions.The pure volume of gas extracted at the optimal LHB location reaches up to 5.52 m 3 min −1 , tripling the volume extracted from other locations.Moreover, gas concentrations measured in the return airway, ranging from 0.17% to 0.46%, fall below the 1% threshold specified by the Coal Mine Safety Regulations in China, affirming the method's validity.

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Pressure-relief gas extraction by the long horizontal boreholes (LHB).

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T A B L E 2 On-site parameters and indoor experimental parameters.I G U R E 5 Fracture channels of vertical "three zones": (A) Fracture evolution; (B) Separation fracture rate.

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I G U R E 6 Deformation and failure characteristics of the long horizontal boreholes with the mining: (A) in caved zone; (B) in fractured zone; and (C) in bending zone.F I G U R E 7 Horizontal four subzones in fractured zone: (A) Separation fracture rate, the subzones here are divided based on the separation fracture rate of middle strata; (B) distribution in the mining simulation model.Subzone I. Initial fissure subzone: The separation fracture rate of this zone is zero, and no new fracture channels are generated.The strata essentially maintain their original state.Subzone Ⅱ. Tensile fractured subzone: The separation fracture rate of this zone is less than 1 mm m −1 , and the fracture channels are slightly developed due to strata in this zone forming a cantilever beam structure affected by mining, resulting in microseparation fractures between the strata.The boundary between the initial fissure subzone and the tensile fractured subzone is marked by a separation fracture rate of the strata greater than 0 mm m −1 .Subzone Ⅲ. Stable fractured subzone (SFSZ): The separation fracture rate of this zone is the highest, with a width of about 25 m.The separation fracture rates of the upper, middle, and lower strata in this zone reach up to 195.6, 148.2, and 122.1 mm m −1 , respectively.The stratum in this zone forms a voussoir beam structure, resulting in the development of fracture areas.The tensile fractured subzone and the SFSZ are delineated by the breaking line of the strata.Subzone Ⅳ. Compaction-fractured subzone: The separation fracture rate of this zone significantly decreases to less than 3 mm m −1 .The broken strata in this zone gradually compacted under the periodic weighting of the main roof.The boundary between the SFSZ and the compaction-fractured subzone is marked by a separation fracture rate of the strata of 3 mm m −1 .These four subzones are symmetrically distributed, with subzone IV at the center.By analyzing the three F I G U R E 8 Diagrams in two-dimensional and three-dimensional for presenting the stable fractured subzone (SFSZ) (Subzone Ⅲ) and the long horizontal boreholes (LHB): (A) Schematic illustration of dip cross-section; (B) three-dimensional diagram.Note: B t , B b , B o , and B i are the top, bottom, outside, and inside boundary of the SFSZ, respectively; ψ s and ψ d are the critical deformation angles of overlying strata in strike and dip, respectively; β s and β d are the breaking angle of overlying strata in strike and dip, respectively.

F I G U R E 9
Mechanical model of Winkler foundation beam.

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I G U R E 11 Division of the stable fractured subzone (SFSZ) and the position of the long horizontal boreholes (LHB) in each part.

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I G U R E 13 Statistics of in each part.T A B L E 5 Relative value of the LHB stability (R s ) of each part in the SFSZ.

F I G U R E 14 DISCUSSION 4 . 1 |
Position criterion value of the long horizontal boreholes in each part.F I G U R E 15 Procedure of the "zone-position" method for determining the position of the long horizontal boreholes (LHB).SFSZ, stable fractured subzone.4| Layout of the LHBThe No. 16031 panel in the Guhanshan coal mine serves as the test site.Utilizing the proposed method, LHBs are arranged to extract pressure-relief gas during the mining process.

( 2 )
The layout position of LHB.The pure volume of gas extracted through boreholes 1-3# at different positions in the SFSZ is shown in Figure19.The maximum pure volumes of gas extracted through boreholes 1-3# are 5.52, 1.27, and 1.05 m 3 min −1 , respectively.The corresponding average pure volumes are about 2.43, 0.61, and 0.41 m 3 min −1 .The data for borehole 1# (at position I) is the largest, and the extraction effect is the best.The average pure volume of gas extracted through the borehole at position I is 3.98 and 5.93 times that at positions II and III, respectively.This verifies the rationality of determining the LHB position according to the proposed "zone-position" method.
Mechanical properties of the strata and the proportion of similar materials in the model.
T A B L E 1 The relative value of mining strata permeability (R p ) of each part in the SFSZ.