Mining stress formation and distribution: Predictive model based on overburden key strata structure

In coal mines, the effective extraction of relief gas and the prevention of dynamic disasters depend on accurate predictions of the spatial distribution of mining stress in the overlying rock. However, at present, the prediction of stress relief and concentration zones based on operational experience or empirical modeling differs significantly from actual measurements in the field. The fundamental problem is the difficulty in modeling the transfer mechanism of the mining overburden load under the influence of key strata. In this study, a mechanical model of the spatial distribution of the mining stress field based on the structure of overburden key strata was established. The model demonstrates that the key strata are the main bearing bodies of the overlying rock, both before and after the fracture, and the overburden rock load can be transferred to the coal and rock mass around the stope through the key strata in the fracture and bending subsidence zones, thus forming a mining stress field. Equations for calculating the plane distributions of mining stress under the key strata at different horizons and abutment pressures on the stope were established, and a spatial distribution prediction method for the mining stress field based on the overburden key strata structure was proposed. The study area was the Gaojiapu Coal Mine, where it was found that the key stratum of the 400.45 m thick Luohe Formation sandstone bore most of the overlying rock load and transferred the load to the coal and rock mass around the stope. This load distribution is the root cause of a high concentration and wide influence range of mining stresses, leading to serious deformation of the main roadway and frequent dynamic disasters. The mining stress concentration was maximized at a mining length of 1458 m × 1458 m.

The fundamental problem is the difficulty in modeling the transfer mechanism of the mining overburden load under the influence of key strata.
In this study, a mechanical model of the spatial distribution of the mining stress field based on the structure of overburden key strata was established.The model demonstrates that the key strata are the main bearing bodies of the overlying rock, both before and after the fracture, and the overburden rock load can be transferred to the coal and rock mass around the stope through the key strata in the fracture and bending subsidence zones, thus forming a mining stress field.Equations for calculating the plane distributions of mining stress under the key strata at different horizons and abutment pressures on the stope were established, and a spatial distribution prediction method for the mining stress field based on the overburden key strata structure was proposed.
The study area was the Gaojiapu Coal Mine, where it was found that the key stratum of the 400.45 m thick Luohe Formation sandstone bore most of the overlying rock load and transferred the load to the coal and rock mass around the stope.This load distribution is the root cause of a high concentration and wide influence range of mining stresses, leading to serious deformation of the main roadway and frequent dynamic disasters.The mining stress concentration was maximized at a mining length of 1458 m × 1458 m.

| INTRODUCTION
Dynamic disasters, such as rockbursts and coal and gas outbursts pose serious challenges for the safe and efficient mining of coal resources.2][3][4][5] The stress and gas pressure of the coal and rock masses were significantly reduced in the mining pressure-relief area, eliminating the risk of dynamic disasters.7][8][9] Therefore, accurately predicting the spatial distribution of the stress field caused by mining activities is critical for efficient and accurate gas extraction in the mining pressure-relief areas.These predictions are also necessary to determine the effective protection range of mining pressure-relief measures and to guide the early warning and prevention of dynamic disasters in stress concentration areas.
Researchers have conducted numerous studies 5,10-15 on the formation mechanism and spatial distribution prediction methods of the mining stress field and proposed a number of hypotheses and theories, [16][17][18][19] such as the arch hypothesis, cantilever beam hypothesis, hinged rock block hypothesis, progenerated fissure hypothesis, masonry beam theory, transfer rock beam theory, and key strata theory of rock strata control.][28][29] These empirical methods do not consider the influence of the key strata of the overlying rock on the spatial distribution of the mining stress field, and the estimates obtained often deviate significantly from actual field measurements.This discrepancy poses a serious problem in coal mine production.
18]34 However, the relationship between the characteristics of key strata fractures and movement at different horizons and the formed bearing structure, load transfer and transmission of the overlying rock during mining, and spatial distribution of the stress field have not been identified, and the coupling effect between key strata at different horizons has not been considered.As a result, existing mining stress prediction methods fail to fully consider the lengths of the mining stope, the influence of the fracture motion characteristics of key strata on the stress field distribution, and the conditions of key strata in the overlying rock, such as the number of key strata, horizon, thickness, stiffness, and interlayer combination.They cannot predict the plane distribution of mining stress under key strata at different horizons in the overlying rock.The formation mechanism and spatial distribution of the mining stress field, incorporating the influence of key strata in the overlying rock, are yet to be satisfactorily ascertained.
Qian et al. 17 pointed out that the occurrence and fracture characteristics of overburden key strata have a significant impact on the spatial distribution of the mining stress field, and called for a more thorough investigation of the quantitative relationship between the fracture and movement of key strata of the overburden and the mining stress field, with the goal of developing predictive models.Our research team conducted preliminary studies on the relationship between the key strata structure in the overlying rock and the mining stress field and proposed an abutment pressure prediction method based on the key strata theory and Winkler elastic foundation theory. 14However, this method only applies to the prediction of the abutment pressure distribution of one main section of a stope when another main section is sufficiently mined, and it is not possible to predict the spatial distribution of the mining stress field for different mining lengths.Thus, the formation mechanism of the mining stress field could not be ascertained.Therefore, the goal of the current study is to develop a model capable of predicting the formation mechanism and spatial distribution of the mining stress field based on the key strata structure of the overlying rock.In particular, the causes of abnormal distribution of the stress field are of interest.The study area was the Gaojiapu Coal Mine, which is the site of large deformation in the mine roadway.In addition, accurately predicting the distribution of the mining stress field will aid in predicting dynamic disasters and in taking preventative measures.

MECHANISM OF MINING STRESS BASED ON THE STRUCTURE OF KEY STRATA IN THE OVERBURDEN
The process of coal mining disrupts the initial ground stress balance, causing the overlying strata to break and bend (subside), resulting in the formation of different zones, such as caving, fissures, and bending subsidence, from the bottom to the top in the vertical strata.Consequently, the overburden stress is redistributed, producing what is known a mining stress field.7][18] The degree to which the overburden stress changed depended primarily on the breaking movements of the key strata.][18] To reveal the mechanical mechanism of the mining stress field formed by the transfer of mining overburden loads under the coupling of key strata at different horizons, it is assumed that the key strata at different horizons in the overburden and their load rock strata comply with the Winkler elastic foundation hypothesis, 14 and that between the adjacent key strata in the overburden, the lower KS and its load rock strata serve as the foundation of the upper KS.Simultaneously, the nonuniform applied force of the upper KS on the foundation is taken as the load of the lower KS.Because the stope formed by longwall mining in coal mines is usually rectangular in shape, there are two main crosssections, namely main cross-section Ι and main cross-section ΙΙ, as shown in Figure 1.For the main cross-section Ι, main cross-section ΙΙ, and any cross-section parallel to the above two cross-sections, the KS i (1 ≤ i ≤ m − 1, i ∈ N + ) at different horizons on the solid coal side in the fracture zone is simplified as a multilayer superposition semi−infinite elastic foundation beam, and the KS i (1 ≤ i ≤ m − 1, i ∈ N + ) at different horizons on the goaf side in fracture zone is simplified as a multilayer superposition "masonry beam."The KS i (m ≤ i ≤ n, i ∈ N + ) at different horizons in the bending subsidence zone is simplified as a multilayer superposition elastic foundation beam of infinite length and a mechanical model of mining stress field evolution based on the key strata structure in overlying rock is established, as shown in Figure 2.
In Figure 1, L 1 and L 2 are half of the mining lengths (m) of main cross-sections Ι and ΙΙ, respectively, Z 5 is the whole mining stress field prediction range (rectangular A 3 B 3 C 3 D 1 region).Z 4 is 1/4 of the predicted range of the mining stress field (rectangular A 1 BC 1 D 1 region).Z 3 is the 1/4 equal subregion on the goaf side (rectangular ABCD region), and Z 2 is the 1/4 equal subregion of the plastic zone on the solid coal side (rectangular A 2 BC 2 D 2 minus rectangular ABCD region).Z 1 is 1/4 of the elastic region on the solid coal side (rectangle A 1 BC 1 D 1 minus rectangle A 2 BC 2 D 2 ).
In Figure 2, the key strata are successively KS i from bottom to top i (1 ≤ i ≤ n, i ∈ N + ).The key strata in the fissure zone were successively KS 1 to KS m − 1 from bottom to top, and the key strata in the bending subsidence zone were successively KS m to KS n from bottom to top.The distribution of the key strata in the overburden is determined by the key strata theory according to the overlying rock column shape of the borehole.The heights of the caving and fissure zones were then calculated according to the occurrence conditions of the key strata, 36 and the key strata distributions in the fissure and bending subsidence zones were determined.
Based on the output of the mechanical model (Figure 2), the broken key strata at different horizons on the goaf side of the fracture zone, the key strata at different horizons on the solid coal side of the fracture zone, and the key strata at different horizons in the bending subsidence zone, forming the multilayer superposed "masonry beam," multilayer superposed semi-infinite length elastic foundation beam and multilayer superposed infinite length elastic foundation beam, respectively, which together constitute the overburden bearing structure.The mining stress field is formed by the transfer and transmission of overlying rock loads under the coupling of key strata structures at different horizons.
The key strata both before and after fracture are the main bodies bearing the overburden load.The overlying rock load can be transferred to the solid coal and rock mass around the stope through the broken block of the key strata in the fracture zone and the unbroken key strata in the bending subsidence zone, which causes the flexural subsidence of the key strata and exerts a force on the underlying coal and rock mass, thus forming a mining stress field in the surrounding coal and rock mass of the stope.

| PREDICTION OF MINING STRESS FIELD BASED ON OVERBURDEN KEY STRATA STRUCTURE
3.1 | Prediction equations of mining stress plane distribution of unbroken key strata

| Main section under full mining
According to the mechanical model presented in Figure 2, the KS i (1 ≤ i ≤ n, i ∈ N + ) at different horizons on the solid coal side in the fracture and bending subsidence zone and the KS i (m ≤ i ≤ n, i ∈ N + ) at different horizons on the goaf side in the bending subsidence zone are simplified as multilayer superposition elastic foundation beams.Under the condition of full mining of the main section ΙΙ (i.e., L 2 ≥ L 0 ), L 0 represents the extent of mining (length of longwall, in m) when the main section Ι or ΙΙ is in full mining motion.The mining stress concentration in the overburden reached a maximum value, followed by stability when the extent of mining in main sections Ι and ΙΙ was L 0 (i.e., full mining reached).In the case of main section Ι, the multilayer superposition elastic foundation beam deflection partial differential equations of key strata i (1 ≤ i ≤ n, i ∈ N + ) on the solid coal side, and key strata i (m ≤ i ≤ n, i ∈ N + ) on the goaf side in the bending subsidence zone can be established, as shown in Equations ( 1) and ( 2), respectively.Based on the relationship between Winkler elastic foundation beam deflection and the load and foundation coefficient, when the main section ΙΙ is in full mining mode, the mining stress distribution equations at the bottom interface of key strata i (1 ≤ i ≤ n, i∈N + ) on the solid coal side and key strata i (m ≤ i ≤ n, i ∈ N+) in bending subsidence zone on the goaf side of main section Ι are shown as Equations ( 3) and ( 4), respectively.At this time, in formula ( 1)-( 4), s, j, y, and L is equal to Ι, x, L 2 , and L 1 , respectively, representing the main section Ι.
Similarly, when the main section Ι is in full mining mode (i.e., L 1 ≥ L 0 ), the multilayer superposition elastic foundation beam deflection partial differential equations of key strata i (1 ≤ i ≤ n, i ∈ N + ) on the solid coal side and key strata i (m ≤ i ≤ n, i ∈ N + ) in the bending subsidence zone on the goaf side in main section ΙΙ can be established, shown here as Equations ( 1) and ( 2), respectively.The mining stress distribution equations at the bottom interface of key strata i (1≤i ≤ n, i ∈ N+) on the solid coal side and key strata i (m ≤ i ≤ n, i ∈ N+) in the bending subsidence zone on the goaf side of the main section ΙΙ are presented here as Equations ( 3) and ( 4), respectively.At this time, in formula ( 1)-( 4), s, j, x, and L is equal to ΙΙ, y, L 1 , and L 2 , respectively, representing the main section II.
where E i is the elastic modulus of KS i at different horizons, 1 ≤ i ≤ n, i∈N + , GPa; I i is the cross sectional moment of inertia of KS i at different horizons, 1 ≤ i ≤ n, i∈N + , m 4 ; s is the variable, and the value can be Ι or ΙΙ; j is the variable, and the value can be x or y; L is the variable, and the value can be L 1 or L 2 ; q i is the dead weight of KS i and its loaded rock strata at different horizons, 1 m is the foundation coefficient of the goaf side of KS m at the bottom of the bending subsidence zone, MN/m 3 ; w Ι,i (x, L 2 ) and w ΙΙ,i (L 1 , y) is the flexural equation of KS i on the coal body side of main sections Ι and ΙΙ, respectively, 1 is the flexural equation of KS i on the goaf side of main sections Ι and ΙΙ, respectively, m ≤ i ≤ n, i ∈ N + , m; σ Ι,i (x, L 2 ) and σ ΙΙ,i (L 1 , y) is the mining stress equation of KS i on the coal body side of main sections Ι and ΙΙ, respectively, is the mining stress equation of KS i on the goaf side for main section Ι and main section ΙΙ, respectively, HAN ET AL.
| 1555 i ∈ N + , MPa; q 0 is the rock body weight between KS 1 and the coal seam, MPa; b is the width of the beam, where the unit width is b = 1, m; Q i is the initial vertical ground stress of KS i at different horizons, 1 ≤ i ≤ n, i ∈ N + , measured in MPa.The method 14 proposed by our research team can be used to solve these equations.

| Main section under different mining lengths
Equations ( 3) and ( 4) are applicable for the prediction of the mining stress distribution of KS i (1 ≤ i ≤ n, i ∈ N + ) at different horizons on the coal mass side and the mining stress distribution of KS i (m ≤ i ≤ n, i ∈ N + ) at different horizons on the goaf side in the bending subsidence zone of the main cross-section Ι, on the condition that the main cross-section ΙΙ has reached full mining mode.In addition, Equations ( 3) and ( 4) are also applicable to predicting mining stress distribution of KS i (1 ≤ i ≤ n, i ∈ N + ) at different horizons on the coal mass side and mining stress distribution of KS i (m ≤ i ≤ n, i ∈ N + ) at different horizons on the goaf side in the bending subsidence zone of main cross-section ΙΙ, on condition that the main cross-section Ι has reached full mining mode.However, in the actual mining operation, due to the influence of the mining lengths, it is possible that the main cross-section Ι or ΙΙ may not be in full mining mode.Based on the mining lengths of the two main sections, there are actually four possible degrees or intensities of mining operations as follows 35 : (1) main section Ι is in a state of incomplete mining and main section ΙΙ is in full mining mode, (2) main section Ι is in full mining mode and main section ΙΙ is incompletely mined, (3) both main sections are in full mining mode, and (4) both main sections are incompletely mined.The mining stress distribution of unbroken key strata under different degrees or states of mining can be calculated by applying a reduction coefficient.Under the condition of variable extent of mining of main crosssection II, the flexion equations of key strata i for the main cross-section Ι in Equations ( 3) and ( 4) should be multiplied by the corresponding reduction coefficient λ ΙΙ,i (1 ≤ i ≤ n, i ∈ N + ), respectively, which represents the reduction multiple of the flexion of key strata i for the main cross-section Ι due to the main cross-section ΙΙ being in a state of incomplete mining.When λ ΙΙ,i (1 ≤ i ≤ n, i ∈ N + ) are all equal to 1, this indicates that the main-section ΙΙ is in full mining mode.Under the condition of variable extent of mining of main crosssection Ι, the flexion equations of key strata i for the main cross-section ΙΙ in Equations ( 3) and ( 4) should be multiplied by the corresponding reduction coefficient λ Ι,i (1 ≤ i ≤ n, i ∈ N + ), respectively, which represents the reduction multiple of the flexion of key strata i in the main cross-section ΙΙ due to the main cross-section Ι being incompletely mined.When λ Ι,i (1 ≤ i ≤ n, i ∈ N + ) are all equal to 1, this indicates that the main section Ι is in full mining mode.
Because the intersection coordinate of main sections Ι and ΙΙ are (L 1 , L 2 ), the deflection of key strata at different horizons of the two main sections are equal at this point under different degrees of mining operation.When both main sections reach full mining mode, λ Ι,i and λ ΙΙ,i (1 ≤ i ≤ n, i ∈ N + ) are both 1. Applying the above two boundary conditions, when s = Ι and s = ΙΙ, λ Ι,i and λ ΙΙ,i (1 ≤ i ≤ n, i ∈ N + ) can be calculated, respectively, as shown in Equation (5).
where W max is the maximum formation subsidence under the geological conditions of the mine (m), which is the product of the coal seam mining thickness M and the subsidence coefficient q.

| Any section parallel to the main section
Following Equations ( 1)-( 5), the mining stress distribution equations of the unbroken key strata at different horizons under different mining lengths can be obtained for the two main sections, but they cannot be used to predict the plane distribution of the mining stress.Due to the profile being parallel to the main cross-sections Ι and ΙΙ, the flexion distribution of key strata at different horizons are similar to the corresponding main cross-section. 35On the y-section parallel to the main section ΙΙ, the deflection distribution of times the deflection equation of the main section ΙΙ, which can be calculated from Equation (6).At this time, in formula (6), s, j, y, and L is equal to Ι, x, L 2 , and L 1 , respectively.When x = L 1 , that is the main section ΙΙ, and ζ Ι,i (x,L 2 ) (1 ≤ i ≤ n, i ∈ N + ) is assumed to be 1.On the x-section parallel to the main section Ι, the deflection distribution of KS i at different horizons is ζ ΙΙ,i (L 1 ,y) (1 ≤ i ≤ n, i ∈ N + ) times the deflection equation of the main section Ι, which can be calculated from Equation (6).At this time, in formula (6), s, j, x, and L is equal to ΙΙ, y, L 1 , and L 2 , respectively.When y = L 2 , that is the main section Ι, and The distribution of mining stress under KS i at different horizons is shown in Equations ( 7) and ( 8) for the solid coal body side and in Equations ( 9) and (10) for the goaf side in the bending subsidence zone.By simplifying Equations ( 9) and (10), it can be seen that the output of these two equations is identical, given that Equations ( 9) and ( 10) are obtained from mining stress distribution equations parallel to main cross sections Ι and ΙΙ, respectively, and are used to calculate the plane distribution of mining stress under the key strata at different horizons within the range of 0 < x ≤ L 1 and 0 < y ≤ L 2 .
where σ i (x,y) (1 ≤ i ≤ n, i ∈ N + ) is the plane distribution equation of mining stress under KS i at different horizons on the solid coal body side, measured in MPa; σ c i (x,y) (m ≤ i ≤ n, i ∈ N + ) is the corresponding plane distribution equation on the goaf side in bending subsidence zone, measured in MPa.

| Prediction equation of mining stress plane distribution of broken key strata on goaf side in fracture zone
Applying Equations ( 7)- (10), the plane distribution of mining stress under the key strata at different horizons on the goaf side in the bending subsidence zone and on the solid coal side can be obtained; however, the corresponding distribution ofthe mining stress in the fracture zone is stillmissing.As the "masonry beam" bearing structure is formed by the breaking of key strata at different horizons on the goaf side in the fracture zone,the broken key strata at different horizons are simplified as multilayer superimposed "masonry beams," and it is assumed that half of the dead weight of the broken KS block "masonry beam" at different horizons is transferred to the coal androck mass around the stope.The other half of theload was transferred to the goaf, and the force on the lower rock mass exhibited a linear distribution.Considering the force of the key strata in the bending subsidence zone on the goaf side on the broken key strata in the fracture zone (at the lower part), the plane distribution equation of the mining stress under the KS i (1 ≤ i ≤ m−1, i ∈ N + ) in the fracture zone at different horizons on the goaf side for the 1/4 equal regions (Z 3 region in Figure 1) is obtained from Equation (11).
By applying Equations ( 7)-( 11), the plane distribution of the mining stress under key strata at different levels in 1/4 of the predicted range (Z 4 region in Figure 1) can be obtained.Furthermore, the symmetry of the model can be used to predict the mining stress plane distribution under key strata at different horizons over the entire prediction range (Z 5 region in Figure 1).
where d c (x,y) is the minimum distance, in meters (m) between any point in the goaf and the goaf boundary and of the broken KS i at different horizons in the fracture zone.

| Prediction equation of abutment pressure plane distribution in stope
Equations ( 7) through (11) can be used to obtain the plane distribution equations σ 1 (x,y) and σ c 1 (x,y) of mining stress under KS 1 on the solid coal side and the goaf side.Considering the rock body weight q 0 between KS 1 and the coal seam and the plastic failure of the coal body under high mining stress concentration, combined with the distribution equations of the coal body in the plastic zone around the stope, 29 the plane distribution equation of the abutment pressure in the stope can be obtained from Equation (12).
where φ is the internal friction angle (°); c is the adhesion stress, (MPa); d(x,y) is the minimum distance, in meters (m) between any point in the solid coal body and the goaf boundary; and υ is the coefficient of horizontal pressure.From Equation ( 12), the plane distribution of the abutment pressure in the stope can be obtained for 1/4 equal regions of the entire prediction range (Z 4 region in Figure 1).The planar distribution of the abutment pressure in the stope can be predicted using the symmetry of the model.

| PREDICTION AND FIELD VERIFICATION OF THE MINING STRESS FIELD IN GAOJIAPU COAL MINE
Utilizing the geological conditions of the Gaojiapu Coal Mine, the spatial distribution of the mining stress field in panels 1 and 2 of the Gaojiapu Coal Mine was predicted using the new prediction method.The output of the model was compared with actual measurements of mining stress and the laws of mine pressure.

| Geological mining conditions of Gaojiapu Coal Mine
The Gaojiapu Coal Mine is located in the northern of Changwu County, Xianyang City, Shaanxi Province, in the Binchang Mining area.The main coal seam is a coal seam No. 4 with an average thickness of 9.81 m and a dip angle of 2°-7°.The sandstone of the overlying Luohe Formation is a medium to strong water-rich aquifer.To avoid communication with the aquifer, the average mining height of the working faces in panels 1 and 2 was approximately 5 m.The layouts of the working faces of the two panels are shown in Figure 3. Using the 30−3 borehole column near the mining areas, the key strata theory 18 and the fracture zone height prediction method 36 were applied to obtain the distribution of the key strata and "three zones" of mining overlying rock, as shown in Figure 4.

| Predicted values from the model
By applying the proposed mining stress prediction method, the distribution of the mining stress of the F I G U R E 3 Working faces layout of panels 1 and 2 in the Gaojiapu Coal Mine.
F I G U R E 4 Key strata and the "three zones" distribution of the overburden in the Gaojiapu Coal Mine.
HAN ET AL.
| 1559 key strata at different horizons in the overlying rock and the stope abutment pressure after mining in panel 1 of the Gaojiapu coal mine were predicted.As shown in Figure 4, there are four key stratain the overlying rock, and two key strata in the fracture and bending subsidence zones.This is reflected in the prediction model, where n = 4 and m = 3.The other calculation parameters are listed in Tables 1 and 2. The calculation length of the prediction model is 1460 m × 1400 m, mining length L 1 of main section Ι, approximately 460 m, and mining length L 2 of main section ΙΙ, approximately 400 m, as shown in Figure 3.The prediction results are shown in Figure 5A.The maximum stress level was reached when the gauges were 22, 23, and 21 m away from the working face, indicating that these distances were plastic zone widths.In addition, because of the proximity of the stress meter to the working face, the complete range of the abutment pressure could not be measured.However, the monitoring results showed that the range of the abutment pressure was much larger than the range of 40-60 m, known by experience, and the range was greater than 310 m.However, with respect to the decline rate of the stress monitoring curve, the abutment can be assumed to be near a steady state.The predictions obtained from the model (as shown in Figure 5A), indicate a peak abutment pressure of 34.4 MPa along panel 1 profile I−I and 34.9 MPa along profile II−II, which are 21.2 and 21.4 m away from the goaf boundary.This prediction was consistent with the in-situ stress measurement results (21-23 m).Generally, if 1.05 times of the original rock stress is taken as the boundary of the influence range of abutment pressure, 14,16 then the influence range of abutment pressure is 363.7 along profile I−I and 379.8 m along profile II−II, which are consistent with the field measured results.These results confirm the accuracy of the proposed prediction model.

| Field microseismic monitoring verification
In the Gaojiapu Coal Mine, a microseismic monitoring system was installed to monitor the distribution of microseismic events caused by mining on the working faces shown in panel 1.The monitoring results are shown in Figure 7, where the blue circles represent the microseismic events.There is a clear positive correlation between microseismic events and the abutment pressure distribution, and the influence range of the abutment pressure can be determined by the distribution range of microseismic events. 5,14As can be seen in Figure 7, along profiles I−I and II−II in panel 1, the microseismic events were distributed in ranges of 362.4 and 364.1 m outside the goaf boundary, respectively, which is consistent with the prediction results of the abutment pressure influence range (363.7 and 379.8 m, Figure 5A), which once again demonstrates the accuracy and reliability of the proposed prediction model.

| Predicted values from the model
The new mining stress field prediction method is used to predict the spatial distribution of the mining stress field after mining the three working faces, as shown in panel 2. The calculated length of the prediction model was 2150 m × 1500 m, and the length of the goaf was approximately 500 m × 1150 m.The other calculation parameters are listed in Tables 1 and 2, and the prediction results are shown in Figure 5B.The stope abutment pressure distribution after mining in the two panels (Figure 5A,B) is superimposed on the spatial distribution of the mining stress field, and the abutment pressure distribution values are predicted, as shown in Figure 8.

| Verification from in situ measurements
In the Gaojiapu Coal Mine, a protective coal pillar with a width of 150 m was set between the goaf boundary and the main roadway.According to conventional understanding, the empirical influence range of the abutment pressure in the stope is only 40-60 m, 14,16,22 and the main roadway is therefore well outside the estimated areas of stress from mining panels 1 and 2. However, actual field measurements indicated that the main roadway was affected by the mining of the two panels.The mining operations in panel 1 have been completed, and working faces 201 + 202 in panel 2 have also been completely mined.In the process of working face 203 in panel 2, serious deformation occurred on the main roadway, and several mine dynamic manifestations were reported.The ARAMIS microseismic monitoring system, installed in the mine, detected a large energy microseismic event of 8.8 × 10 6 J that occurred in the main roadway.The specific locations are shown in Figure 8.On the main roadway, the gunite roof layer, located within several 100 meters of the main roadway, collapsed.The extent of the collapse was estimated to be 2.0 m × 0.5 m × 1.0 m, and the floor heave was 0.3-1.5 m, the roadway section was reduced to 8 m 3 and the belt conveyor was overturned.The site of the damage to the main roadway is illustrated in Figure 9.
As shown in Figure 5A,B, the predicted influence range of abutment pressure is greater than 350 m in panels 1 and 2, much larger than the empirical range of 40-60 m.The minimum distance between the two panel areas and main roadway was 150 m.The main roadway is affected by the concentrated stress of the mining abutment pressure in the two panels, which leads to serious deformation of the main roadway and several dynamic mine manifestations.In addition, as indicated by the predicted abutment pressure distribution along the section of the main roadway (Figure 8), the stress concentration is greatest near main roadway No. 22, which is approximately 300 m from the mining boundary of working face 101 in panel 1, and 190 m from the mining boundary of working face 201 in panel 2. The aforementioned high-energy microseismic event (8.8 × 10 5 J) on August 16, 2018 20:06:06 s, occurred near the No. 22 gauge in the main roadway.The stress concentration location of the high mining abutment pressure predicted by the model was consistent with the mine pressure recorded on site, which can be considered as further verification of the accuracy of the proposed model.

| RESULTS AND DISCUSSIONS
5.1 | Spatial evolution laws of mining stress field under ultra-thick and hard KS Using the new prediction method, the spatial evolution of the mining stress field in the overburden of the Gaojiapu Coal Mine with a 400.45 m thick KS of the Luohe Formation sandstone under different mining dimensions was investigated.After working faces 201, 202, and 203 of panel 2 were successively mined, the extent of mining L 1 along main section Ι of panel 2 was approximately 1150 m, and the extent of mining L 2 along the main section II was approximately 132, 298, and 500 m, respectively.The other calculation parameters are listed in Tables 1 and 2. The predicted spatial distributions of the mining stress field in the overburden are shown in Figures 5B and 10.
The mining stress of KS 1, KS 2, KS 3, and KS 4 and abutment pressure concentration gradually increased with the mining of working faces 201, 202, and 203, and the concentration of mining stress on main section ΙΙ was obviously higher than that on main section Ι.The degree of stress recovery in the goaf also increases gradually.The peak abutment pressures on the stope in main section I were 27.4,32.1, and 38.4 MPa, respectively.The abutment pressure influence ranges were 118.6, 296.1, and 353.8 m, and the corresponding central stress values of the goaf were 3.6, 6.8, and 11.1 MPa, respectively.
Our calculations show that the mining stress concentration in the overburden reached a maximum value, followed by stability when the extent of mining in main sections Ι and ΙΙ was 1458 m (i.e., full mining reached), and the central stress of the goaf returned to the original rock stress of 25.37 MPa.The peak abutment pressure of the stope in the two main sections was 51.9 MPa, and the influence range of the abutment pressure in both sections was 389.8 m, as shown in Figure 11A.It can be seen that the mining stress concentration of the overlying rock increases with an increase in the extent or area of the mining length, but it does not increase without limit.The maximum value was obtained when the mining length reached 1458 m × 1458 m in the Gaojiapu Coal Mine.

| Model discussions
To analyze the adaptability and the sensitivity of the model under different geological conditions, as well as its effectiveness and superiority.The sections reached 51.9 MPa, 25.37 MPa and 389.8 m, respectively, as shown in Figure 11A.
It can be seen that the conditions of the key strata in the overlying rock have a significant influence on the distribution of the mining stress field.So, the differences of the abutment pressure distribution curves along the main section Ι, where the thickness of KS 4 was 30, 80, 200, and 400.45 m, respectively, were then further compared and analyzed using the new model, as shown in Figure 12.In Figure 12, the mining dimensions were 1600 m × 1600 m to ensure that the mining stress concentration of the overlying rock reached the maximum value.In addition, when the thickness of KS 4 was 400.45 m, the differences of abutment pressure distribution curves along the main section Ι, where the mining lengths was 132 m × 1600 m, 298 m × 1600 m, 500 m × 1600 m and 1600 m × 1600 m, respectively, were further compared and analyzed using the new model, as shown in Figure 13.Simultaneously, the aforementioned abutment pressure distribution curves were compared with the prediction results using the existing model 16,[23][24][25] based on the limit equilibrium theory, as shown in Figures 12 and 13.
As shown in Figures 5B, 11, and 12, the change in the KS thickness was found to have a significant influence on the distribution of mining stress.The greater the thickness of the KS, the larger is the critical mining length (area) corresponding to the stable extreme mining stress of the overlying rock, and therefore the more difficult it is for the stress in the goaf to recover to the original rock stress level.This resulted in the greatest degree of stress concentration after a stable mining stress was reached.In the Gaojiapu Coal Mine, there is a 400.45 m thick KS of the Luohe Formation sandstone in the overlying rock, which bears most of the rock load in the upper layers (nearest to the surface) and transfers the load to the coal and rock masses on both sides of the mining area, resulting in a high mining stress concentration around the stope and an abnormal increase in the influence range of the stress concentration.4][25] The larger the thickness of the KS, the more obvious the difference.This shows that the mining stress field prediction model proposed in this study has obvious advantages under mining conditions in which there are typically thick and hard key strata in the overlying rock.
According to the analysis in Section 5.1 and Figure 13, it can be concluded that the mining length has a significant influence on the distribution of the mining stress, and the mining stress concentration increases with the increase in mining length, but does not increase without any limitations.4][25] The prediction results of the abutment pressure predicted by the models found in Qian and colleagues 16,[23][24][25] cannot effectively show the dynamic evolution laws of mining stress with mining lengths, whereas the new prediction model of the mining stress field proposed in this study has obvious and clear advantages in this respect.
In summary, the new prediction model for the mining stress field proposed in this study considers the influence of key strata conditions, mining lengths, mining height, and other conditions on the mining stress field.Therefore, the new method is suitable for mining conditions where there are typical key strata in the overlying rock, especially in the case of ultra-thick and hard KS or multilayer key strata in the overlying rock.It has obvious and clear advantages over the existing methods and can effectively show the dynamic evolution laws of the mining stress field of the overlying rock with mining lengths.

| CONCLUSIONS
(1) The key strata at different horizons in the fissure zone on the solid coal side are simplified as multilayer superposition semi−infinite length elastic foundation beams, the key strata at different horizons in the fissure zone on the goaf side are simplified as multilayer superposition "masonry beams," and the key strata at different horizons in the bending subsidence zone are simplified as multilayer superposition infinite length elastic foundation beams.Equations for calculating the plane distribution of the mining stress of the key strata at different horizons and stope abutment pressures are established, and a spatial distribution prediction method for the mining stress field based on the structure of the key strata in the overburden is proposed.The new prediction method avoids the deficiencies of existing methods, which fail to consider the influence of key strata conditions on the mining stress field.The new method is suitable for mining conditions where there are typical key strata in the overlying rock, particularly in the case of ultra-thick and hard KS or multilayer key strata in the overlying rock.(2) The physical mechanism of the mining stress field formed by the transfer and transmission of the load of the overlying strata under the coupling of the key strata structure at different horizons was revealed.The key strata were found to be the main bearing bodies of the overlying rock, both before and after the fracture, and the overburdened rock load could be transferred to the coal and rock mass around the stope through the broken key strata block in the fracture zone and the key strata in the bending subsidence zone.This process causes the flexural subsidence of key strata and exerts a force on the underlying coal and rock mass, thereby forming a mining stress field.(3) The spatial evolution of the mining stress field in the overlying rock was investigated, and the effectiveness of the new prediction model was verified by actual measurements of mining stress and the laws of mine pressure in the Gaojiapu Coal Mine.It was found that the mining stress concentration in the overlying rock increased with an increase in mining length but did not increase without limitation.The maximum value was reached when the mining length was 1458 m × 1458 m in the Gaojiapu Coal Mine.The greater the thickness of the KS, the larger is the critical mining area required to reach the maximum value, the more difficult it is for the goaf stress to recover to the original rock stress, and the greater is the stress concentration after the mining stress reaches the stability point.(4) The reason for the abnormal distribution of the mining stress field in the Gaojiapu Coal Mine was identified.The KS of Luohe Formation sandstone, which is 400.45 m thick in the overlying rock at the mine site and bears most of the rock load from the KS itself up to the upper layers (nearest the surface), which prevents the load from being transferred to the goaf; thus, the load is transferred to the coal and rock mass on both sides of the stope.Consequently, the mining stress in the Gaojiapu Coal Mine is highly concentrated and has a wide range of influences, leading to serious deformation of the main roadway and frequent dynamic manifestations.

F I G U R E 2
Evolutionary mechanical model of mining stress field based on key strata structure in overlying rock.(A) Simplified model of bearing structure of mining overburden along the vertical profile.(B) Mining stress analysis of key strata and coal seam in overburden along the vertical profile.

4. 2 . 2 |
Field stress measurement verification The borehole stress gauges No. 1, No. 2, and No. 3 were used to monitor the relative stress change laws of the coal body in front of working face 101 in panel 1, The three gauges were installed at approximately 310, 220, and 130 m, respectively, in front of the working face.The monitoring results are shown in Figure 6.

F I G U R E 6
The relative stress change laws of the coal body in front of working face 101 in panel 1.F I G U R E 7 Microseismic events distribution in panel 1.HAN ET AL.| 1561

F
I G U R E 8 Prediction results of abutment pressure distribution on stope after mining of panels 1 and 2 in Gaojiapu Coal Mine.(A) Abutment pressure distribution on stope.(B) Abutment pressure distribution along x = 260 m profile.(C) Abutment pressure distribution along main roadway profile.

F I G U R E 9
Deformation of the main roadway in the vicinity of Gaojiapu Coal Mine.
proposed model was used to predict the spatial distributions when the thickness of KS 4 was 80 and 400.45 m, and the prediction results when the mining dimension was 500 m × 1150 m (working faces 201 + 202 + 203) are shown in Figures 11B and 5B, respectively.The results of our comparative analysis show that when the thickness of KS 4 was 80 m, the mining stress concentration reached its maximum at a critical length of 437 m × 437 m.After the mining of three working faces in panel 2, the mining stress concentration reached the maximum value, and the peak abutment pressure stress of the stope on two main sections was 46.1 MPa.The central stress of the goaf was restored to the original rock stress of 25.37 MPa, and the influence range of abutment pressure was 116.2 m.However, when the thickness of KS 4 was 400.45 m, the peak abutment pressure along main sections Ι was 38.4 MPa, and the stress concentration ranges reached 353.8 m.At this point, the central stress of the goaf was restored to 11.1 MPa (43.8% of the original rock stress), but the mining stress concentration of the overlying rock did not reach the maximum value.When the mining area reached 1458 m × 1458 m, the peak stress, the central stress of the goaf and the influence range of abutment pressure on the two main F I G U R E 10 Prediction results of the mining field distribution under different mining dimensions.(A) Longwall face 201, (B) longwall faces 201 + 202.

F
I G U R E 11 Prediction results of the mining stress field distribution under different KS thicknesses.(A) KS 4 thickness of 400.45 m, (B) KS 4 thickness of 80 m.

F I G U R E 12
Abutment pressure distribution curves along the main section Ι under different thicknesses of KS 4. F I G U R E 13 Abutment pressure distribution curves along the main section Ι under different mining lengths.

1
Calculation parameters of the key strata.
T A B L E 2 Other calculation parameters.