# The Effect of Joint Damage on a Coal Wall and the Influence of Joints on the Abutment Pressure on a Fully Mechanised Working Face with Large Mining Height

Authors: Weibin Guo; Shengwei Zhang; Yuhui Li
Journal: Shock and Vibration
 (2021)

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## Abstract

Coal wall spalling is regarded as a key technical problem influencing safe and efficient mining of large-mining-height working faces while the distribution of abutment pressure within the limit equilibrium zone (LEZ) influences coal wall spalling within a large-mining-height working face. This research attempted to explore the distribution characteristics of abutment pressure within the LEZ in a large-mining-height working face. For this purpose, the influences of the orientation of joints on mechanical characteristics of coal with joints and on the distribution of abutment pressure within the LEZ in the large-mining-height working face were analysed by theoretical analysis and numerical simulation. Research results show that the damage variable of coal with joints first rises, then decreases, and finally increases with increasing dip angle of the joints; as the azimuth of the joints increases, the damage variable first declines, then increases; the damage variable gradually declines with increasing joint spacing; an increase in the dip angle of joints corresponds to first reduction, then growth, and a final decrease of the abutment pressure at the same position in front of the coal walls; on certain conditions, the abutment pressure at the same position within the LEZ first rises, then declines as the azimuth of joints increases; with the growth of the joint spacing, the abutment pressure at the same position within the LEZ rises. The dip angle and azimuth of joints marginally affect the abutment pressure within the LEZ.


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## Body

## 1. Introduction

Coal wall spalling is considered as a key technical problem influencing the safe, efficient, green, and intelligent mining of a fully mechanised working face with a large mining height (the mining height is bigger than 3.5 m), while the abutment pressure within the limit equilibrium zone (LEZ) during mining affects the stability of a coal wall [1–9]. There are many researches about the abutment pressure on the working face [10–15], which are mainly about the influences of roof structure, mining height, or the coal macroscopic mechanical parameters on the abutment pressure. The joint influence on the abutment pressure within the LEZ on the working face is almost rare. It is very important to analyse the joint influence to reveal the micro mechanism of the abutment pressure distribution within the LEZ in the large-mining-height working face.This paper attempted to find the relationship between the joint and the abutment pressure within the LEZ in the large-mining-height working face. Coal is formed slowly and numerous joints have developed under the complex geological conditions together with those induced by mining. From the perspective of damage mechanics, joints in coal account for the damage therein; therefore, it is possible to analyse the damage effect of joints on coal by establishing a constitutive equation for coal with joints. According to the limit equilibrium theory, the abutment pressure is mainly influenced by various factors (including support capacity of coal walls and mining height) within the LEZ in front of a large-mining-height working face [16]. In a large-mining-height working face, the support capacity of coal walls can be calculated by using the theory on stability of columns [17–19]. Therefore, the support capacity of coal walls in a large-mining-height working face is mainly influenced by the dimensions of the coal walls and physico-mechanical parameters of the coal in the working face. Based on the limit equilibrium theory, the support capacity of coal walls in a large-mining-height working face is explored to reveal the distribution of abutment pressure within the LEZ in the large-mining-height working face based on joints and their displacement. It is of engineering significance to thus guarantee the stability of coal walls within the large-mining-height working faces.The Brady Constitutive Equation for coal with joints was built firstly to analyse the influence of joints’ parameters on damage in a coal wall, including the joints’ dip angle, azimuth, and spacing. The relationships of the damage variable of coal containing through-going joints with the dip angle, azimuth, and spacing of joints are expressed by a formula. Then, based on the damage effect of joints on the coal, the abutment pressure within the LEZ in a large-mining-height working face was expressed by the formula containing the parameters of joints. Finally, the numerical simulation was used to verify the rationality of the formula of abutment pressure which reveal the distribution characteristics of abutment pressure within the LEZ influenced by the joints in a large-mining-height working face.


## 2. Influence of Joints on Damage in a Coal Wall

### 2.1. Brady Constitutive Equation for Coal with Joints

Coal generally contains a group or multiple groups of joints with dominant orientation developed under long-term geological effects and mining-induced stress. Thus, it is feasible to simplify coal as rock containing a group or multiple groups of regularly distributed joints. On this basis, the influence of the orientation of joints on mechanical characteristics of coal can be attained according to the Brady model built by Olsson [20] and Brady et al. [21, 22].Figure1 shows the Brady mechanical model for coal with joints and the φ in Figure 1 means the internal frictional angle of the coal-rock blocks [21]. To simplify the analysis, the whole model for coal with joints is divided into two parts: joints with length Lg, in which only the part with the intermediate length of lg is allowed to slide; coal-rock blocks in the upper and lower sides of joints.Figure 1
Brady model of coal body containing joints. (a) Coal with a single joint. (b) Equivalent physical model.
(a)(b)The equivalent elastic stiffness of coal with joints can be deduced through analysis based on the Brady model [21]:(1)1k=HWBbE+cos2αKnLgBb+sin2αKsLgBb,where(2)Lg=Wcosα,α≤arctanHW,Hsinα,α>arctanHW,where k refers to the equivalent elastic stiffness of coal with a single joint; H, W, and Bb separately represent the height, width, and length of the model; E and a denote the elastic modulus of intact coal blocks and the dip angle of joints, respectively; Kn and Ks separately denote the normal and tangential stiffnesses of the joints.


### 2.2. The Influence of the Dip Angle of Joints

Through analysis from the perspective of damage mechanics, the coal with joints can be considered as a damaged body. By introducing the damage variableD, the elastic modulus Ee for coal with joints is expressed as follows [23]:(3)Ee=1−DE.Under compression, the axial stiffness of coal with joints is calculated as follows [24]:(4)k=WBbHEe.Based on Equations (1) to (4), the damage variable D of coal with a single joint is expressed as follows:(5)D=EKnsin2αcosα+EKscos3αHKnKs+EKnsin2αcosα+EKscos3α,α≤arctanHW,EWKnsin3α+EWKscos2αsinαH2KnKs+EWKnsin3α+EWKscos2αsinα,α>arctanHW.As shown in Equation (5), the equivalent elastic modulus of coal with joints is related to the elastic modulus of coal blocks, the dip angle, normal stiffness, and tangential stiffness of joints as well as the height of coal-rock blocks containing the joints. When E = 10 GPa, Kn = 10 GPa/m, Ks = 4 GPa/m [25], and H = 2W = 2 m [21], the change in the damage variable of coal with a single joint with the dip angle of the joint is displayed in Figure 2.Figure 2
The change in the damage variable of coal body containing a joint with inclination angle of the joint.It can be seen from Figure2 that an increase of the dip angle of the joint corresponds to initial growth, then a decrease, and a final increase of the damage variable of coal with a single joint; the damage variable varies between 0.33 and 0.39: the change in the dip angle of the joint influences the damage, albeit to an insignificant extent.


### 2.3. The Influence of the Azimuth of the Joints

In the Brady model, the lengthLg of joints certainly varies when their dip angle satisfies α ≤ arctan (H/W) under the influence of β, the azimuth of joints. The relationship of Lg to α and β is attained:(6)Lg=Bbcosαcosβ,β≤arctanWBb,Wcosαsinβ,β>arctanWBb.The length of joints satisfies Equation (2) when their dip angle satisfies α > arctan (H/W). According to Equation (1), the equivalent elastic stiffness of coal with a single joint at different azimuths still can be calculated. It is only necessary to replace Lg in the equation with Equation (2) or Equation (6) according to different conditions. The rationality of the above analysis can be validated by employing 3DEC numerical simulation, as shown in Figure 3. The parameters used in the numerical simulation are equal to the parameters used in the theoretical analysis. It can be seen from the figure that the curves obtained through numerical simulation are consistent with those attained through theoretical analysis under different dip angles and azimuths of joints, which reveals the rationality of the above theoretical analysis.Figure 3
Comparison of numerical and theoretical results at different azimuth angles (a)α = 45° and β = 15°. (b) α = 45° and β = 30°. (c) α = 45° and β = 60°. (d) α = 45° and β = 75°. (e) α = 70° and β = 30°. (f) α = 70° and β = 60°.
(a)(b)(c)(d)(e)(f)It can be found from the above analysis that at different azimuths of joints, the damage variableD of coal with a single joint is unaffected by the azimuth while being associated only with the dip angle of the joint when the dip angle satisfies α > arctan (H/W). In this case, the expression of the damage variable is the same as that in Equation (5); at α ≤ arctan (H/W), the damage variable D of coal with a single joint is expressed in Equation (7) due to changes in azimuth and the dip angle:(7)D=EWKnsin2αcosαcosβ+EWKscos3αcosβBbHKnKs+EWKnsin2αcosαcosβ+EWKscos3αcosβ,β≤arctanWBb,EKnsin2αcosαsinβ+EKscos3αsinβHKnKs+EKnsin2αcosαsinβ+EKscos3αsinβ,β>arctanWBb.According to Equation (7), the change in the damage variable of coal with joint with the azimuth under different dip angles of the joint is attained given E = 10 GPa, Kn = 10 GPa/m, Ks = 4 GPa/m, and H = 2Bb = 2W = 2 m, as shown in Figure 4.Figure 4
The change in the damage variable of a coal body containing a joint with azimuth angle of the joint.As shown in Figure4, the damage variables of coal with a single joint first decrease, then increase under the influence of the azimuth at different dip angles of the joint; however, the difference varies; at B = W, the azimuth β = 45° is taken as the dividing point in Equation (7) and therefore the damage variables are all minimised in this condition. At the dip angle of the joint of 30°, the damage variable varies from 0.30 to 0.37; the damage variable varies between 0.30 and 0.38 at the dip angle of 60°; at the dip angle of 45°, the damage variable varies between 0.27 and 0.35. As a result, the change of the azimuth of a joint affects the coal with the joint (albeit to an insignificant extent).


### 2.4. The Influence of the Joint Spacing

Apart from the dip angleα and azimuth β, the spacing d is also considered an important parameter for joints. According to the superposition principle, the Brady model can be extended to complex situations containing two or multiple parallel joints. In this way, the influence of the joint spacing on the damage variable of coal with joints is ascertained. The complex situation containing two or multiple parallel joints can be considered as comprising two (or more) simple Brady mechanical models and one or more models for intact coal-rock blocks. By taking a model for coal with two joints as an example, the model for coal can be equivalent to two simple Brady models for coal with joints and a model for intact coal-rock blocks (Figure 5) to analyse the damage modulus of coal containing joints.Figure 5
Model of coal body containing two joints. (a) Combined models for coal containing two joints. (b) The equivalent physical combined models.
(a)(b)The global displacement of coal with two joints is calculated as follows:(8)Ua=Ub+Uc−U0,where Ub, Uc, and U0 separately refer to displacements of various component elements. The equivalent elastic stiffness of coal containing two joints is expressed as follows:(9)1k2=HWBbE+2cos2αKnLgBb+2sin2αKsLgBb,where the meanings of various physico-mechanical parameters follow those in Equations (1) and (2).By takingH = 2W = 2 m and α = 45° as an example, the curves attained through 3DEC numerical simulation software highly coincide with those obtained through theoretical analysis (Figure 6), which indicates the rationality of the above theoretical analysis.Figure 6
Comparison of numerical and theoretical results of coal body containing two joints. (a) When two joints are located at two ends of the model. (b) When two joints are situated in the middle of the model.
(a)(b)In the Brady model, it is supposed that the normal stress on joints is uniformly distributed and joints are elastically extended; stress concentration (especially, normal stress concentration on joints) occurs during numerical simulation. Therefore, the curves attained through numerical simulation are not completely in line with those obtained through theoretical analysis (Figures3 and 6).According to the above analysis, the damage variableD2 of two coal containing joints is calculated as follows:(10)D2=2EKnsin2αcosα+2EKscos3αHKnKs+2EKnsin2αcosα+2EKscos3α,α≤arctanHW,2EWKnsin3α+2EWKscos2αsinαH2KnKs+2EWKnsin3α+2EWKscos2αsinα,α>arctanHW.Similarly, whenn (a positive integer) through-going joints are found in coal, the damage variable Dn is calculated as follows:(11)Dn=nEKnsin2αcosα+nEKscos3αHKnKs+nEKnsin2αcosα+nEKscos3α,α≤arctanHW,nEWKnsin3α+nEWKscos2αsinαH2KnKs+nEWKnsin3α+nEWKscos2αsinα,α>arctanHW.According to Equation (11), the change in the damage variable of coal with the number of joints therein at different dip angles when E = 10 GPa, Kn = 10 GPa/m, Ks = 4 GPa/m, and H = 2W = 2 m can be attained (Figure 7 and Table 1).Figure 7
The change in the damage variable of coal with the number of joints.Table 1
The influence of the number of joints on the damage variable of coal containing through-going joints.
Dip angle of joints (°)Number of through-going joints3045607510.370.380.350.3720.540.550.520.5430.640.650.610.6340.700.710.680.7050.750.760.730.74⋮⋮⋮⋮⋮100.860.860.840.85⋮⋮⋮⋮⋮200.920.930.910.92⋮⋮⋮⋮⋮1000.980.980.980.98The change curves of the damage variable at different dip angles of joints basically coincide, which indicates consistent changes to the damage variable with the number of joints; with the growth of the number of joints, the damage variable of coal with through-going joints gradually increases; the damage variable grows much more when the number of joints is less than 20 while varies less when there are more than 20 joints (Figure7).In a case where two, three, five, ten, and twenty through-going joints are present in coal containing joints, the damage variables at different dip angles of joints are all larger than 0.5, 0.6, 0.7, 0.8, and 0.9, respectively; when the number of joints tends to be infinite, the damage variables all approached to 1. On this condition, the coal with joints is completely damaged (Table1), which implies that the number of joints plays a decisive role in damage to the coal. Given fixed dimensions of coal with joints, the joint spacing (d) is inversely proportional to the number of joints. Thus, the lower the joint spacing, the larger the damage variable of coal containing joints.Above all, the relationships of the damage variableD of coal containing through-going joints with the dip angle α, azimuth β, and spacing d (number n) of joints are expressed as follows:(12)D=nEWKnsin2αcosαcosβ+nEWKscos3αcosβBbHKnKs+nEWKnsin2αcosαcosβ+nEWKscos3αcosβ,β≤arctanWBb,α≤arctanHW,nEKnsin2αcosαsinβ+nEKscos3αsinβHKnKs+nEKnsin2αcosαsinβ+nEKscos3αsinβ,β>arctanWBb,α≤arctanHW,nEWKnsin3α+nEWKscos2αsinαH2KnKs+nEWKnsin3α+nEWKscos2αsinα,α>arctanHW.WhenH = 6 m and W = Bb = 1s m, the curves attained by using 3DEC numerical simulation software remain similar to those obtained through theoretical analysis (Equation (12)), as shown in Figure 8. It reveals that it is feasible to analyse the influence of the orientation of joints on the support capacity of coal walls in a large-mining-height working face based on Equation (12).Figure 8
Comparison of numerical and theoretical results under different conditions with the coal with joints atH = 6 m. (a) α = 45°, β = 0° and n = 1. (b) α = 45°, β = 45° and n = 1. (c) α = 45°, β = 45° and n = 2 (joints located at two ends of the model). (d) α = 45°, β = 45° and n = 2 (joints located in the middle of the model).
(a)(b)(c)(d)


## 2.1. Brady Constitutive Equation for Coal with Joints

Coal generally contains a group or multiple groups of joints with dominant orientation developed under long-term geological effects and mining-induced stress. Thus, it is feasible to simplify coal as rock containing a group or multiple groups of regularly distributed joints. On this basis, the influence of the orientation of joints on mechanical characteristics of coal can be attained according to the Brady model built by Olsson [20] and Brady et al. [21, 22].Figure1 shows the Brady mechanical model for coal with joints and the φ in Figure 1 means the internal frictional angle of the coal-rock blocks [21]. To simplify the analysis, the whole model for coal with joints is divided into two parts: joints with length Lg, in which only the part with the intermediate length of lg is allowed to slide; coal-rock blocks in the upper and lower sides of joints.Figure 1
Brady model of coal body containing joints. (a) Coal with a single joint. (b) Equivalent physical model.
(a)(b)The equivalent elastic stiffness of coal with joints can be deduced through analysis based on the Brady model [21]:(1)1k=HWBbE+cos2αKnLgBb+sin2αKsLgBb,where(2)Lg=Wcosα,α≤arctanHW,Hsinα,α>arctanHW,where k refers to the equivalent elastic stiffness of coal with a single joint; H, W, and Bb separately represent the height, width, and length of the model; E and a denote the elastic modulus of intact coal blocks and the dip angle of joints, respectively; Kn and Ks separately denote the normal and tangential stiffnesses of the joints.


## 2.2. The Influence of the Dip Angle of Joints

Through analysis from the perspective of damage mechanics, the coal with joints can be considered as a damaged body. By introducing the damage variableD, the elastic modulus Ee for coal with joints is expressed as follows [23]:(3)Ee=1−DE.Under compression, the axial stiffness of coal with joints is calculated as follows [24]:(4)k=WBbHEe.Based on Equations (1) to (4), the damage variable D of coal with a single joint is expressed as follows:(5)D=EKnsin2αcosα+EKscos3αHKnKs+EKnsin2αcosα+EKscos3α,α≤arctanHW,EWKnsin3α+EWKscos2αsinαH2KnKs+EWKnsin3α+EWKscos2αsinα,α>arctanHW.As shown in Equation (5), the equivalent elastic modulus of coal with joints is related to the elastic modulus of coal blocks, the dip angle, normal stiffness, and tangential stiffness of joints as well as the height of coal-rock blocks containing the joints. When E = 10 GPa, Kn = 10 GPa/m, Ks = 4 GPa/m [25], and H = 2W = 2 m [21], the change in the damage variable of coal with a single joint with the dip angle of the joint is displayed in Figure 2.Figure 2
The change in the damage variable of coal body containing a joint with inclination angle of the joint.It can be seen from Figure2 that an increase of the dip angle of the joint corresponds to initial growth, then a decrease, and a final increase of the damage variable of coal with a single joint; the damage variable varies between 0.33 and 0.39: the change in the dip angle of the joint influences the damage, albeit to an insignificant extent.


## 2.3. The Influence of the Azimuth of the Joints

In the Brady model, the lengthLg of joints certainly varies when their dip angle satisfies α ≤ arctan (H/W) under the influence of β, the azimuth of joints. The relationship of Lg to α and β is attained:(6)Lg=Bbcosαcosβ,β≤arctanWBb,Wcosαsinβ,β>arctanWBb.The length of joints satisfies Equation (2) when their dip angle satisfies α > arctan (H/W). According to Equation (1), the equivalent elastic stiffness of coal with a single joint at different azimuths still can be calculated. It is only necessary to replace Lg in the equation with Equation (2) or Equation (6) according to different conditions. The rationality of the above analysis can be validated by employing 3DEC numerical simulation, as shown in Figure 3. The parameters used in the numerical simulation are equal to the parameters used in the theoretical analysis. It can be seen from the figure that the curves obtained through numerical simulation are consistent with those attained through theoretical analysis under different dip angles and azimuths of joints, which reveals the rationality of the above theoretical analysis.Figure 3
Comparison of numerical and theoretical results at different azimuth angles (a)α = 45° and β = 15°. (b) α = 45° and β = 30°. (c) α = 45° and β = 60°. (d) α = 45° and β = 75°. (e) α = 70° and β = 30°. (f) α = 70° and β = 60°.
(a)(b)(c)(d)(e)(f)It can be found from the above analysis that at different azimuths of joints, the damage variableD of coal with a single joint is unaffected by the azimuth while being associated only with the dip angle of the joint when the dip angle satisfies α > arctan (H/W). In this case, the expression of the damage variable is the same as that in Equation (5); at α ≤ arctan (H/W), the damage variable D of coal with a single joint is expressed in Equation (7) due to changes in azimuth and the dip angle:(7)D=EWKnsin2αcosαcosβ+EWKscos3αcosβBbHKnKs+EWKnsin2αcosαcosβ+EWKscos3αcosβ,β≤arctanWBb,EKnsin2αcosαsinβ+EKscos3αsinβHKnKs+EKnsin2αcosαsinβ+EKscos3αsinβ,β>arctanWBb.According to Equation (7), the change in the damage variable of coal with joint with the azimuth under different dip angles of the joint is attained given E = 10 GPa, Kn = 10 GPa/m, Ks = 4 GPa/m, and H = 2Bb = 2W = 2 m, as shown in Figure 4.Figure 4
The change in the damage variable of a coal body containing a joint with azimuth angle of the joint.As shown in Figure4, the damage variables of coal with a single joint first decrease, then increase under the influence of the azimuth at different dip angles of the joint; however, the difference varies; at B = W, the azimuth β = 45° is taken as the dividing point in Equation (7) and therefore the damage variables are all minimised in this condition. At the dip angle of the joint of 30°, the damage variable varies from 0.30 to 0.37; the damage variable varies between 0.30 and 0.38 at the dip angle of 60°; at the dip angle of 45°, the damage variable varies between 0.27 and 0.35. As a result, the change of the azimuth of a joint affects the coal with the joint (albeit to an insignificant extent).


## 2.4. The Influence of the Joint Spacing

Apart from the dip angleα and azimuth β, the spacing d is also considered an important parameter for joints. According to the superposition principle, the Brady model can be extended to complex situations containing two or multiple parallel joints. In this way, the influence of the joint spacing on the damage variable of coal with joints is ascertained. The complex situation containing two or multiple parallel joints can be considered as comprising two (or more) simple Brady mechanical models and one or more models for intact coal-rock blocks. By taking a model for coal with two joints as an example, the model for coal can be equivalent to two simple Brady models for coal with joints and a model for intact coal-rock blocks (Figure 5) to analyse the damage modulus of coal containing joints.Figure 5
Model of coal body containing two joints. (a) Combined models for coal containing two joints. (b) The equivalent physical combined models.
(a)(b)The global displacement of coal with two joints is calculated as follows:(8)Ua=Ub+Uc−U0,where Ub, Uc, and U0 separately refer to displacements of various component elements. The equivalent elastic stiffness of coal containing two joints is expressed as follows:(9)1k2=HWBbE+2cos2αKnLgBb+2sin2αKsLgBb,where the meanings of various physico-mechanical parameters follow those in Equations (1) and (2).By takingH = 2W = 2 m and α = 45° as an example, the curves attained through 3DEC numerical simulation software highly coincide with those obtained through theoretical analysis (Figure 6), which indicates the rationality of the above theoretical analysis.Figure 6
Comparison of numerical and theoretical results of coal body containing two joints. (a) When two joints are located at two ends of the model. (b) When two joints are situated in the middle of the model.
(a)(b)In the Brady model, it is supposed that the normal stress on joints is uniformly distributed and joints are elastically extended; stress concentration (especially, normal stress concentration on joints) occurs during numerical simulation. Therefore, the curves attained through numerical simulation are not completely in line with those obtained through theoretical analysis (Figures3 and 6).According to the above analysis, the damage variableD2 of two coal containing joints is calculated as follows:(10)D2=2EKnsin2αcosα+2EKscos3αHKnKs+2EKnsin2αcosα+2EKscos3α,α≤arctanHW,2EWKnsin3α+2EWKscos2αsinαH2KnKs+2EWKnsin3α+2EWKscos2αsinα,α>arctanHW.Similarly, whenn (a positive integer) through-going joints are found in coal, the damage variable Dn is calculated as follows:(11)Dn=nEKnsin2αcosα+nEKscos3αHKnKs+nEKnsin2αcosα+nEKscos3α,α≤arctanHW,nEWKnsin3α+nEWKscos2αsinαH2KnKs+nEWKnsin3α+nEWKscos2αsinα,α>arctanHW.According to Equation (11), the change in the damage variable of coal with the number of joints therein at different dip angles when E = 10 GPa, Kn = 10 GPa/m, Ks = 4 GPa/m, and H = 2W = 2 m can be attained (Figure 7 and Table 1).Figure 7
The change in the damage variable of coal with the number of joints.Table 1
The influence of the number of joints on the damage variable of coal containing through-going joints.
Dip angle of joints (°)Number of through-going joints3045607510.370.380.350.3720.540.550.520.5430.640.650.610.6340.700.710.680.7050.750.760.730.74⋮⋮⋮⋮⋮100.860.860.840.85⋮⋮⋮⋮⋮200.920.930.910.92⋮⋮⋮⋮⋮1000.980.980.980.98The change curves of the damage variable at different dip angles of joints basically coincide, which indicates consistent changes to the damage variable with the number of joints; with the growth of the number of joints, the damage variable of coal with through-going joints gradually increases; the damage variable grows much more when the number of joints is less than 20 while varies less when there are more than 20 joints (Figure7).In a case where two, three, five, ten, and twenty through-going joints are present in coal containing joints, the damage variables at different dip angles of joints are all larger than 0.5, 0.6, 0.7, 0.8, and 0.9, respectively; when the number of joints tends to be infinite, the damage variables all approached to 1. On this condition, the coal with joints is completely damaged (Table1), which implies that the number of joints plays a decisive role in damage to the coal. Given fixed dimensions of coal with joints, the joint spacing (d) is inversely proportional to the number of joints. Thus, the lower the joint spacing, the larger the damage variable of coal containing joints.Above all, the relationships of the damage variableD of coal containing through-going joints with the dip angle α, azimuth β, and spacing d (number n) of joints are expressed as follows:(12)D=nEWKnsin2αcosαcosβ+nEWKscos3αcosβBbHKnKs+nEWKnsin2αcosαcosβ+nEWKscos3αcosβ,β≤arctanWBb,α≤arctanHW,nEKnsin2αcosαsinβ+nEKscos3αsinβHKnKs+nEKnsin2αcosαsinβ+nEKscos3αsinβ,β>arctanWBb,α≤arctanHW,nEWKnsin3α+nEWKscos2αsinαH2KnKs+nEWKnsin3α+nEWKscos2αsinα,α>arctanHW.WhenH = 6 m and W = Bb = 1s m, the curves attained by using 3DEC numerical simulation software remain similar to those obtained through theoretical analysis (Equation (12)), as shown in Figure 8. It reveals that it is feasible to analyse the influence of the orientation of joints on the support capacity of coal walls in a large-mining-height working face based on Equation (12).Figure 8
Comparison of numerical and theoretical results under different conditions with the coal with joints atH = 6 m. (a) α = 45°, β = 0° and n = 1. (b) α = 45°, β = 45° and n = 1. (c) α = 45°, β = 45° and n = 2 (joints located at two ends of the model). (d) α = 45°, β = 45° and n = 2 (joints located in the middle of the model).
(a)(b)(c)(d)


## 3. The Influence of Joints on the Distribution of Abutment Pressure on a Large-Mining-Height Working Face

According to a previous study [10], the abutment pressure σy at a position x away from the coal walls within the LEZ in front of the working face is calculated as follows:(13)σy=N0e2fx/M1+sinφ/1−sinφ,where N0, f, φ, and M denote the support capacity of coal walls, friction coefficient between strata, internal friction angle of coal, and the mining height of the working face, respectively.According to Equation (13), it is found that the abutment pressure at x = 0 denotes the support capacity of coal walls. The abutment pressure within the LEZ is influenced by various factors such as the support capacity of coal walls, mining height, the friction coefficient between strata, and the internal friction angle of the coal.The critical pressure (support capacity) on coal walls can be calculated according to the theory of the stability of columns [26–28].(14)σ0=π2EemI4M2S,(15)Eem=1−DEm,where Eem, Em, and D represent the elastic modulus of coal after mining-induced damage, the elastic modulus of intact coal, and the damage variable, respectively [29]; I refers to the moment of inertia of the neutral axis of a section and I = πdc4/64 as for a circular section, in which dc denotes the diameter of the section; S denotes the cross-sectional area of the column, with S = πdc2/4. According to Equation (14), it can be obtained that the support capacity N0 of the coal walls is related not only to the mining height but also to the elastic modulus of the coal.When the diameter of the cross section of the column for coal walls is the unit length, the support capacity of coal walls presents an analogous hyperbolic relationship with the mining height if the elastic modulus of damaged coal is taken as 0.5 GPa (Figure9(a)); by setting the mining height to 6 m, the support capacity of coal walls is linearly correlated with the elastic modulus of damaged coal (Figure 9(b)); the result obtained through numerical simulation also verifies the relationships of the support capacity of coal walls with the mining height and elastic modulus of coal (Figure 10).Figure 9
Influence factors of coal wall supporting ability. (a) The influence of the mining height (Eem = 0.5 GPa). (b) The influence of the elastic modulus of coal (M = 6.0 m).
(a)(b)Figure 10
Vertical stress on working face. (a) The influence of the mining height (Eem = 0.5 GPa). (b) The influence of the elastic modulus of coal (M = 6.0 m).
(a)(b)Based on Equations (13) and (14), the abutment pressure σy at a position x away from the coal walls within the LEZ in a large-mining-height working face based on the theory on stability of columns of coal walls can be attained:(16)σy=π2EemI4M2Se2fx/M1+sinφ/1−sinφ.As a result, the abutment pressure at the same position within the LEZ in a large-mining-height working face under given conditions is mainly influenced by mechanical parameters of coal. Therefore, the influence of parameters of joints on the abutment pressure within the LEZ in a large-mining-height working face can be elucidated according to the influence of the joints on the damage to the coal.


### 3.1. Theoretical Analysis on the Influence of the Orientation of Joints

#### 3.1.1. The Influence of the Dip Angle of the Joints

According to Equations (5) and (16) and assuming H = M, the relationship between the abutment pressure σy at a position x away from the coal walls within the LEZ in a large-mining-height working face and the dip angle of joints can be expressed as follows:(17)σy=π2EmIKnKs4MSMKnKs+EKnsin2αcosα+EKscos3αee2fx/M1+sinφ/1−sinφ,α≤arctanMW,π2EmIKnKs4SM2KnKs+EWKnsin3α+EWKscos2αsinαee2fx/M1+sinφ/1−sinφ,α>arctanMW.As shown in Equation (17), the change in abutment pressure at x = 0.5 m within the LEZ in a large-mining-height working face with the dip angle of joints is obtained under the mining height of the working face of M = 6 m, W=Bb = 1 m, Em = 10 GPa, Kn = 10 GPa/m, and Ks = 4 GPa/m, as shown in Figure 11.Figure 11
Change in abutment pressure in LEZ with inclination angle of joints in a fully mechanised working face with a large mining height.As shown in Figure11, the abutment pressure within the LEZ in a large-mining-height working face first decreases, then rises, and finally increases when increasing the dip angle of the joints in coal seams: this influence is opposite to that of the dip angle of joints on the damage to intact coal; the abutment pressure varies between 6.39 and 7.45 MPa. The result indicates that the change of the dip angle of joints in coal seams affects the abutment pressure within the LEZ in the large-mining-height working face to some extent.


#### 3.1.2. The Influence of the Azimuth of the Joints

According to the above analysis, the azimuth of joints in coal seams does not influence the damage to the coal whenα > arctan (H/W); according to Equations (7) and (16) and assuming H = M, the relationship between the abutment pressure σy at a position x away from coal walls within the LEZ in a large-mining-height working face and the azimuth of joints is shown in Equation (18) at α ≤ arctan (H/W):(18)σy=π2EmIBbKnKs4MSBbMKnKs+EWKnsin2αcosαcosβ+EWKscos3αcosβee2fx/M1+sinφ/1−sinφ,β≤arctanWBb,π2EmIKnKs4MSMKnKs+EKnsin2αcosαsinβ+EKscos3αsinβee2fx/M1+sinφ/1−sinφ,β>arctanWBb.As shown in Equation (18), the change in the abutment pressure at x = 0.5 m within the LEZ in a large-mining-height working face with the dip angle of joints is attained under the mining height of the working face of M = 6 m, W = Bb = 1 m, Em = 10 GPa, Kn = 10 GPa/m, and Ks = 4 GPa/m, as shown in Figure 12.Figure 12
Change in the abutment pressure in LEZ with azimuth angle of joints in a fully mechanised working face with large mining height.It can be seen from Figure12 that the abutment pressure within the LEZ in a large-mining-height working face first increases, then decreases with the increasing azimuth at different dip angles of the joints. The maximum abutment pressure is found at the azimuth of β = 45° (Figure 12). At dip angles of the joints of 30°, 45°, and 60°, the abutment pressures vary in the ranges of 6.43 to 6.76, 6.39 to 6.73, and 6.55 to 6.85 MPa: this indicates that the azimuth of through-going joints in coal seams shows a certain (albeit slight) influence on the abutment pressure within the LEZ.


#### 3.1.3. Joint Spacing

Based on the above analysis, the joint spacing in coal seams is inversely proportional to the number of joints within a certain range. Thus, it is feasible to obtain the influence of the joint spacing by analysing the influence of the number of joints on the abutment pressure within the LEZ in a large-mining-height working face.According to Equations (11) and (16), and assuming H = M, the relationship between the abutment pressure σy at a position x away from coal walls within the LEZ in a large-mining-height working face and the number of joints can be attained:(19)σy=π2EmIKnKs4MSMKnKs+nEKnsin2αcosα+nEKscos3αee2fx/M1+sinφ/1−sinφ,α≤arctanMW,KnKs4SM2KnKs+nEWKnsin3α+nEWKscos2αsinαee2fx/M1+sinφ/1−sinφ,α>arctanMW.As shown in Equation (19), under the mining height of the working face M = 6 m, W = Bb = 1 m, Em = 10 GPa, Kn = 10 GPa/m, and Ks = 4 GPa/m, the change law of the abutment pressure at the position of x = 0.5 m within the LEZ in a large-mining-height working face with the dip angle of joints is shown in Figure 13.Figure 13
Change in abutment pressure in LEZ with number of joints in a fully mechanised working face with large mining height.As shown in Figure13, the abutment pressures within the LEZ in a large-mining-height working face all gradually decrease with an increase in the number of joints at different dip angles. The advanced abutment pressure within the LEZ decreases significantly when there are fewer than 20 joints, while it does so much less when the number of joints is greater than 20. By taking the dip angle of the joints as α = 45° as an example, the abutment pressure at x = 0.5 m within the LEZ is about 7.71 MPa for coal seams without joints while it is about 1.50 MPa in the case that 20 joints are present in the coal seams. This indicates that the number of joints in coal seams significantly influences the abutment pressure within the LEZ in a large-mining-height working face. The result suggests that the joint spacing in coal seams delivers a great influence on the abutment pressure within the LEZ; moreover, with the reduction of joint spacing, the abutment pressure at the same distance from the working face within the LEZ gradually decreases.


### 3.2. Numerical Simulation Analysis of the Influence of Joint Orientation

To verify the rationality of the theoretical analysis, the influence of the orientation of the joints on the abutment pressure of the LEZ in a large-mining-height working face during the mining of coal seams was simulated and analysed by using 3DEC numerical simulation software.The 4309 working face was used as the numerical engineering background. The 4309 working face belongs to the Sihe Coal Mine, located in Jincheng, Shanxi province, Central China. The thickness of the coal seam is 6.14 m and the immediate roof is sandy mudstone, 12.58 m, as shown in Figure14.Figure 14
Comprehensive Column of 4309 working face.To ensure the rationality and operability of the numerical simulation, a total of nine numerical models were established according to the field measurements [30–32] and research objective, as shown in Table 2 and Figure 15.Table 2
Occurrence of joints with different parameters in coal seam.
Serial numberProperties of jointsParameters of jointsRemarksDip angleα (°)Azimuthβ (°)Spacingd (m)1Primary joint4505A model290B Model3135C Model44545D model5135E model6Primary joint9002F ModelSecondary joint457Primary joint902G modelSecondary joint451.418Primary joint902H ModelSecondary joint1359Primary joint902I ModelSecondary joint1351.41Note: The dip angleα of joints refers to the included angle between the dip direction of joints and the Y-axis positive direction (advancing direction) in 3DEC software; the azimuth β denotes the included angle between the strike direction of joints and X-axis positive direction (the direction along the length of the working face).Figure 15
Model section of joints with different parameters in a coal seam. (a) Model A. (b) Model B. (c) Model C. (d) Model D. (e) Model E. (f) Model F. (g) Model G. (h) Model H. (i) Model I.
(a)(b)(c)(d)(e)(f)(g)(h)(i)


#### 3.2.1. The Dip Angle of Joints

Figure16 shows the changes in abutment pressures at the same position within the LEZ in the large-mining-height working face under different dip angles of joints: the advanced abutment pressures within the LEZ in the large-mining-height working face vary under the effect of the dip angle of joints; at joint dip angles of 45° and 135°, the abutment pressures at the same position within the LEZ are similar while they are both lower than that at 90°. This conforms to the result obtained through theoretical analysis, which indicates the rationality thereof.Figure 16
Abutment pressure distribution in the limit equilibrium area with different joint inclination angles.


#### 3.2.2. The Azimuth of the Joints

Figure17 displays the changes in abutment pressures at the same position within the LEZ in the large-mining-height working face under different joint azimuths: the advanced abutment pressures within the LEZ in the large-mining-height working face differ due to the influence of the azimuth of joints; when the azimuths of joints are separately 45° and 135°, the abutment pressures at the same position within the LEZ are quasi-equivalent while they are both larger than that at the azimuth of 0°. This matches the result attained through theoretical analysis, which reveals the rationality thereof.Figure 17
Abutment pressure distribution in the limit equilibrium area with different joint azimuth angles.


#### 3.2.3. The Joint Spacing

Figure18 shows the changes in abutment pressures at the same position within the LEZ in the large-mining-height working face with different joint spacings in the coal seams: under the influence of the spacings of through-going joints in coal seams, the advanced abutment pressures at the same position within the LEZ in the large-mining-height working face are different; the highest and lowest abutment pressures are present in the LEZ under the corresponding joint spacings of 5 and 1.41 m, respectively; this is consistent with the result acquired through theoretical analysis, indicative of the rationality of the theoretical analysis.Figure 18
Abutment pressure distribution in the limit equilibrium area with different joint spacings. (a) Dip angle of joint of 45°. (b) Dip angle of joint of 135°.
(a)(b)With the excavation of the working face, the abutment pressures within the LEZ in the large-mining-height working face under different orientations of joints all present the same periodic fluctuation under the influence of periodic weighting of the roof. This suggests that the orientation of joints in coal seams influences the abutment pressure within the LEZ only by affecting the support capacity of the large-mining-height coal walls. It does not affect the spatiotemporal change in the advanced abutment pressure in the large-mining-height working face with the advance of the working face.Overall, the influence of the orientation of joints in coal seams on the abutment pressure within the LEZ in the large-mining-height working face is summarised as follows: with increasing dip angle of the joints, the abutment pressure at the same position within the LEZ first decreases, then increases, and finally decreases; under certain conditions, the abutment pressure at the same position within the LEZ first increases, then decreases with the increasing azimuth of the joints; as the joint spacing increases, the number of joints gradually decreases and correspondingly the abutment pressure at the same position within the LEZ rises; however, the dip angle and azimuth of joints only marginally influence the abutment pressure within the LEZ. In addition, the orientation of through-going joints in coal seams only affects the abutment pressure within the LEZ while it shows no influence on the spatiotemporal change in the advanced abutment pressure in the large-mining-height working face with the advance of the working face.Above all, the relationship between the orientation of joints in coal seams and the abutment pressure within the LEZ in the large-mining-height working face is described as follows:(20)σy=π2EmIBKnKs4MSBMKnKs+nEWKnsin2αcosαcosβ+nEWKscos3αcosβee2fx/M1+sinφ/1−sinφ,β≤arctanWB,α≤arctanMW,π2EmIKnKs4MSMKnKs+nEKnsin2αcosαsinβ+nEKscos3αsinβee2fx/M1+sinφ/1−sinφ,β>arctanWB,α≤arctanMW,π2EmIKnKs4SM2KnKs+nEWKnsin3α+nEWKscos2αsinαee2fx/M1+sinφ/1−sinφ,α>arctanMW.


## 3.1. Theoretical Analysis on the Influence of the Orientation of Joints

### 3.1.1. The Influence of the Dip Angle of the Joints

According to Equations (5) and (16) and assuming H = M, the relationship between the abutment pressure σy at a position x away from the coal walls within the LEZ in a large-mining-height working face and the dip angle of joints can be expressed as follows:(17)σy=π2EmIKnKs4MSMKnKs+EKnsin2αcosα+EKscos3αee2fx/M1+sinφ/1−sinφ,α≤arctanMW,π2EmIKnKs4SM2KnKs+EWKnsin3α+EWKscos2αsinαee2fx/M1+sinφ/1−sinφ,α>arctanMW.As shown in Equation (17), the change in abutment pressure at x = 0.5 m within the LEZ in a large-mining-height working face with the dip angle of joints is obtained under the mining height of the working face of M = 6 m, W=Bb = 1 m, Em = 10 GPa, Kn = 10 GPa/m, and Ks = 4 GPa/m, as shown in Figure 11.Figure 11
Change in abutment pressure in LEZ with inclination angle of joints in a fully mechanised working face with a large mining height.As shown in Figure11, the abutment pressure within the LEZ in a large-mining-height working face first decreases, then rises, and finally increases when increasing the dip angle of the joints in coal seams: this influence is opposite to that of the dip angle of joints on the damage to intact coal; the abutment pressure varies between 6.39 and 7.45 MPa. The result indicates that the change of the dip angle of joints in coal seams affects the abutment pressure within the LEZ in the large-mining-height working face to some extent.


### 3.1.2. The Influence of the Azimuth of the Joints

According to the above analysis, the azimuth of joints in coal seams does not influence the damage to the coal whenα > arctan (H/W); according to Equations (7) and (16) and assuming H = M, the relationship between the abutment pressure σy at a position x away from coal walls within the LEZ in a large-mining-height working face and the azimuth of joints is shown in Equation (18) at α ≤ arctan (H/W):(18)σy=π2EmIBbKnKs4MSBbMKnKs+EWKnsin2αcosαcosβ+EWKscos3αcosβee2fx/M1+sinφ/1−sinφ,β≤arctanWBb,π2EmIKnKs4MSMKnKs+EKnsin2αcosαsinβ+EKscos3αsinβee2fx/M1+sinφ/1−sinφ,β>arctanWBb.As shown in Equation (18), the change in the abutment pressure at x = 0.5 m within the LEZ in a large-mining-height working face with the dip angle of joints is attained under the mining height of the working face of M = 6 m, W = Bb = 1 m, Em = 10 GPa, Kn = 10 GPa/m, and Ks = 4 GPa/m, as shown in Figure 12.Figure 12
Change in the abutment pressure in LEZ with azimuth angle of joints in a fully mechanised working face with large mining height.It can be seen from Figure12 that the abutment pressure within the LEZ in a large-mining-height working face first increases, then decreases with the increasing azimuth at different dip angles of the joints. The maximum abutment pressure is found at the azimuth of β = 45° (Figure 12). At dip angles of the joints of 30°, 45°, and 60°, the abutment pressures vary in the ranges of 6.43 to 6.76, 6.39 to 6.73, and 6.55 to 6.85 MPa: this indicates that the azimuth of through-going joints in coal seams shows a certain (albeit slight) influence on the abutment pressure within the LEZ.


### 3.1.3. Joint Spacing

Based on the above analysis, the joint spacing in coal seams is inversely proportional to the number of joints within a certain range. Thus, it is feasible to obtain the influence of the joint spacing by analysing the influence of the number of joints on the abutment pressure within the LEZ in a large-mining-height working face.According to Equations (11) and (16), and assuming H = M, the relationship between the abutment pressure σy at a position x away from coal walls within the LEZ in a large-mining-height working face and the number of joints can be attained:(19)σy=π2EmIKnKs4MSMKnKs+nEKnsin2αcosα+nEKscos3αee2fx/M1+sinφ/1−sinφ,α≤arctanMW,KnKs4SM2KnKs+nEWKnsin3α+nEWKscos2αsinαee2fx/M1+sinφ/1−sinφ,α>arctanMW.As shown in Equation (19), under the mining height of the working face M = 6 m, W = Bb = 1 m, Em = 10 GPa, Kn = 10 GPa/m, and Ks = 4 GPa/m, the change law of the abutment pressure at the position of x = 0.5 m within the LEZ in a large-mining-height working face with the dip angle of joints is shown in Figure 13.Figure 13
Change in abutment pressure in LEZ with number of joints in a fully mechanised working face with large mining height.As shown in Figure13, the abutment pressures within the LEZ in a large-mining-height working face all gradually decrease with an increase in the number of joints at different dip angles. The advanced abutment pressure within the LEZ decreases significantly when there are fewer than 20 joints, while it does so much less when the number of joints is greater than 20. By taking the dip angle of the joints as α = 45° as an example, the abutment pressure at x = 0.5 m within the LEZ is about 7.71 MPa for coal seams without joints while it is about 1.50 MPa in the case that 20 joints are present in the coal seams. This indicates that the number of joints in coal seams significantly influences the abutment pressure within the LEZ in a large-mining-height working face. The result suggests that the joint spacing in coal seams delivers a great influence on the abutment pressure within the LEZ; moreover, with the reduction of joint spacing, the abutment pressure at the same distance from the working face within the LEZ gradually decreases.


## 3.1.1. The Influence of the Dip Angle of the Joints

According to Equations (5) and (16) and assuming H = M, the relationship between the abutment pressure σy at a position x away from the coal walls within the LEZ in a large-mining-height working face and the dip angle of joints can be expressed as follows:(17)σy=π2EmIKnKs4MSMKnKs+EKnsin2αcosα+EKscos3αee2fx/M1+sinφ/1−sinφ,α≤arctanMW,π2EmIKnKs4SM2KnKs+EWKnsin3α+EWKscos2αsinαee2fx/M1+sinφ/1−sinφ,α>arctanMW.As shown in Equation (17), the change in abutment pressure at x = 0.5 m within the LEZ in a large-mining-height working face with the dip angle of joints is obtained under the mining height of the working face of M = 6 m, W=Bb = 1 m, Em = 10 GPa, Kn = 10 GPa/m, and Ks = 4 GPa/m, as shown in Figure 11.Figure 11
Change in abutment pressure in LEZ with inclination angle of joints in a fully mechanised working face with a large mining height.As shown in Figure11, the abutment pressure within the LEZ in a large-mining-height working face first decreases, then rises, and finally increases when increasing the dip angle of the joints in coal seams: this influence is opposite to that of the dip angle of joints on the damage to intact coal; the abutment pressure varies between 6.39 and 7.45 MPa. The result indicates that the change of the dip angle of joints in coal seams affects the abutment pressure within the LEZ in the large-mining-height working face to some extent.


## 3.1.2. The Influence of the Azimuth of the Joints

According to the above analysis, the azimuth of joints in coal seams does not influence the damage to the coal whenα > arctan (H/W); according to Equations (7) and (16) and assuming H = M, the relationship between the abutment pressure σy at a position x away from coal walls within the LEZ in a large-mining-height working face and the azimuth of joints is shown in Equation (18) at α ≤ arctan (H/W):(18)σy=π2EmIBbKnKs4MSBbMKnKs+EWKnsin2αcosαcosβ+EWKscos3αcosβee2fx/M1+sinφ/1−sinφ,β≤arctanWBb,π2EmIKnKs4MSMKnKs+EKnsin2αcosαsinβ+EKscos3αsinβee2fx/M1+sinφ/1−sinφ,β>arctanWBb.As shown in Equation (18), the change in the abutment pressure at x = 0.5 m within the LEZ in a large-mining-height working face with the dip angle of joints is attained under the mining height of the working face of M = 6 m, W = Bb = 1 m, Em = 10 GPa, Kn = 10 GPa/m, and Ks = 4 GPa/m, as shown in Figure 12.Figure 12
Change in the abutment pressure in LEZ with azimuth angle of joints in a fully mechanised working face with large mining height.It can be seen from Figure12 that the abutment pressure within the LEZ in a large-mining-height working face first increases, then decreases with the increasing azimuth at different dip angles of the joints. The maximum abutment pressure is found at the azimuth of β = 45° (Figure 12). At dip angles of the joints of 30°, 45°, and 60°, the abutment pressures vary in the ranges of 6.43 to 6.76, 6.39 to 6.73, and 6.55 to 6.85 MPa: this indicates that the azimuth of through-going joints in coal seams shows a certain (albeit slight) influence on the abutment pressure within the LEZ.


## 3.1.3. Joint Spacing

Based on the above analysis, the joint spacing in coal seams is inversely proportional to the number of joints within a certain range. Thus, it is feasible to obtain the influence of the joint spacing by analysing the influence of the number of joints on the abutment pressure within the LEZ in a large-mining-height working face.According to Equations (11) and (16), and assuming H = M, the relationship between the abutment pressure σy at a position x away from coal walls within the LEZ in a large-mining-height working face and the number of joints can be attained:(19)σy=π2EmIKnKs4MSMKnKs+nEKnsin2αcosα+nEKscos3αee2fx/M1+sinφ/1−sinφ,α≤arctanMW,KnKs4SM2KnKs+nEWKnsin3α+nEWKscos2αsinαee2fx/M1+sinφ/1−sinφ,α>arctanMW.As shown in Equation (19), under the mining height of the working face M = 6 m, W = Bb = 1 m, Em = 10 GPa, Kn = 10 GPa/m, and Ks = 4 GPa/m, the change law of the abutment pressure at the position of x = 0.5 m within the LEZ in a large-mining-height working face with the dip angle of joints is shown in Figure 13.Figure 13
Change in abutment pressure in LEZ with number of joints in a fully mechanised working face with large mining height.As shown in Figure13, the abutment pressures within the LEZ in a large-mining-height working face all gradually decrease with an increase in the number of joints at different dip angles. The advanced abutment pressure within the LEZ decreases significantly when there are fewer than 20 joints, while it does so much less when the number of joints is greater than 20. By taking the dip angle of the joints as α = 45° as an example, the abutment pressure at x = 0.5 m within the LEZ is about 7.71 MPa for coal seams without joints while it is about 1.50 MPa in the case that 20 joints are present in the coal seams. This indicates that the number of joints in coal seams significantly influences the abutment pressure within the LEZ in a large-mining-height working face. The result suggests that the joint spacing in coal seams delivers a great influence on the abutment pressure within the LEZ; moreover, with the reduction of joint spacing, the abutment pressure at the same distance from the working face within the LEZ gradually decreases.


## 3.2. Numerical Simulation Analysis of the Influence of Joint Orientation

To verify the rationality of the theoretical analysis, the influence of the orientation of the joints on the abutment pressure of the LEZ in a large-mining-height working face during the mining of coal seams was simulated and analysed by using 3DEC numerical simulation software.The 4309 working face was used as the numerical engineering background. The 4309 working face belongs to the Sihe Coal Mine, located in Jincheng, Shanxi province, Central China. The thickness of the coal seam is 6.14 m and the immediate roof is sandy mudstone, 12.58 m, as shown in Figure14.Figure 14
Comprehensive Column of 4309 working face.To ensure the rationality and operability of the numerical simulation, a total of nine numerical models were established according to the field measurements [30–32] and research objective, as shown in Table 2 and Figure 15.Table 2
Occurrence of joints with different parameters in coal seam.
Serial numberProperties of jointsParameters of jointsRemarksDip angleα (°)Azimuthβ (°)Spacingd (m)1Primary joint4505A model290B Model3135C Model44545D model5135E model6Primary joint9002F ModelSecondary joint457Primary joint902G modelSecondary joint451.418Primary joint902H ModelSecondary joint1359Primary joint902I ModelSecondary joint1351.41Note: The dip angleα of joints refers to the included angle between the dip direction of joints and the Y-axis positive direction (advancing direction) in 3DEC software; the azimuth β denotes the included angle between the strike direction of joints and X-axis positive direction (the direction along the length of the working face).Figure 15
Model section of joints with different parameters in a coal seam. (a) Model A. (b) Model B. (c) Model C. (d) Model D. (e) Model E. (f) Model F. (g) Model G. (h) Model H. (i) Model I.
(a)(b)(c)(d)(e)(f)(g)(h)(i)


### 3.2.1. The Dip Angle of Joints

Figure16 shows the changes in abutment pressures at the same position within the LEZ in the large-mining-height working face under different dip angles of joints: the advanced abutment pressures within the LEZ in the large-mining-height working face vary under the effect of the dip angle of joints; at joint dip angles of 45° and 135°, the abutment pressures at the same position within the LEZ are similar while they are both lower than that at 90°. This conforms to the result obtained through theoretical analysis, which indicates the rationality thereof.Figure 16
Abutment pressure distribution in the limit equilibrium area with different joint inclination angles.


### 3.2.2. The Azimuth of the Joints

Figure17 displays the changes in abutment pressures at the same position within the LEZ in the large-mining-height working face under different joint azimuths: the advanced abutment pressures within the LEZ in the large-mining-height working face differ due to the influence of the azimuth of joints; when the azimuths of joints are separately 45° and 135°, the abutment pressures at the same position within the LEZ are quasi-equivalent while they are both larger than that at the azimuth of 0°. This matches the result attained through theoretical analysis, which reveals the rationality thereof.Figure 17
Abutment pressure distribution in the limit equilibrium area with different joint azimuth angles.


### 3.2.3. The Joint Spacing

Figure18 shows the changes in abutment pressures at the same position within the LEZ in the large-mining-height working face with different joint spacings in the coal seams: under the influence of the spacings of through-going joints in coal seams, the advanced abutment pressures at the same position within the LEZ in the large-mining-height working face are different; the highest and lowest abutment pressures are present in the LEZ under the corresponding joint spacings of 5 and 1.41 m, respectively; this is consistent with the result acquired through theoretical analysis, indicative of the rationality of the theoretical analysis.Figure 18
Abutment pressure distribution in the limit equilibrium area with different joint spacings. (a) Dip angle of joint of 45°. (b) Dip angle of joint of 135°.
(a)(b)With the excavation of the working face, the abutment pressures within the LEZ in the large-mining-height working face under different orientations of joints all present the same periodic fluctuation under the influence of periodic weighting of the roof. This suggests that the orientation of joints in coal seams influences the abutment pressure within the LEZ only by affecting the support capacity of the large-mining-height coal walls. It does not affect the spatiotemporal change in the advanced abutment pressure in the large-mining-height working face with the advance of the working face.Overall, the influence of the orientation of joints in coal seams on the abutment pressure within the LEZ in the large-mining-height working face is summarised as follows: with increasing dip angle of the joints, the abutment pressure at the same position within the LEZ first decreases, then increases, and finally decreases; under certain conditions, the abutment pressure at the same position within the LEZ first increases, then decreases with the increasing azimuth of the joints; as the joint spacing increases, the number of joints gradually decreases and correspondingly the abutment pressure at the same position within the LEZ rises; however, the dip angle and azimuth of joints only marginally influence the abutment pressure within the LEZ. In addition, the orientation of through-going joints in coal seams only affects the abutment pressure within the LEZ while it shows no influence on the spatiotemporal change in the advanced abutment pressure in the large-mining-height working face with the advance of the working face.Above all, the relationship between the orientation of joints in coal seams and the abutment pressure within the LEZ in the large-mining-height working face is described as follows:(20)σy=π2EmIBKnKs4MSBMKnKs+nEWKnsin2αcosαcosβ+nEWKscos3αcosβee2fx/M1+sinφ/1−sinφ,β≤arctanWB,α≤arctanMW,π2EmIKnKs4MSMKnKs+nEKnsin2αcosαsinβ+nEKscos3αsinβee2fx/M1+sinφ/1−sinφ,β>arctanWB,α≤arctanMW,π2EmIKnKs4SM2KnKs+nEWKnsin3α+nEWKscos2αsinαee2fx/M1+sinφ/1−sinφ,α>arctanMW.


## 3.2.1. The Dip Angle of Joints

Figure16 shows the changes in abutment pressures at the same position within the LEZ in the large-mining-height working face under different dip angles of joints: the advanced abutment pressures within the LEZ in the large-mining-height working face vary under the effect of the dip angle of joints; at joint dip angles of 45° and 135°, the abutment pressures at the same position within the LEZ are similar while they are both lower than that at 90°. This conforms to the result obtained through theoretical analysis, which indicates the rationality thereof.Figure 16
Abutment pressure distribution in the limit equilibrium area with different joint inclination angles.


## 3.2.2. The Azimuth of the Joints

Figure17 displays the changes in abutment pressures at the same position within the LEZ in the large-mining-height working face under different joint azimuths: the advanced abutment pressures within the LEZ in the large-mining-height working face differ due to the influence of the azimuth of joints; when the azimuths of joints are separately 45° and 135°, the abutment pressures at the same position within the LEZ are quasi-equivalent while they are both larger than that at the azimuth of 0°. This matches the result attained through theoretical analysis, which reveals the rationality thereof.Figure 17
Abutment pressure distribution in the limit equilibrium area with different joint azimuth angles.


## 3.2.3. The Joint Spacing

Figure18 shows the changes in abutment pressures at the same position within the LEZ in the large-mining-height working face with different joint spacings in the coal seams: under the influence of the spacings of through-going joints in coal seams, the advanced abutment pressures at the same position within the LEZ in the large-mining-height working face are different; the highest and lowest abutment pressures are present in the LEZ under the corresponding joint spacings of 5 and 1.41 m, respectively; this is consistent with the result acquired through theoretical analysis, indicative of the rationality of the theoretical analysis.Figure 18
Abutment pressure distribution in the limit equilibrium area with different joint spacings. (a) Dip angle of joint of 45°. (b) Dip angle of joint of 135°.
(a)(b)With the excavation of the working face, the abutment pressures within the LEZ in the large-mining-height working face under different orientations of joints all present the same periodic fluctuation under the influence of periodic weighting of the roof. This suggests that the orientation of joints in coal seams influences the abutment pressure within the LEZ only by affecting the support capacity of the large-mining-height coal walls. It does not affect the spatiotemporal change in the advanced abutment pressure in the large-mining-height working face with the advance of the working face.Overall, the influence of the orientation of joints in coal seams on the abutment pressure within the LEZ in the large-mining-height working face is summarised as follows: with increasing dip angle of the joints, the abutment pressure at the same position within the LEZ first decreases, then increases, and finally decreases; under certain conditions, the abutment pressure at the same position within the LEZ first increases, then decreases with the increasing azimuth of the joints; as the joint spacing increases, the number of joints gradually decreases and correspondingly the abutment pressure at the same position within the LEZ rises; however, the dip angle and azimuth of joints only marginally influence the abutment pressure within the LEZ. In addition, the orientation of through-going joints in coal seams only affects the abutment pressure within the LEZ while it shows no influence on the spatiotemporal change in the advanced abutment pressure in the large-mining-height working face with the advance of the working face.Above all, the relationship between the orientation of joints in coal seams and the abutment pressure within the LEZ in the large-mining-height working face is described as follows:(20)σy=π2EmIBKnKs4MSBMKnKs+nEWKnsin2αcosαcosβ+nEWKscos3αcosβee2fx/M1+sinφ/1−sinφ,β≤arctanWB,α≤arctanMW,π2EmIKnKs4MSMKnKs+nEKnsin2αcosαsinβ+nEKscos3αsinβee2fx/M1+sinφ/1−sinφ,β>arctanWB,α≤arctanMW,π2EmIKnKs4SM2KnKs+nEWKnsin3α+nEWKscos2αsinαee2fx/M1+sinφ/1−sinφ,α>arctanMW.


## 4. Conclusion

(1)
The damage variable of coal with joints first increases, then decreases, and finally increases with increasing dip angle of the joints; an increase in the azimuth of joints corresponds to the first decrease and then growth in the damage variable of coal with joints; the damage variable of coal with joints gradually decreases as the joint spacing is increased.(2)
Based on the theory on the stability of columns of coal walls in the large-mining-height working face, the distribution and the main influencing factors of the abutment pressure within the LEZ were investigated. As for a large-mining-height working face in the given conditions, the abutment pressure at the same position within the LEZ is mainly affected by mechanical parameters of the coal.(3)
With increasing joint dip angle, the abutment pressure at the same position in front of coal walls first decreases, then increases, only to decrease again; under certain conditions, the abutment pressure at the same position within the LEZ first increases, then decreases as the azimuth of the joints increases; an increase in the joint spacing corresponds to the growth of the abutment pressure at the same position within the LEZ. The dip angle and azimuth of the joints exert an insignificant influence on the abutment pressure within the LEZ.



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*Source: 9963175-2021-11-13.xml*