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

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. )is 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-miningheight 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.)e dip angle and azimuth of joints marginally affect the abutment pressure within the LEZ.


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][2][3][4][5][6][7][8][9]. ere are many researches about the abutment pressure on the working face [10][11][12][13][14][15], which are mainly about the influences of roof structure, mining height, or the coal macroscopic mechanical parameters on the abutment pressure. e 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 largemining-height working face.
is 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][18][19]. erefore, 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-miningheight working faces. e 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. e 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.
en, 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.

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.
us, 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]. Figure 1 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 L g , in which only the part with the intermediate length of l g is allowed to slide; coal-rock blocks in the upper and lower sides of joints. e equivalent elastic stiffness of coal with joints can be deduced through analysis based on the Brady model [21]: where where k refers to the equivalent elastic stiffness of coal with a single joint; H, W, and B b 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; K n and K s separately denote the normal and tangential stiffnesses of the joints.

e Influence of the Dip Angle of Joints.
rough analysis from the perspective of damage mechanics, the coal with joints can be considered as a damaged body. By introducing the damage variable D, the elastic modulus E e for coal with joints is expressed as follows [23]: Under compression, the axial stiffness of coal with joints is calculated as follows [24]: Based on Equations (1) to (4), the damage variable D of coal with a single joint is expressed as follows: D � EK n sin 2 α cos α + EK s cos 3 α HK n K s + EK n sin 2 α cos α + EK s cos 3 α , α ≤ arctan H W , EWK n sin 3 α + EWK s cos 2 α sin α H 2 K n K s + EWK n sin 3 α + EWK s cos 2 α sin α , α > arctan H W .
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, K n � 10 GPa/m, K s � 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.
It can be seen from Figure 2 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 2 Shock and Vibration and 0.39: the change in the dip angle of the joint influences the damage, albeit to an insignificant extent.

e Influence of the Azimuth of the Joints.
In the Brady model, the length L g of joints certainly varies when their dip angle satisfies α ≤ arctan (H/W) under the influence of β, the azimuth of joints. e relationship of L g to α and β is attained: e 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 L g in the equation with Equation (2) or Equation (6) according to different conditions. e rationality of the above analysis can be validated by employing 3DEC numerical simulation, as shown in Figure 3. e 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.
It can be found from the above analysis that at different azimuths of joints, the damage variable D 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: D � EWK n sin 2 α cos α cos β + EWK s cos 3 α cos β B b HK n K s + EWK n sin 2 α cos α cos β + EWK s cos 3 α cos β , β ≤ arctan W B b , EK n sin 2 α cos α sin β + EK s cos 3 α sin β HK n K s + EK n sin 2 α cos α sin β + EK s cos 3 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, K n � 10 GPa/m, K s � 4 GPa/m, and H � 2B b � 2W � 2 m, as shown in Figure 4.
As shown in Figure 4, 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 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. e 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 coalrock 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. e global displacement of coal with two joints is calculated as follows: where U b , U c , and U 0 separately refer to displacements of various component elements. e equivalent elastic stiffness of coal containing two joints is expressed as follows: where the meanings of various physico-mechanical parameters follow those in Equations (1) and (2). By taking H � 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.
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.
erefore, the curves attained through numerical simulation are not completely in line with those obtained through theoretical analysis (Figures 3 and 6).
According to the above analysis, the damage variable D 2 of two coal containing joints is calculated as follows: Similarly, when n (a positive integer) through-going joints are found in coal, the damage variable D n is calculated as follows: D n � nEK n sin 2 α cos α + nEK s cos 3 α HK n K s + nEK n sin 2 α cos α + nEK s cos 3 α , α ≤ arctan H W , nEWK n sin 3 α + nEWK s cos 2 α sin α H 2 K n K s + nEWK n sin 3 α + nEWK s cos 2 α sin α , α > arctan H W .
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, K n � 10 GPa/m, K s � 4 GPa/m, and H � 2W � 2 m can be attained (Figure 7 and Table 1). e 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 (Figure 7). In a case where two, three, five, ten, and twenty throughgoing 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 (Table 1), 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. us, the lower the joint spacing, the larger the damage variable of coal containing joints.
Above all, the relationships of the damage variable D of coal containing through-going joints with the dip angle α, azimuth β, and spacing d (number n) of joints are expressed as follows: When H � 6 m and W � B b � 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).

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: where N 0 , 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. e 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. e critical pressure (support capacity) on coal walls can be calculated according to the theory of the stability of columns [26][27][28].
where E em , E m , 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 N 0 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 (Figure 9(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).
Based on Equations (13) and (14), the abutment pressure σ y 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: 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. erefore, the influence of parameters of joints on the abutment pressure within the LEZ in a largemining-height working face can be elucidated according to the influence of the joints on the damage to the coal.

eoretical Analysis on the Influence of the Orientation of
As shown in Equation (17), the change in abutment pressure at x � 0.5 m within the LEZ in a large-miningheight working face with the dip angle of joints is obtained under the mining height of the working face of M � 6 m, W � B b � 1 m, E m � 10 GPa, K n � 10 GPa/m, and K s � 4 GPa/ m, as shown in Figure 11.
As shown in Figure 11, 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. e 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.
e 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 when α > arctan (H/W); according to Equations (7) and (16) and assuming H � M, the relationship between the abutment pressure σ y 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): As shown in Equation (18), the change in the abutment pressure at x � 0.5 m within the LEZ in a large-miningheight working face with the dip angle of joints is attained under the mining height of the working face of M � 6 m, W � B b � 1 m, E m � 10 GPa, K n � 10 GPa/m, and K s � 4 GPa/ m, as shown in Figure 12.
It can be seen from Figure 12 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. e 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 throughgoing joints in coal seams shows a certain (albeit slight) influence on the abutment pressure within the LEZ.

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. us, 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 σ y at a position x away from coal walls within the LEZ in a largemining-height working face and the number of joints can be attained: σ y � π 2 E m IK n K s 4MS MK n K s + nEK n sin 2 α cos α + nEK s cos 3 α e e 2fx/M(1+sin φ/1−sin φ) , α ≤ arctan M W , K n K s 4S M 2 K n K s + nEWK n sin 3 α + nEWK s cos 2 α sin α e e 2fx/M(1+sin φ/1−sin φ) , α > arctan M W .
As shown in Equation (19), under the mining height of the working face M � 6 m, W � B b � 1 m, E m � 10 GPa, K n � 10 GPa/m, and K s � 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.

Shock and Vibration 11
As shown in Figure 13, 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. e 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°a s 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. is indicates that the number of joints in coal seams significantly influences the abutment pressure within the LEZ in a large-mining-height working face. e 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.

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. e 4309 working face was used as the numerical engineering background. e 4309 working face belongs to the Sihe Coal Mine, located in Jincheng, Shanxi province, Central China. e thickness of the coal seam is 6.14 m and the immediate roof is sandy mudstone, 12.58 m, as shown in Figure 14.
To ensure the rationality and operability of the numerical simulation, a total of nine numerical models were established according to the field measurements [30][31][32] and research objective, as shown in Table 2 and Figure 15. Figure 16 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°.

e Dip Angle of Joints.
is conforms to the result obtained through theoretical analysis, which indicates the rationality thereof.

3.2.2.
e Azimuth of the Joints. Figure 17 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 quasiequivalent while they are both larger than that at the azimuth of 0°. is matches the result attained through theoretical analysis, which reveals the rationality thereof. Figure 18 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.

e Joint Spacing.
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. is suggests that the orientation of joints in coal seams influences the abutment pressure within the LEZ only by affecting the support capacity of the largemining-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 largemining-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 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:   Note: e dip angle α 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).    16 Shock and Vibration