E ﬀ ect of Principal Stress Field on the Development of Plastic Zone ahead of the Gateroad

: The distribution of a plastic zone ahead of a gateroad plays a signiﬁcant role in maintaining the long-term stability of mining spaces. For a long time, the principal stress ﬁeld such as the values, the direction, etc. have been observed to have impacts on plastic zone development, but has not been looked into deeply and systematically. To this end, the inﬂuence of principal stress ﬁeld including the maximum principal stress ( P 1 ), the angle between the P 1 direction and the Z -axis ( α ), the minimum principal stress ( P 3 ), and the ratio of maximum principal stress to minimum principal stress ( P 1 / P 3 ) on the expansion of the plastic zone ahead of the gateroad is investigated by the (Fast Lagrangian Analysis of Continua) FLAC 3D models. The results show that: (1) The plastic zone volume increases ﬁrst and then decreases with the increase of α , and the direction of butterﬂy-shaped plastic zone ahead of gateroad is rotating with the evolution of α . (2) The plastic zone volume ahead of excavation face increases gradually with the increase of P 1 / P 3 . Mutagenicity of butterﬂy-shaped plastic zone occurs ahead of the gateroad under a certain value of P 1 / P 3 . (3) With the increase of P 1 and decrease of P 3 , the plastic zone volume is of exponential growth. The plastic zone volume approaches inﬁnity when the critical value of maximum principal stress ([ P 1 ]) and the minimum principal stress ([ P 1 ]) is obtained. (4) The study of the e ﬀ ect of principal stress ﬁeld on the expansion of plastic zone ahead of the gateroad is helpful for revealing the mechanisms of coal and gas outbursts. The critical stress state of butterﬂy-shaped plastic zone mutagenicity ahead of the gateroad can be used as an important indicator for assessing the risk of coal and gas outburst. The research can also guide the prevention of coal and gas outburst ahead of the gateroad.

gateroad [29,30]. However, the individual components of 3D in-situ stress tensor were not considered in the existing studies. Kang et al. (2010) indicated that the minimum horizontal in-situ stress was approximately half of the maximum one, and the direction of the two stress components was generally different in different orientations [31]. The principal stress field also played an important role in keeping the long-term stability of an underground gateroad. Therefore, it is necessary to investigate the influence of principal stress field on the distribution of the plastic zone ahead of the gateroad. This paper established several numerical models by FLAC 3D to investigate the influence of principal stress field on the expansion of plastic zone ahead of the gateroad. Influence factors included the maximum principal stress (P 1 ), the angle between the P 1 direction and the Z-axis (α), the minimum principal stress (P 3 ), and the ratio of maximum principal stress to minimum principal stress (P 1 /P 3 ). Then, the distribution characteristics of plastic zone are summarized under different principal stress fields, and the implications for the coal and gas outburst induced by the expansion plastic zone ahead of gateroad is also discussed. The following study is expected to provide some new insights into the mechanism, prediction, and prevention of dynamic disasters ahead of the gateroad.

Numerical Model Setup
In order to simulate the plastic zone distribution characteristics around the gateroad, a layered rock mass numerical modelling was established by FLAC 3D software, which is shown as Figure 1. In the numerical model, the Mohr-Coulomb constitutive model was used. The size of numerical model was 50 m in the X-axial, 80 m in the Y-axial, and 80 m in the Z-axis. The section of gateroad was a rectangle. The length and width were 5 and 4 m, respectively. In the numerical model, the non-excavation planes were fixed with displacement constraints at all directions. The excavation planes were fixed with displacement constraints at the X-axial and the Y-axial directions. The gateroad was located as shown in Figure 1, in which the excavation direction was along the γ-axis.
Energies 2020, 13, x FOR PEER REVIEW 3 of 15 in the existing studies. Kang et al. (2010) indicated that the minimum horizontal in-situ stress was approximately half of the maximum one, and the direction of the two stress components was generally different in different orientations [31]. The principal stress field also played an important role in keeping the long-term stability of an underground gateroad. Therefore, it is necessary to investigate the influence of principal stress field on the distribution of the plastic zone ahead of the gateroad. This paper established several numerical models by FLAC 3D to investigate the influence of principal stress field on the expansion of plastic zone ahead of the gateroad. Influence factors included the maximum principal stress (P1), the angle between the P1 direction and the Z-axis (α), the minimum principal stress (P3), and the ratio of maximum principal stress to minimum principal stress (P1/P3). Then, the distribution characteristics of plastic zone are summarized under different principal stress fields, and the implications for the coal and gas outburst induced by the expansion plastic zone ahead of gateroad is also discussed. The following study is expected to provide some new insights into the mechanism, prediction, and prevention of dynamic disasters ahead of the gateroad.

Numerical Model Setup
In order to simulate the plastic zone distribution characteristics around the gateroad, a layered rock mass numerical modelling was established by FLAC 3D software, which is shown as Figure 1. In the numerical model, the Mohr-Coulomb constitutive model was used. The size of numerical model was 50 m in the X-axial, 80 m in the Y-axial, and 80 m in the Z-axis. The section of gateroad was a rectangle. The length and width were 5 and 4 m, respectively. In the numerical model, the nonexcavation planes were fixed with displacement constraints at all directions. The excavation planes were fixed with displacement constraints at the X-axial and the Y-axial directions. The gateroad was located as shown in Figure 1, in which the excavation direction was along the -axis. The mechanical parameters for coal and rock are given in Table 1, which were mainly determined by laboratory testing. The exploration drilling was conducted in the case study coal mine in order to obtain the standard samples and test the geotechnical parameters. The density was calculated by measuring the mass and volume of standard coal/rock samples. The uniaxial compressive tests were carried out to obtain the compressive strength, Poisson's ratio, and elastic modulus. The internal friction angle and cohesion were acquired by shear tests. Moreover, the bulk modulus and shear modulus were calculated by the following formulae: where K is bulk modulus, G is shear modulus, E is elastic modulus, and ν is Poisson's ratio. The mechanical parameters for coal and rock are given in Table 1, which were mainly determined by laboratory testing. The exploration drilling was conducted in the case study coal mine in order to obtain the standard samples and test the geotechnical parameters. The density was calculated by measuring the mass and volume of standard coal/rock samples. The uniaxial compressive tests were carried out to obtain the compressive strength, Poisson's ratio, and elastic modulus. The internal friction angle and cohesion were acquired by shear tests. Moreover, the bulk modulus and shear modulus were calculated by the following formulae: where K is bulk modulus, G is shear modulus, E is elastic modulus, and ν is Poisson's ratio. It should be noted that three kinds of coal are presented in Table 1 with different mechanical parameters, which were numbered No. I, No. II and, No. III coal.

Modelling Plans
In mining practice, the original stress field of rock mass is a three-dimensional unequal compressive stress field, which is mainly composed of the self-weight stress field and tectonic stress field. The magnitudes and directions of three principal stresses are different with the spatial positions. Generally, the initial balanced stress field can be affected by the mining-induced stress, which will lead to the size and direction change of principal stresses at different degrees [32]. Based on the existing results, the following four calculation numerical schemes were designed to study the influences of principal stress direction, ratio, and magnitude on the expansionary law of plastic zone in coal and rock mass ahead of the gateroad.

Plan 1
The magnitude of principal stress in the numerical model was invariant, which was set as follows: P 1 = 36.5 MPa, P 2 = 20 MPa, P 3 = 10 MPa. The lithology of the coal seam was consistent with No. II coal in Table 1. When P 1 and P 3 were rotated along the X-axis, an angle α was formed by P 1 direction and the Z-axis shown in Figure 2. In Plan 1, the plastic zone distribution characteristics ahead of the gateroad were studied when α was 0 • , 15 • , 30 • , 45 • , 60 • , and 75 • , respectively.  It should be noted that three kinds of coal are presented in Table 1 with different mechanical parameters, which were numbered No. I, No. II and, No. III coal.

Modelling Plans
In mining practice, the original stress field of rock mass is a three-dimensional unequal compressive stress field, which is mainly composed of the self-weight stress field and tectonic stress field. The magnitudes and directions of three principal stresses are different with the spatial positions. Generally, the initial balanced stress field can be affected by the mining-induced stress, which will lead to the size and direction change of principal stresses at different degrees [32]. Based on the existing results, the following four calculation numerical schemes were designed to study the influences of principal stress direction, ratio, and magnitude on the expansionary law of plastic zone in coal and rock mass ahead of the gateroad.

Plan 1
The magnitude of principal stress in the numerical model was invariant, which was set as follows: P1 = 36.5 MPa, P2 = 20 MPa, P3 = 10 MPa. The lithology of the coal seam was consistent with No. II coal in Table 1. When P1 and P3 were rotated along the X-axis, an angle α was formed by P1 direction and the Z-axis shown in Figure 2. In Plan 1, the plastic zone distribution characteristics ahead of the gateroad were studied when α was 0°, 15°, 30°, 45°, 60°, and 75°, respectively.

Plan 2
P2 was equal to P3 in the numerical model of Plan 2. α was set at 50°, and the physical and mechanical parameter of coal seam met with those of No. II coal in Table 1. In order to study the effect of P1/P3 (the ratio of maximum principal stress to minimum principal stress) on the plastic zone distribution, the magnitude of P1/P3 was set as 1, 1.5, 2, 2.5, 3, and 3.5, respectively.   Table 1. In order to study the effect of P 1 /P 3 (the ratio of maximum principal stress to minimum principal stress) on the plastic zone distribution, the magnitude of P 1 /P 3 was set as 1, 1.5, 2, 2.5, 3, and 3.5, respectively. 3.3. Plan 3 P 2 , P 3 , and α in the numerical model were invariant in Plan 3, which were set as follows: P 2 = 20 MPa, P 3 = 10 MPa, α = 50 • . The lithology of coal seam is consistent with No. I, II and III coal in Table 1. The plastic zone distribution characteristics ahead of the gateroad were studied in Plan 3 when the maximum principal stress P 1 was 25, 8, 31, 33, 35, and 36.5 MPa, respectively.
3.4. Plan 4 P 1 , P 2 and α in the numerical model were invariant in Plan 4, which were set as follows: P 1 = 36 MPa, P 2 = 20 MPa, α = 50 • . The lithology of coal seam was consistent with No. I, II, and III coal in Table 1. The plastic zone distribution characteristic ahead of the gateroad was studied in Plan 3 when the minimum principal stress P 3 was 15, 13, 12, 11, 10, and 9.8 MPa, respectively.

Influence of α (Angle between the P1 Direction and the Z-Axis)
The results from Plan 1 are shown in Figure 3. It shows that the plastic zone is mainly located ahead of the road when α is 0 • , which has a relatively small area, and the plastic zone has no butterfly-shaped characteristics. The plastic zone volume is 302 m 3 when the α is 15 • . It is primarily distributed in the upper-front part of the gateroad. The shape of plastic zone is like a butterfly wing when α is 30 • and 45 • , and the volume of plastic zone is 972 m 3 and 1476 m 3 , respectively. It should be noted that the butterfly wing morphology in the plastic zone is relatively complete. Afterwards, the butterfly wing in the plastic zone gradually disappears. When α is 60 • , the plastic zone shape is unchanged. However, the volume of plastic zone decreases. The magnitude is 720 m 3 . Similarly, the plastic zone volume decreases significantly when α is 75 • . It drops to 308 m 3 , and the plastic zone is mainly distributed at the bottom of the gateroad.  Table  1. The plastic zone distribution characteristics ahead of the gateroad were studied in Plan 3 when the maximum principal stress P1 was 25, 8, 31, 33, 35, and 36.5 MPa, respectively.

Plan 4
P1, P2 and α in the numerical model were invariant in Plan 4, which were set as follows: P1 = 36 MPa, P2 = 20 MPa, α = 50°. The lithology of coal seam was consistent with No. I, II, and III coal in Table 1. The plastic zone distribution characteristic ahead of the gateroad was studied in Plan 3 when the minimum principal stress P3 was 15, 13, 12, 11, 10, and 9.8 MPa, respectively.

Influence of α (Angle between the P1 Direction and the Z-Axis)
The results from Plan 1 are shown in Figure 3. It shows that the plastic zone is mainly located ahead of the road when α is 0°, which has a relatively small area, and the plastic zone has no butterflyshaped characteristics. The plastic zone volume is 302 m 3 when the α is 15°. It is primarily distributed in the upper-front part of the gateroad. The shape of plastic zone is like a butterfly wing when α is 30° and 45°, and the volume of plastic zone is 972 m 3 and 1476 m 3 , respectively. It should be noted that the butterfly wing morphology in the plastic zone is relatively complete. Afterwards, the butterfly wing in the plastic zone gradually disappears. When α is 60°, the plastic zone shape is unchanged. However, the volume of plastic zone decreases. The magnitude is 720 m 3 . Similarly, the plastic zone volume decreases significantly when α is 75°. It drops to 308 m 3 , and the plastic zone is mainly distributed at the bottom of the gateroad. Overall, the morphological characteristics of the butterfly wing in the plastic zone are gradually obvious when α ranges from 0° to 45°, and the morphological distribution of butterfly wing is disappeared when the α ranges from 45° to 90°. The plastic zone volume increases first and then decreases with the increase of α. That is, the plastic zone volume fits the normal distribution. The maximum volume of plastic zone is obtained when α is 45°. In this situation, the butterfly wingshaped plastic zone is deflected into the coal seam. That is, the direction of butterfly-shaped plastic zone ahead of gateroad is rotating with the evolution of α. When the butterfly-shaped plastic zone is in the same direction with the coal seam, the most complete shape and volume of the plastic zone are obtained.

Influence of P1/P3 (Ratio of Maximum Principal Stress to Minimum Principal Stress)
The relationship of plastic zone volume and P1/P3 are shown in Figures 4 and 5, which are obtained from the numerical calculation results in Plan 2.   Overall, the morphological characteristics of the butterfly wing in the plastic zone are gradually obvious when α ranges from 0 • to 45 • , and the morphological distribution of butterfly wing is disappeared when the α ranges from 45 • to 90 • . The plastic zone volume increases first and then decreases with the increase of α. That is, the plastic zone volume fits the normal distribution. The maximum volume of plastic zone is obtained when α is 45 • . In this situation, the butterfly wing-shaped plastic zone is deflected into the coal seam. That is, the direction of butterfly-shaped plastic zone ahead of gateroad is rotating with the evolution of α. When the butterfly-shaped plastic zone is in the same direction with the coal seam, the most complete shape and volume of the plastic zone are obtained.

Influence of P 1 /P 3 (Ratio of Maximum Principal Stress to Minimum Principal Stress)
The relationship of plastic zone volume and P 1 /P 3 are shown in Figures 4 and 5, which are obtained from the numerical calculation results in Plan 2. Overall, the morphological characteristics of the butterfly wing in the plastic zone are gradually obvious when α ranges from 0° to 45°, and the morphological distribution of butterfly wing is disappeared when the α ranges from 45° to 90°. The plastic zone volume increases first and then decreases with the increase of α. That is, the plastic zone volume fits the normal distribution. The maximum volume of plastic zone is obtained when α is 45°. In this situation, the butterfly wingshaped plastic zone is deflected into the coal seam. That is, the direction of butterfly-shaped plastic zone ahead of gateroad is rotating with the evolution of α. When the butterfly-shaped plastic zone is in the same direction with the coal seam, the most complete shape and volume of the plastic zone are obtained.

Influence of P1/P3 (Ratio of Maximum Principal Stress to Minimum Principal Stress)
The relationship of plastic zone volume and P1/P3 are shown in Figures 4 and 5, which are obtained from the numerical calculation results in Plan 2.   (1). When the magnitude of P1/P3 ranges from 1 to 3, the plastic zone volume ahead of gateroad increases linearly. The growth slope is approximately the same when P1/P3 is 1, 1.5, and 2. In these situations, the plastic zone volume is almost the same if P1 is constant. The shape of plastic zone in Figure 5 corroborates the above explanation. As shown in Figure 5a-c, the plastic zone volume is 68 m 3 , 59 m 3 , and 71 m 3 when the P1/P3 is 1, 1.5, and 2. (2). The growth slope increases when P1/P3 is 2.5 and 3. In these situations, significant differences of plastic zone volume are observed when P1 is constant. The larger the value of P1/P3, the larger the plastic zone volume. In Figure 4, the plastic zone volume is 116 m 3 and 232 m 3 when the P1/P3 is 2.5 and 3, which is also shown as Figure 5d,e. (3). When the magnitude of P1/P3 is 3.5, the plastic zone volume ahead of gateroad presents approximately exponential growth along with the increasing of maximum principal stress. The magnitude reaches to 1878 m 3 when the P1 equals to 44 MPa. Shown as Figure 5f, the distribution range of plastic zone is obviously increased ahead of gateroad. It should be noted that the dashed line in the Figure 4 refers to the critical value of maximum principal stress (P1) when the P1/P3 is 3.5. When the green line going asymptotically upwards to the dashed line, the plastic zone volume increases rapidly along with the growth of P1. Ultimately, it increases to infinity when the critical value of P1 is obtained. (1). When the magnitude of P 1 /P 3 ranges from 1 to 3, the plastic zone volume ahead of gateroad increases linearly. The growth slope is approximately the same when P 1 /P 3 is 1, 1.5, and 2. In these situations, the plastic zone volume is almost the same if P 1 is constant. The shape of plastic zone in Figure 5 corroborates the above explanation. As shown in Figure 5a-c, the plastic zone volume is 68 m 3 , 59 m 3 , and 71 m 3 when the P 1 /P 3 is 1, 1.5, and 2. (2). The growth slope increases when P 1 /P 3 is 2.5 and 3. In these situations, significant differences of plastic zone volume are observed when P 1 is constant. The larger the value of P 1 /P 3 , the larger the plastic zone volume. In Figure 4, the plastic zone volume is 116 m 3 and 232 m 3 when the P 1 /P 3 is 2.5 and 3, which is also shown as Figure 5d,e. (3). When the magnitude of P 1 /P 3 is 3.5, the plastic zone volume ahead of gateroad presents approximately exponential growth along with the increasing of maximum principal stress. The magnitude reaches to 1878 m 3 when the P 1 equals to 44 MPa. Shown as Figure 5f, the distribution range of plastic zone is obviously increased ahead of gateroad. It should be noted that the dashed line in the Figure 4 refers to the critical value of maximum principal stress (P 1 ) when the P 1 /P 3 is 3.5. When the green line going asymptotically upwards to the dashed line, the plastic zone volume increases rapidly along with the growth of P 1 . Ultimately, it increases to infinity when the critical value of P 1 is obtained.

Influence of P 1 (Maximum Principal Stress)
The distribution range and shape of plastic zone in Plan 3 are shown in Figure 6, in which the physical and mechanical parameters of coal seam are the same as those of No. II coal in Table 1. In this situation, the volume of plastic zone ahead of the gateroad increases with the growth of maximum principal stress. When P 1 is 25 MP, 35 MP, and 36.5 MPa, P 2 = 20 MPa, P 3 = 10 MPa, α = 50 • , the volumes of plastic zone ahead of the gateroad are 55 m 3 , 272 m 3 and 1439 m 3 , respectively. It should be noted that the shape of plastic zone in these situations evolves like a flat ball.

Influence of P1 (Maximum Principal Stress)
The distribution range and shape of plastic zone in Plan 3 are shown in Figure 6, in which the physical and mechanical parameters of coal seam are the same as those of No. II coal in Table 1 Table 1. Apparently, the curves at different situations show a similar evolution trend. With the increase of P1, the exponential growth of plastic zone volume is presented approximately. The plastic zone volume approaches infinity when the critical value of maximum principal stress ([P1]) is obtained. It also indicated that the critical value of P1 is increasing with the growth of coal mass strength.   Table 1. Apparently, the curves at different situations show a similar evolution trend. With the increase of P 1 , the exponential growth of plastic zone volume is presented approximately. The plastic zone volume approaches infinity when the critical value of maximum principal stress ([P 1 ]) is obtained. It also indicated that the critical value of P 1 is increasing with the growth of coal mass strength.

Influence of P3 (Minimum Principal Stress)
The numerical modelling results in Plan 4 are presented in Figure 8. Evolution of plastic zone with the change of minimum principal stress is studied. Please recall that In Plan 4 the physical and mechanical parameters of coal seam follow those of No. II coal in Table 1

Influence of P 3 (Minimum Principal Stress)
The numerical modelling results in Plan 4 are presented in Figure 8. Evolution of plastic zone with the change of minimum principal stress is studied. Please recall that In Plan 4 the physical and mechanical parameters of coal seam follow those of No. II coal in Table 1

Influence of P3 (Minimum Principal Stress)
The numerical modelling results in Plan 4 are presented in Figure 8. Evolution of plastic zone with the change of minimum principal stress is studied. Please recall that In Plan 4 the physical and mechanical parameters of coal seam follow those of No. II coal in Table 1 The relationship between the volume of plastic zone and the minimum principal stress is shown in Figure 9. The physical and mechanical parameters of coal seam are those of No. I, No. II, and No. III coal in Table 1. Overall, the three curves with different parameters of coal demonstrate a similar evolution trend. With the decrease of P3, an approximately exponential growth of plastic zone volume is observed. Moreover, a corresponding critical value of P3 can be spotted when the strength of coal mass is different. The volume of plastic zone approaches positive infinity when the critical value [P3] is obtained. Meanwhile, the critical value of P3 is at its minimum in situation III, while the maximum value has appeared in situation I. That is, the following expression is met in the three situations: [P3]I > [P3]II > [P3]III. It is also indicated that the critical value of P3 decreases with the increase of coal mass strength.

Rotation of Butterfly-Shaped Plastic Zone's Direction ahead of the Gateroad
The numerical model shown in Figure 1 is extended to 200 m in the Y-axis direction, and gateroad A is designed along the X-axis direction as shown in Figure 10. In order to reduce the mutual mining-induced influences, gateroad A is 120 m away from the tunnel face. In this situation, the initial stress field of gateroad A is regarded to be the same as that of pre-mining situation. The relationship between the volume of plastic zone and the minimum principal stress is shown in Figure 9. The physical and mechanical parameters of coal seam are those of No. I, No. II, and No. III coal in Table 1. Overall, the three curves with different parameters of coal demonstrate a similar evolution trend. With the decrease of P 3 , an approximately exponential growth of plastic zone volume is observed. Moreover, a corresponding critical value of P 3 can be spotted when the strength of coal mass is different. The volume of plastic zone approaches positive infinity when the critical value [P 3 ] is obtained. Meanwhile, the critical value of P 3 is at its minimum in situation III, while the maximum value has appeared in situation I. That is, the following expression is met in the three situations: It is also indicated that the critical value of P 3 decreases with the increase of coal mass strength. The relationship between the volume of plastic zone and the minimum principal stress is shown in Figure 9. The physical and mechanical parameters of coal seam are those of No. I, No. II, and No. III coal in Table 1. Overall, the three curves with different parameters of coal demonstrate a similar evolution trend. With the decrease of P3, an approximately exponential growth of plastic zone volume is observed. Moreover, a corresponding critical value of P3 can be spotted when the strength of coal mass is different. The volume of plastic zone approaches positive infinity when the critical value [P3] is obtained. Meanwhile, the critical value of P3 is at its minimum in situation III, while the maximum value has appeared in situation I. That is, the following expression is met in the three situations: [P3]I > [P3]II > [P3]III. It is also indicated that the critical value of P3 decreases with the increase of coal mass strength.

Rotation of Butterfly-Shaped Plastic Zone's Direction ahead of the Gateroad
The numerical model shown in Figure 1 is extended to 200 m in the Y-axis direction, and gateroad A is designed along the X-axis direction as shown in Figure 10. In order to reduce the mutual mining-induced influences, gateroad A is 120 m away from the tunnel face. In this situation, the initial stress field of gateroad A is regarded to be the same as that of pre-mining situation.

Rotation of Butterfly-Shaped Plastic Zone's Direction ahead of the Gateroad
The numerical model shown in Figure 1 is extended to 200 m in the Y-axis direction, and gateroad A is designed along the X-axis direction as shown in Figure 10. In order to reduce the mutual mining-induced influences, gateroad A is 120 m away from the tunnel face. In this situation, the initial stress field of gateroad A is regarded to be the same as that of pre-mining situation. According to the numerical results in Plan 1, the plastic zone around gateroad A is shown in Figure 11a when the α is 0°. Apparently, the shape of plastic zone around gateroad A is like a butterfly. Moreover, the butterfly wings are located near the bisector of the angle between the maximum and minimum principal stress. Due to the competence of roof and floor strata, the size of butterfly wing is relatively small in these areas.
As shown in Figure 11b, when α is 45°, the butterfly wings are mainly within the coal seam. In this situation, the size of butterfly wing is relatively large due to the lower strength of coal seam.
For the gateroad, the distribution characteristics of plastic zone are the same as that in Figure 3. When α is 45°, there is a butterfly-shaped plastic zone around the gateroad. Only one butterfly wing is observed, which is similar with that in Figure 11b. It is also located near the bisector of the angle between the maximum and minimum principal stress. Due to the spatial effect of the gateroad, the butterfly wing's shape is like a flat ball. Learned from Figure 3, the butterfly-shaped plastic zone around the gateroad evolves with the rotation of principal stress' direction. That is, the direction of butterfly-shaped plastic zone around the gateroad is also rotating.

Mutagenicity of Butterfly-Shaped Plastic Zone ahead of the Gateroad
For a homogeneous circular gateroad, the expansion of butterfly-shaped plastic zone is determined by the size and ratio of principal stress (P1/P3) when the surrounding rock conditions are According to the numerical results in Plan 1, the plastic zone around gateroad A is shown in Figure 11a when the α is 0 • . Apparently, the shape of plastic zone around gateroad A is like a butterfly. Moreover, the butterfly wings are located near the bisector of the angle between the maximum and minimum principal stress. Due to the competence of roof and floor strata, the size of butterfly wing is relatively small in these areas. According to the numerical results in Plan 1, the plastic zone around gateroad A is shown in Figure 11a when the α is 0°. Apparently, the shape of plastic zone around gateroad A is like a butterfly. Moreover, the butterfly wings are located near the bisector of the angle between the maximum and minimum principal stress. Due to the competence of roof and floor strata, the size of butterfly wing is relatively small in these areas.
As shown in Figure 11b, when α is 45°, the butterfly wings are mainly within the coal seam. In this situation, the size of butterfly wing is relatively large due to the lower strength of coal seam.
For the gateroad, the distribution characteristics of plastic zone are the same as that in Figure 3. When α is 45°, there is a butterfly-shaped plastic zone around the gateroad. Only one butterfly wing is observed, which is similar with that in Figure 11b. It is also located near the bisector of the angle between the maximum and minimum principal stress. Due to the spatial effect of the gateroad, the butterfly wing's shape is like a flat ball. Learned from Figure 3, the butterfly-shaped plastic zone around the gateroad evolves with the rotation of principal stress' direction. That is, the direction of butterfly-shaped plastic zone around the gateroad is also rotating.

Mutagenicity of Butterfly-Shaped Plastic Zone ahead of the Gateroad
For a homogeneous circular gateroad, the expansion of butterfly-shaped plastic zone is determined by the size and ratio of principal stress (P1/P3) when the surrounding rock conditions are As shown in Figure 11b, when α is 45 • , the butterfly wings are mainly within the coal seam. In this situation, the size of butterfly wing is relatively large due to the lower strength of coal seam.
For the gateroad, the distribution characteristics of plastic zone are the same as that in Figure 3. When α is 45 • , there is a butterfly-shaped plastic zone around the gateroad. Only one butterfly wing is observed, which is similar with that in Figure 11b. It is also located near the bisector of the angle between the maximum and minimum principal stress. Due to the spatial effect of the gateroad, the butterfly wing's shape is like a flat ball. Learned from Figure 3, the butterfly-shaped plastic zone around the gateroad evolves with the rotation of principal stress' direction. That is, the direction of butterfly-shaped plastic zone around the gateroad is also rotating.

Mutagenicity of Butterfly-Shaped Plastic Zone ahead of the Gateroad
For a homogeneous circular gateroad, the expansion of butterfly-shaped plastic zone is determined by the size and ratio of principal stress (P 1 /P 3 ) when the surrounding rock conditions are constant. Moreover, the mutagenicity is presented for the butterfly-shaped plastic zone. When the principal stress is close to certain critical stress value, the butterfly wing plastic zone is very sensitive to the change of the principal stress. A small change of principal stress may cause a sudden mutation of the butterfly wing's size of the plastic zone. That is, a large extension has appeared for the butterfly-shaped plastic zone.
According to the numerical results of Figure 4, the plastic zone volume ahead of excavation face increases gradually with the increase of P 1 /P 3 under certain surrounding rock and stress conditions, and the morphology of plastic zone becomes a flat-ball butterfly wing. In other words, the expansion of butterfly-shaped plastic zone is determined by the magnitude and direction of principal stress and the ratio of maximum principal stress to minimum principal stress (P 1 /P 3 ). Figure 5 also shows that: when P 1 /P 3 is smaller, there is no sharp change for the plastic zone even if P 1 is increased to 100 MPa, which is extremely rare in current underground coal mining. Moreover, the butterfly-shaped plastic zone of coal and rock mass ahead of the excavation face will be extremely sensitive to the change of principal stress when the value of principal stress is close to a certain critical stress. That is, the mutagenicity of butterfly-shaped plastic zone occurs ahead of the gateroad under a certain stress condition.

Expansion of Butterfly-Shaped Plastic Zone ahead of the Gateroad
According to the numerical results mentioned in 4.3 and 4.4, the butterfly-shaped plastic zone volume is growing gradually with the increase of maximum principal stress and the decreasing of minimum principal stress. For the specific coal mass, the corresponding critical value of [P 1 ] and [P 3 ] have existed for the maximum principal stress and the minimum principal stress. In this situation, the plastic zone volume approaches positive infinity. In other words, the infinite expansion of the butterfly-shaped plastic zone occurs.

Implications for Coal and Gas Outburst Induced by the Expansion Plastic Zone ahead of Gateroad
Based on the mutagenicity of butterfly-shaped plastic zone, the rapid expansion mechanical mechanism of plastic zone around the excavation gateway is studied. Combined with the field physical rockburst phenomena in the gateroad, the mechanism of butterfly-shaped rock burst in the roadway are revealed. According to the evolution law of plastic zone of coal and rock mass ahead of gateroad, the expansion analysis model of plastic zone ahead of gateroad was established, which is shown in Figure 12. The initial plastic zone means the areas appeared under the static stress in the coal and rock mass around the gateroad. The dynamic stress may be the slight disturbances causing small changes in the rock stress field. It may also be the strong disturbances leading to the large changes of stress field magnitude and direction, such as earthquakes, fault activation, roof fracture, abutment pressure, and excavation activities. When the regional static stress field of gateroad is disturbed by the outside dynamic stress, the stress field will adjust to a new balanced state. As a result, the initial plastic zone will expand and evolve into a transient plastic zone.
shown in Figure 12. The initial plastic zone means the areas appeared under the static stress in the coal and rock mass around the gateroad. The dynamic stress may be the slight disturbances causing small changes in the rock stress field. It may also be the strong disturbances leading to the large changes of stress field magnitude and direction, such as earthquakes, fault activation, roof fracture, abutment pressure, and excavation activities. When the regional static stress field of gateroad is disturbed by the outside dynamic stress, the stress field will adjust to a new balanced state. As a result, the initial plastic zone will expand and evolve into a transient plastic zone.  During the mining process, there may be large differences in the regional principal stress field and the disturbance stress source of the load of gateroad at different positions and excavation periods. In order to make an illustration, a typical example obtained from the results of Figure 6 is listed to analyze the plastic zone expansion process of coal and rock mass around, which is based on a mechanical model.
The initial state of static stress field of the gateroad is: P 1 = 35 MPa, P 2 = 20 MPa, P 3 = 10 MPa, α = 50 • . At the same time, the initial plastic zone volume is 272 m 3 ahead of the gateroad. If the regional maximum principal stress increases to 1.5 MPa, the transient plastic zone will be formed, which is caused by the external dynamic disturbance. The new volume is 1439 m 3 , that is, the plastic zone volume increases by 1167 m 3 in the evolution process ( Figure 13). During the mining process, there may be large differences in the regional principal stress field and the disturbance stress source of the load of gateroad at different positions and excavation periods. In order to make an illustration, a typical example obtained from the results of Figure 6 is listed to analyze the plastic zone expansion process of coal and rock mass around, which is based on a mechanical model.
The initial state of static stress field of the gateroad is: P1 = 35 MPa, P2 = 20 MPa, P3 = 10 MPa, α = 50°. At the same time, the initial plastic zone volume is 272 m 3 ahead of the gateroad. If the regional maximum principal stress increases to 1.5 MPa, the transient plastic zone will be formed, which is caused by the external dynamic disturbance. The new volume is 1439 m 3 , that is, the plastic zone volume increases by 1167 m 3 in the evolution process ( Figure 13). The coal and rock bursts occur along with the sudden failure of coal-rock mass and the quick release of methane, which includes the gas-bearing coal and rock mass deformation and destruction of, as well as the energy conversion and release. Based on the expansion plastic zone of coal and rock mass ahead of the gateroad, the occurrence process of coal and gas outburst is described as follows: when the plastic zone ahead of gateroad expands instantaneously under the outside dynamic stress, several longitudinal fractures will appear in the plastic zone of coal and rock mass. In more serious situations, the coal and rock mass ahead of the gateroad will be fractured or fragmented. Then, the adsorbed methane will be desorbed within a very short period and the free methane will be quickly accumulated. Consequently, a methane pack will be generated quickly in the plastic zone of coal and rock mass ahead of the gateroad. It should be noted that: the released elastic energy in the failure process of coal and rock and the accumulated gas in the methane pack increases with the volume of the new-born plastic zone. When the released total energy is large enough, the coal and gas outburst will be induced.
Above all, the sudden new-born plastic zone is the key prerequisite for the occurrence of coal and gas outburst, which provides the inducing conditions for the outburst disaster. When the gas parameter is constant, the larger the volume of the new-born plastic zone, the more energy will be released in a short period of time, and the higher the outburst risk. Therefore, the critical stress state of the butterfly-shaped plastic zone's mutagenicity ahead of the gateroad can be used as an important indicator for assessment of the coal and gas outburst risk. The coal and rock bursts occur along with the sudden failure of coal-rock mass and the quick release of methane, which includes the gas-bearing coal and rock mass deformation and destruction of, as well as the energy conversion and release. Based on the expansion plastic zone of coal and rock mass ahead of the gateroad, the occurrence process of coal and gas outburst is described as follows: when the plastic zone ahead of gateroad expands instantaneously under the outside dynamic stress, several longitudinal fractures will appear in the plastic zone of coal and rock mass. In more serious situations, the coal and rock mass ahead of the gateroad will be fractured or fragmented. Then, the adsorbed methane will be desorbed within a very short period and the free methane will be quickly accumulated. Consequently, a methane pack will be generated quickly in the plastic zone of coal and rock mass ahead of the gateroad. It should be noted that: the released elastic energy in the failure process of coal and rock and the accumulated gas in the methane pack increases with the volume of the new-born plastic zone. When the released total energy is large enough, the coal and gas outburst will be induced.

Conclusions
Above all, the sudden new-born plastic zone is the key prerequisite for the occurrence of coal and gas outburst, which provides the inducing conditions for the outburst disaster. When the gas parameter is constant, the larger the volume of the new-born plastic zone, the more energy will be released in a short period of time, and the higher the outburst risk. Therefore, the critical stress state of the butterfly-shaped plastic zone's mutagenicity ahead of the gateroad can be used as an important indicator for assessment of the coal and gas outburst risk.

Conclusions
The paper presents a study of influence of principal stress field including the maximum principal stress (P 1 ), the angle between the P 1 direction and the Z-axis (α), the minimum principal stress (P 3 ), and the ratio of maximum principal stress to minimum principal stress (P 1 /P 3 ) on the expansion of plastic zone ahead of the gateroad. The following conclusions are obtained: (1). The shape and range of plastic zone ahead of gateroad are determined by the maximum principal stress (P 1 ) and the angle between the P 1 direction and the Z-axis (α). It is also related closely to the minimum principal stress (P 3 ) and the ratio of maximum principal stress to minimum principal stress (P 1 /P 3 ). Under a certain stress state, a spheroid butterfly-shaped plastic zone will appear in the coal-rock mass ahead of the gateroad, which has a shape of more or less a flat-ball. (2). The plastic zone volume increases first and then decreases with the increase of α, and the direction of butterfly-shaped plastic zone ahead of gateroad is rotating with the evolution of α. (3). The plastic zone volume ahead of excavation face increases gradually with the increase of P 1 /P 3 .
The mutagenicity of butterfly-shaped plastic zone is presented ahead of the gateroad under a certain value of P 1 /P 3 . (4). With the increase of P 1 and decreasing of P 3 , the plastic zone volume is of exponential growth.
The plastic zone volume approaches infinity when the critical value of maximum principal stress ([P 1 ]) and the minimum principal stress ([P 1 ]) is obtained. (5). The study of the effect of principal stress field on the expansion of plastic zone ahead of the gateroad is helpful for revealing the mechanisms of coal and gas outbursts. The critical stress state of butterfly-shaped plastic zone's mutagenicity ahead of the gateroad can be used as an important indicator for assessing the risk of coal and gas outburst.
It should be noted that the numerical modelling is one of the alternative methods to investigate the effect of principal stress field on the expansion of plastic zone ahead of the gateroad. FLAC 3D is mainly used to analyze the stress distribution and plastic zone evolution of continuous medium. The discontinuous numerical modelling, the similar material simulation and the in-situ monitoring should be further investigated to supplement and compensate the above conclusions in the future research.