Effect of Principal Stress Field on the Development of Plastic Zone ahead of the Gateroad
Abstract
:1. Introduction
2. Numerical Model Setup
3. Modelling Plans
3.1. Plan 1
3.2. Plan 2
3.3. Plan 3
3.4. Plan 4
4. Numerical Modelling Results
4.1. Influence of α (Angle between the P1 Direction and the Z-Axis)
4.2. Influence of P1/P3 (Ratio of Maximum Principal Stress to Minimum Principal Stress)
- (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 m3, 59 m3, and 71 m3 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 m3 and 232 m3 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 m3 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.
4.3. Influence of P1 (Maximum Principal Stress)
4.4. Influence of P3 (Minimum Principal Stress)
5. Discussion
5.1. Rotation of Butterfly-Shaped Plastic Zone’s Direction ahead of the Gateroad
5.2. Mutagenicity of Butterfly-Shaped Plastic Zone ahead of the Gateroad
5.3. Expansion of Butterfly-Shaped Plastic Zone ahead of the Gateroad
5.4. Implications for Coal and Gas Outburst Induced by the Expansion Plastic Zone ahead of Gateroad
6. Conclusions
- (1).
- The shape and range of plastic zone ahead of gateroad are determined by the maximum principal stress (P1) and the angle between the P1 direction and the Z-axis (α). It is also related closely to the minimum principal stress (P3) and the ratio of maximum principal stress to minimum principal stress (P1/P3). 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 P1/P3. The mutagenicity of butterfly-shaped plastic zone is presented ahead of the gateroad under a certain value of P1/P3.
- (4).
- With the increase of P1 and decreasing of P3, the plastic zone volume is of exponential growth. The plastic zone volume approaches infinity when the critical value of maximum principal stress ([P1]) and the minimum principal stress ([P1]) 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.
Author Contributions
Funding
Conflicts of Interest
References
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Lithology | Thickness/m | Friction Angle/(°) | Cohesion/MPa | Density/(kg/m3) | Shear Modulus/GPa | Bulk Modulus/GPa | |
---|---|---|---|---|---|---|---|
Roof | 23 | 38 | 6 | 2600 | 8.0 | 8.2 | |
Ⅰ | 4 | 25 | 1.0 | 1050 | 4.7 | 5.2 | |
Coal | Ⅱ | 4 | 30 | 2 | 1100 | 4.9 | 5.7 |
Ⅲ | 4 | 35 | 3 | 1300 | 5.2 | 6.1 | |
Floor | 23 | 40 | 6.5 | 2700 | 8.0 | 8.5 |
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Liu, H.; Guo, L.; Zhao, X.; Wang, P. Effect of Principal Stress Field on the Development of Plastic Zone ahead of the Gateroad. Energies 2020, 13, 4356. https://doi.org/10.3390/en13174356
Liu H, Guo L, Zhao X, Wang P. Effect of Principal Stress Field on the Development of Plastic Zone ahead of the Gateroad. Energies. 2020; 13(17):4356. https://doi.org/10.3390/en13174356
Chicago/Turabian StyleLiu, Hongtao, Linfeng Guo, Xidong Zhao, and Pengfei Wang. 2020. "Effect of Principal Stress Field on the Development of Plastic Zone ahead of the Gateroad" Energies 13, no. 17: 4356. https://doi.org/10.3390/en13174356