In this section, FLAC3D was used to analyze the influence of rock bolt parameters on the mechanical properties of anchorage body. Therefore, it is necessary to adopt the control variable method. The related parameters of the rock bolt are mainly the spacing, pre-tightening force, length and diameter. Experimental parameters are shown in Table 1.
Table 1 Experimental parameters of rock bolt
Rock bolt parameter
|
Value
|
Spacing (m)
|
0.6
|
0.8
|
1.0
|
1.2
|
1.4
|
Pre-tightening force (kN)
|
40
|
60
|
80
|
100
|
120
|
Length (m)
|
2.2
|
2.4
|
2.6
|
2.8
|
3.0
|
Diameter (mm)
|
16
|
18
|
20
|
22
|
24
|
This experiment was based on the original mechanical parameters of 3# coal seam in the second mining area of Xinjulong coal mine, as shown in Table 2. FLAC3D software was used for modeling, which is calculated by Mohr-Coulomb failure criterion. The size of the model was 3.5m(length) × 3.0m (width)× 3.5m (height), which were divided into 36,750 cells and 40,176 nodes, as shown in Fig.4.
Table 2 Rock mechanics parameters of 3# coal seam in Xinjulong Coal Mine
Uniaxial
compressive strength
(MPa)
|
Uniaxial
tensile strength
(MPa)
|
Elastic Modulus
(GPa)
|
Poisson ratio
|
Cohesion
(MPa)
|
Internal friction angle
(°)
|
10.40
|
0.51
|
26.28
|
0.29
|
3.1
|
28.5
|
Because the compressing speed of the compression member during the compression test will have a certain effect on the final stress-strain result, in order to fit the original parameters, the numerical simulation of the specimen with different loading speed by FLAC3D was carried out many times. In the process of numerical simulation, the test specimens were subjected to three mechanical tests of uniaxial compression, 1MPa confining pressure and 2MPa confining pressure, as shown in Fig.5 (a), and the corresponding Mohr-Coulomb stress circle were obtained, as shown Fig.5 (b). The original elastic modulus of the experimental body is 26.2GPa, the uniaxial compressive strength is 10.35MPa, the cohesion is 3.08MPa and the internal friction angle is 28.46°.
3.1 Influence of rock bolt spacing on mechanical properties of anchorage body
According to the rock bolt spacing designed in table 1, other variables are controlled as rock bolt pre-tightening force of 40kN, rock bolt diameter of 16 mm and rock bolt length of 2.2m.
Repeat tests for each model: test uniaxial compressive strength first; Then, under the condition of 1, 2Mpa confining pressure, the compressive strength experiment was conducted to get the cohesion and internal friction angle. The shear strength of anchorage body was calculated from the above data. The experimental results are summarized to obtain the influence curves of rock bolt spacing on the uniaxial compressive strength, shear strength, cohesion and internal friction angle and of anchorage body, as shown in Fig.6.
As shown in Fig.6 (a), the uniaxial compressive strength and the shear strength of anchorage body shows an increasing trend with the increase of rock bolt density. The uniaxial compressive strength of the 0.6m spacing is 0.43MPa higher than that of the 1.4m spacing and 0.54MPa higher than the original rock parameter. The shear strength of the 0.6m spacing increases by 0.65MPa compared with that of 1.4m spacing, and 0.82MPa compared with the original rock parameter.
As shown in Fig.6 (b), with the decrease of rock bolt spacing, the cohesion and internal friction angle of anchorage body increase. The cohesion increase is not obvious, which is only 0.04MPa when the spacing decrease from 1.4m to 0.6m. The internal friction angle of the 0.6m spacing is 1.4° higher than that of the 1.4m spacing and 1.83° higher than the original rock parameter.
In summary, the effects of the rock bolt spacing on uniaxial compressive strength σ, internal friction angle φ, cohesion c and shear strength τ all increase with increasing support density, but the increase rate decreases after 0.8 m. Each mechanical parameter has the largest increment between 0.8 and 1.2 m, and subsequent studies control the rock bolt spacing to 0.8 m.
3.2 Influence of rock bolt pre-tightening force on mechanical properties of anchorage body
According to Table 1, the rock bolt pre-tightening force is designed as 40 kN, 60 kN, 80 kN, 100 kN and 120 kN. The rock bolt spacing is 0.8m, and other variables are controlled as rock bolt diameter of 16mm and rock bolt length of 2.2 m. The experimental results are shown in Fig.7.
As shown in Fig. 7 (a), the uniaxial compressive strength and the shear strength of anchorage body shows an increasing trend with the increase of rock bolt pre-tightening force. When the rock bolt pre-tightening force increases from 40 kN to 120 kN, the uniaxial compressive strength increases by 0.49 MPa, and finally increases by 0.98 MPa compared with the original rock parameter. The shear strength of 120 kN is 0.6 MPa higher than that of 40 kN, and 1.36 MPa higher than the original rock parameter.
As shown in Fig.7 (b), the cohesion and internal friction angle of anchorage body also increase with the increase of rock bolt pre-tightening force. When the rock bolt pre-tightening force is 120 kN, the cohesion increment is the largest, which is 0.09 MPa higher than that of 40 kN, 0.131 MPa higher than that of the original. And the effect of rock bolt pre-tightening force on the internal friction angle is significant. The internal friction angle with pre-tightening force of 120 kN is 0.82° more than that of the 40 kN, and has an increase of 2.47° from the original rock parameter.
According to the comprehensive analysis of Fig.7, with the increase of rock bolt pre-tightening force, the uniaxial compressive strength σ, internal friction angle φ, cohesion c and shear strength τ increase gradually. Considering that the increase rate decreases rapidly when pre-tightening force reaches 80kN, the rock bolt pre-tightening force is taken as 80 kN.
3.3 Influence of rock bolt diameter on mechanical properties of anchorage body
According to Table 1, the rock bolt diameter is selected as 16 mm, 18 mm, 20 mm, 22 mm and 24 mm. The rock bolt spacing is 0.8m, the rock bolt pre-tightening force is 80 kN and the rock bolt length is 2.2 m. The experimental results are shown in Fig.8.
As shown in Figure 8 (a), the uniaxial compressive strength and the shear strength of anchorage body increase with the increase of rock bolt diameter. When the anchor diameter reaches 24 mm, the uniaxial compressive strength increases by 0.27 MPa compared with that of 16 mm, and increases 1.1 MPa compared with the original rock parameter. And the shear strength with rock bolt diameter of 24 mm increases by 0.4 MPa compared with that of 16 mm diameter, and increases by 1.54 MPa compared that of the original.
As shown in Fig. 8 (b), the cohesion and internal friction angle of anchorage body also increase with the increase of rock bolt diameter. When the rock bolt diameter is 24 mm, the cohesion is 0.026 MPa larger than that of 16 mm, 0.13 MPa larger than the original rock parameter. The internal friction angle with the diameter of 24mm is 0.78° higher than that of 16mm and 2.96° higher than that of the original.
Comprehensive analysis shows that when the rock bolt diameter reaches 22 mm, the mechanical properties increment is large, but the increase rate slows down when rock bolt diameter exceeds 22 mm. Therefore, the rock bolt diameter is taken as 22 mm.
3.4 Influence of rock bolt length on mechanical properties of anchorage body
According to table 1, the design rock bolt length is 2.2 m, 2.4 m, 2.6 m, 2.8 m and 3.0 m respectively. The rock bolt spacing is 0.8 m, the rock bolt pre-tightening force is 80 kN and the rock bolt diameter is 22 mm. The experimental results are shown in Fig. 9.
As shown in Fig.9 (a), when the anchor rock bolt length increases from 2.2m to 3.0m, the uniaxial compressive strength and the shear strength of anchorage body show an increasing trend. The uniaxial compression strength of 3.0 m rock bolt length increases by 0.34 MPa compared with that of 2.2 m, and 1.42 MPa compared with that of the original. And the shear strength of 3.0 m increases by 0.49 MPa compared with that of 2.2 m, and 1.98 MPa compared with the original rock parameter.
As shown in Fig. 9 (b), with the increase of rock bolt length, the cohesion and internal friction angle of anchorage body increase. When the rock bolt length is 3.0 m, the cohesion and the internal friction angle is respectively 0.048 MPa and 0.86° larger than that of 2.2 m, which is 0.168 MPa and 3.77°larger than original rock parameters.
According to the comprehensive analysis of Fig. 9, the rock bolt length is positively related to all parameters, while the length of 2.4m is the inflection point. When the rock bolt length reaches 2.4 m, the growth rate of mechanical parameters starts to increase rapidly. In order to get the most efficient increment, the rock bolt length is taken as 3.0 m.
3.5 Optimal support parameters of side rock bolts for air-return entry
In the above section, the influence of rock bolt spacing, pre-tightening force, diameter and length on the mechanical parameters of anchorage body are studied respectively, and the reasonable values of rock bolt support parameters are determined as the rock bolt spacing of 0.8m, the rock bolt pre-tightening force of 80 kN, the rock bolt diameter of 22 mm and the rock bolt length of 3.0 m. The mechanical properties of anchorage body in this support scheme are the uniaxial compressive strength of 11.78 MPa, the shear strength of 10.67 MPa, the internal friction angle of 1.98 MPa and the cohesion of 3.24 MPa. The above parameters are respectively increased by 1.42 MPa, 1.98 MPa, 3.77 °, 0.168 MPa compared with the original rock parameters.
By comparing the variation interval of mechanical properties caused by the variation of various parameters of the rock bolt, combining with the actual engineering situation, it is found that the rock bolt pre-tightening force and spacing have a great influence; the length and diameter of rock bolt have little effect on the mechanical properties of anchorage body. Therefore, in the actual production, the design of rock bolt support scheme should focus on the rock bolt spacing and pre-tightening force.