In this section, FLAC3D was used to analyze the influence of rock bolt parameters on 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, as 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 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 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 specimen was 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 was obtained, as shown Fig. 5 (b). The original elastic modulus of the experimental body is 26.2 GPa, the uniaxial compressive strength is 10.35 MPa, the cohesion is 3.08 MPa and the internal friction angle is 28.46°.
4.1 Influence of rock bolt spacing on mechanical properties of anchorage body
According to the rock bolt spacing designed in Table 1, other variables were controlled as rock bolt pre-tightening force of 40 kN, rock bolt diameter of 16 mm and rock bolt length of 2.2 m.
Repeat tests for each model: test uniaxial compressive strength first; Then, under the condition of 1, 2 MPa 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 were summarized to obtain influence curves of rock bolt spacing on the uniaxial compressive strength, shear strength, cohesion and internal friction angle of anchorage body, as shown in Fig. 6.
As shown in Fig. 6 (a), the uniaxial compressive strength and shear strength of anchorage body showed an increasing trend with the increase of rock bolt density. The uniaxial compressive strength of the 0.6 m spacing was 0.43 MPa higher than that of the 1.4 m spacing and 0.54 MPa higher than the original rock parameter. The shear strength of the 0.6 m spacing increased by 0.65 MPa compared with that of 1.4 m spacing, and 0.82 MPa 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 increased. The cohesion increase was not obvious, which was only 0.04 MPa when the spacing decrease from 1.4 m to 0.6 m. The internal friction angle of the 0.6 m spacing was 1.4° higher than that of the 1.4 m spacing and 1.83° higher than the original rock parameter.
In summary, effects of the rock bolt spacing on uniaxial compressive strength σ, internal friction angle φ, cohesion c and shear strength τ all increased with increasing support density, but the increase rate decreased after 0.8 m. Each mechanical parameter had the largest increment between 0.8 m and 1.2 m, and subsequent studies control the rock bolt spacing to 0.8 m.
4.2 Influence of rock bolt pre-tightening force on mechanical properties of anchorage body
According to Table 1, the rock bolt pre-tightening force was designed as 40 kN, 60 kN, 80 kN, 100 kN and 120 kN. The rock bolt spacing was 0.8 m, and other variables were controlled as diameter of 16 mm and length of 2.2 m. The experimental results are shown in Fig. 7.
As shown in Fig. 7 (a), the uniaxial compressive strength and shear strength of anchorage body showed an increasing trend with the increase of rock bolt pre-tightening force. When the rock bolt pre-tightening force increased from 40 kN to 120 kN, the uniaxial compressive strength increased by 0.49 MPa, and finally increased by 0.98 MPa compared with the original rock parameter. The shear strength of 120 kN was 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 increased with the increase of rock bolt pre-tightening force. When the rock bolt pre-tightening force was 120 kN, the cohesion increment was the largest, which was 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 was significant. The internal friction angle with pre-tightening force of 120 kN was 0.82° more than that of the 40 kN, and had 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 increased gradually. Considering that the increase rate decreased rapidly when pre-tightening force reached 80 kN, the rock bolt pre-tightening force is taken as 80 kN.
4.3 Influence of rock bolt diameter on mechanical properties of anchorage body
According to Table 1, the rock bolt diameter was selected as 16 mm, 18 mm, 20 mm, 22 mm and 24 mm. The rock bolt spacing was 0.8 m, the pre-tightening force was 80 kN and the length was 2.2 m. The experimental results are shown in Fig. 8.
As shown in Fig. 8 (a), the uniaxial compressive strength and shear strength of anchorage body increased with the increase of rock bolt diameter. When the anchor diameter reached 24 mm, the uniaxial compressive strength increased by 0.27 MPa compared with that of 16 mm, and increased 1.1 MPa compared with the original rock parameter. And the shear strength with rock bolt diameter of 24 mm increased by 0.4 MPa compared with that of 16 mm diameter, and increased by 1.54 MPa compared with that of the original.
As shown in Fig. 8 (b), the cohesion and internal friction angle of anchorage body also increased with the increase of rock bolt diameter. When the rock bolt diameter was 24 mm, the cohesion was 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 24 mm was 0.78° higher than that of 16 mm and 2.96° higher than that of the original.
Comprehensive analysis shows that when the rock bolt diameter reached 22 mm, the increment of mechanical properties was large, but the increase rate slowed down when rock bolt diameter exceeded 22 mm. Therefore, the rock bolt diameter is taken as 22 mm.
4.4 Influence of rock bolt length on mechanical properties of anchorage body
According to Table 1, the design rock bolt length was 2.2 m, 2.4 m, 2.6 m, 2.8 m and 3.0 m respectively. The rock bolt spacing was 0.8 m, the pre-tightening force was 80 kN and the diameter was 22 mm. The experimental results are shown in Fig. 9.
As shown in Fig. 9 (a), when the rock bolt length increased from 2.2 m to 3.0 m, the uniaxial compressive strength and shear strength of anchorage body showed an increasing trend. The uniaxial compression strength of 3.0 m rock bolt length increased 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 increased 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 increased. When the rock bolt length was 3.0 m, the cohesion and internal friction angle was respectively 0.048 MPa and 0.86° larger than that of 2.2 m, which was 0.168 MPa and 3.77° larger than original rock parameters.
According to the comprehensive analysis of Fig. 9, the rock bolt length was positively related to all parameters, while the length of 2.4 m was the inflection point. When the rock bolt length reached 2.4 m, the growth rate of mechanical parameters started to increase rapidly. In order to get the most efficient increment, the rock bolt length is taken as 3.0 m.
4.5 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 mechanical parameters of anchorage body were studied respectively, and the reasonable values of rock bolt support parameters are determined as rock bolt spacing of 0.8 m, rock bolt pre-tightening force of 80 kN, rock bolt diameter of 22 mm and 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, shear strength of 10.67 MPa, cohesion of 3.24 MPa and internal friction angle of 32.2°. The above parameters are respectively increased by 1.42 MPa, 1.98 MPa, 0.168 MPa, 3.77 °compared with 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 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.