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Structural plane is a key factor in controlling the stability of rock mass engineering. To study the influence of structural plane microscopic parameters on direct shear strength, this paper established the direct shear mechanical model of the structural plane by using the discrete element code PFC2D. From the mesoscopic perspective, the research on the direct shear test for structural plane has been conducted. The bonding strength and friction coefficient of the structural plane are investigated, and the effect of mesoscopic parameters on the shear mechanical behavior of the structural plane has been analyzed. The results show that the internal friction angle

The large-scale existence of structural plane has severely damaged the continuity and integrity of rock mass, thereby exerting a profound influence on the strength of the rock mass. Structural plane is a key factor in controlling the stability of rock mass engineering [

Numerical simulation of the shear strength test is divided into two categories, namely, nonlimit and restrictive shear strength tests. The nonlimit shear strength test only has shear stress on the shear surface without the existence of normal stress. The restricted shear strength test has normal stress in addition to the shear stress on the shear plane [

The impact of particle contact stiffness ratio _{n}/_{s} on shear strength is shown in Table _{n}/_{s}. However, the change range of cohesion is small, indicating that particle contact stiffness ratio _{n}/_{s} has less effect on the cohesion.

Shear strength parameter values of different particle contact stiffness ratio.

Particle contact stiffness ratio | Friction angle (°) | Cohesion (MPa) |
---|---|---|

0.5 | 21.16 | 8.75 |

1 | 24.28 | 8.94 |

1.45 | 20.30 | 9.29 |

2 | 24.56 | 8.73 |

3 | 22.73 | 8.43 |

4 | 20.41 | 8.52 |

5 | 19.34 | 8.49 |

6 | 18.62 | 8.52 |

7 | 17.80 | 8.48 |

8 | 18.52 | 8.25 |

9 | 19.49 | 8.19 |

10 | 15.70 | 8.29 |

The effect of particle contact stiffness ratio on the internal friction angle is shown in Figure _{n}/_{s}. In the conventional triaxial compression simulation test, shear failure is the specimen failure mode, and the internal friction angle in the shear strength parameter is approximately the same as that obtained in the direct shear simulation test. However, in the direct shear simulation experiment, the particle contact stiffness ratio of _{n}/_{s} = 1.45 and _{n}/_{s} = 0.5, and the size differences between internal friction angle is extremely small, indicating if the normal stiffness is close to the tangential stiffness, then the friction angle will decrease. In the direct shear test, when the particle contact stiffness ratio increases gradually, the internal friction angle of the structure increases gradually. When the particle contact stiffness ratio of _{n}/_{s} = 2.0, the internal friction angle reaches the peak of the specimens, which is _{n}/_{s} = 1.0, the internal friction angle is also relatively large at _{n}/_{s} increases to a certain value. The particles during normal stiffness are larger than those during tangential stiffness. A small internal friction angle can enhance shear strength. However, the general trend means that the internal friction angle of the specimens decreases with the increase of the particle contact stiffness ratio. The influence of particle contact stiffness ratio on cohesion is analyzed, as shown in Figure _{n}/_{s}. Under the two test conditions, the cohesion of the specimen has the same change trend as that of _{n}/_{s}, and the influence of _{n}/_{s} on adhesion

Influence of particle contact stiffness on friction angle.

Influence of particle contact stiffness on cohesion.

Parallel bond stiffness ratio is a specific parameter in the simulation of parallel bonding model, which represents the ratio of the normal stiffness to the tangential stiffness between two particles. The shear strength parameter values of different parallel bond stiffness ratios are recorded, as shown in Table _{max} = 9.29 MPa is reached when the cohesion

Shear strength parameter values of different parallel bond stiffness ratios.

Parallel bond stiffness ratio | Friction angle (°) | Cohesion (MPa) |
---|---|---|

0.5 | 22.93 | 8.35 |

1 | 22.20 | 8.79 |

1.45 | 20.30 | 9.29 |

2 | 20.76 | 9.14 |

3 | 23.85 | 8.79 |

4 | 21.55 | 8.58 |

5 | 19.95 | 8.76 |

6 | 18.83 | 8.48 |

7 | 20.71 | 8.05 |

8 | 21.31 | 7.67 |

9 | 20.20 | 7.63 |

10 | 21.80 | 7.25 |

The influence of parallel bond stiffness on internal friction angle is analyzed, as shown in Figure

Influence of parallel bond stiffness on friction angle.

Influence of parallel bond stiffness on cohesion.

EC is the Young’s modulus between particles, and the shear strength parameter values under different particle contact moduli are recorded, as shown in Table _{C} ≤ 2.8 GPa, the change internal friction angle is significant, with a difference of 6.3°. The particle contact modulus, which strongly influences the internal friction angle, is relatively small. In actual simulation, EC should be adjusted constantly to match the actual internal friction angle. If EC is large, then the internal friction angle changes with it. The influence of EC on cohesion

Shear strength parameter values under different particle contact moduli.

Particle contact modulus (GPa) | Friction angle (°) | Cohesion (MPa) |
---|---|---|

1 | 19.80 | 8.33 |

1.5 | 26.10 | 8.37 |

2 | 25.17 | 7.66 |

2.5 | 24.23 | 9.01 |

2.8 | 20.30 | 9.29 |

3.5 | 27.02 | 8.67 |

4 | 27.92 | 7.50 |

4.5 | 29.25 | 8.04 |

5 | 30.54 | 8.06 |

6 | 24.7 | 9.24 |

7 | 30.11 | 8.56 |

The influence of EC on friction angle is shown in Figure

Influence of particle contact modulus on friction angle.

Influence of particle contact modulus on cohesion.

The elastic modulus

Shear strength parameters of different parallel bond elastic moduli.

Parallel bond elastic modulus (GPa) | Friction angle (°) | Cohesion (MPa) |
---|---|---|

1 | 24.84 | 9.71 |

1.5 | 22.20 | 9.56 |

2 | 20.66 | 9.51 |

2.5 | 21.90 | 9.10 |

2.8 | 20.30 | 9.29 |

3.5 | 20.46 | 9.04 |

4 | 20.46 | 8.89 |

4.5 | 19.54 | 8.87 |

5 | 18.42 | 8.92 |

6 | 19.40 | 8.63 |

7 | 19.44 | 8.60 |

The influence of the parallel bond elastic modulus on the internal friction angle is analyzed, as shown in Figure

The effect of parallel bond elastic modulus on friction angle.

Influence of parallel bond elastic modulus on cohesion.

According to the numerical simulation test and studies by other scholars, the size of a particle significantly influences the shear strength of the specimen [

Shear strength of different particle size specimens under normal stress.

Minimum particle size (mm) | Normal stress (MPa) | |||||
---|---|---|---|---|---|---|

2.5 | 5 | 7.5 | 10 | 12.5 | 15 | |

0.20 | 8.64 | 10.64 | 12.02 | 13.04 | 13.28 | 14.19 |

0.25 | 8.21 | 11.08 | 12.01 | 12.42 | 13.60 | 14.51 |

0.28 | 9.82 | 11.25 | 12.62 | 12.85 | 13.96 | 14.60 |

0.4 | 10.00 | 11.57 | 12.34 | 12.48 | 12.85 | 14.48 |

0.5 | 9.71 | 10.93 | 12.20 | 12.73 | 13.32 | 14.28 |

0.8 | 10.86 | 12.39 | 14.03 | 15.16 | 15.67 | 16.41 |

1.0 | 10.81 | 11.68 | 12.88 | 13.90 | 14.72 | 15.33 |

1.2 | 10.97 | 12.46 | 13.04 | 13.59 | 13.81 | 14.88 |

1.5 | 11.43 | 13.06 | 13.77 | 15.17 | 15.40 | 16.35 |

Table _{max} = 24.28° and _{min} = 15.43°, respectively.

Shear strength parameter values of different particle sizes.

Minimum particle size (mm) | Friction angle (°) | Cohesion (MPa) |
---|---|---|

0.2 | 22.73 | 8.30 |

0.25 | 24.28 | 8.03 |

0.28 | 20.30 | 9.29 |

0.4 | 16.75 | 9.64 |

0.5 | 19.24 | 9.14 |

0.8 | 23.89 | 10.21 |

1.0 | 20.51 | 9.95 |

1.2 | 15.43 | 10.71 |

1.5 | 20.66 | 10.89 |

The particle size ratio is the ratio of the maximum particle size to the minimum particle size. Controlling the minimum particle size (0.28 mm), changing the particle size ratio of 1.5, 2.0, 2.5, and 3.0, and obtaining the shear strength of the specimens with different particle size ratios under normal stress are shown in Table

Shear strength of specimens with different particle size ratios under normal stress.

Particle size ratio | Normal stress (MPa) | |||||
---|---|---|---|---|---|---|

2.5 | 5 | 7.5 | 10 | 12.5 | 15 | |

1.5 | 9.82 | 11.25 | 12.62 | 12.85 | 13.96 | 14.60 |

2.0 | 9.72 | 11.27 | 12.73 | 13.62 | 14.02 | 15.45 |

2.5 | 9.20 | 10.65 | 12.00 | 12.60 | 13.19 | 13.78 |

3.0 | 8.57 | 10.59 | 11.28 | 11.88 | 12.64 | 13.76 |

The shear strength parameter values of different particle size ratios (Table

Shear strength parameter values of different particle size ratios.

Particle size ratio | Friction angle (°) | Cohesion (MPa) |
---|---|---|

1.5 | 20.30 | 9.29 |

2.0 | 23.36 | 9.03 |

2.5 | 19.60 | 8.79 |

3.0 | 20.51 | 8.18 |

The internal friction angle

In the same parallel bond stiffness ratio

The influence of particle contact modulus EC on cohesion

The shear strength of the specimens increases with particle size. Cohesion increases with the particle size. The shear strength of the specimen gradually decreases with the increase of the particle size ratio. The impact of particle size ratio on the cohesion of the specimen is relatively small.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare no conflicts of interest.