Submitted:
02 June 2026
Posted:
03 June 2026
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Abstract
Keywords:
1. Introduction
2. Theoretical Analysis of Load Transfer Mechanisms in Anchored Rock Joints
2.1. Classification of Active and Passive Strength Enhancement Stages
- Initial Slip Stage
- 2.
- Elastic Stage
- 3.
- Yielding Stage
- 4.
- Softening Stage
2.2. Calculation of Shear Strength Improvement of Rock Joints by Bolt Active and Passive Actions
2.3. Failure Modes and Stress Evolution Laws of Bolts
3. Laboratory Direct Shear Testing of Anchored Rock Joints
3.1. Specimen Fabrication and Design of Anchorage Parameters
3.2. Experimental Scheme Design
- Preheating and Inspection: The testing machine was preheated, and the indicators of all sensors were checked to ensure they were within the normal operating range.
- Specimen Protection: Before placing the specimen, steel plates with pre-drilled holes were positioned on the left and right sides of the specimen. The portion of the bolt extending out of the specimen was inserted into the holes of the steel plates to prevent damage to the ends of the anchored specimen during loading.
- Sensor Setup: Horizontal and vertical displacement sensors were arranged appropriately, and their positions were adjusted to ensure normal readings.
- Horizontal Confinement: A horizontal stress of 0.05 MPa was first applied to fix the specimen. Once the horizontal stress reached the predetermined value, it was maintained as a constant.
- Vertical Loading: The vertical loading rate was set to 0.3 mm/min, with a maximum displacement observation limit of 12 mm.
- Data Acquisition: Real-time shear data were recorded by computer. The test was terminated and unloaded once the shear stress-shear displacement curve showed a peak or the bolt fractured.
- Documentation: Photographic records of the specimens were taken during the test, and all data were preserved for subsequent analysis.
3.3. Shear Mechanical Characteristics of Specimens Under Fully Grouted and End-Anchored Conditions
3.3.1. Failure Characteristics of Fully Grouted Bolts
- Initial Stage: The shear stress increases sharply with shear displacement, exhibiting a steep slope.
- Strengthening Stage: Compared to the initial stage, the growth rate of shear stress slows down, showing a relatively reduced slope.
- Failure Stage: The bolt within the rock joints fractures, leading to a rapid drop in shear stress. The residual shear stress corresponds to the inherent shear strength of the rock joints (). At this point, the increment of shear strength provided by the bolt () is quantified as the difference between the peak stress and
3.3.2. Failure Characteristics of End-Anchored Bolts
- Elastic Stage: The shear stress increases linearly with shear displacement, characterized by a relatively steep slope.
- Yielding Stage: The shear stress stabilizes and maintains a constant value despite continued dislocation of the rock joints.

3.4. Evolution Law of Shear Strength in Rock Joints

4. Numerical Simulation Analysis of Shear Characteristics in Anchored Rock Joints
4.1. Establishment of the Numerical Model
- Model Segmentation: The bolt model was constructed using solid elements. A 10 cm section of the bolt was cut at a distance of 10 cm from the bearing plate.
- Stress Application: Normal stresses equivalent to the pre-stress magnitude were applied to the exposed ends of the remaining bolt segments. The model was then solved until equilibrium was reached, simulating the pre-tensioning of the bolt.
- Equilibrium Restoration: The cut bolt element was restored, the mesh was released, and the model was solved again until a new equilibrium state was achieved. This allowed the pre-stress to diffuse throughout the bolt system, as illustrated in Figure 13b.
4.2. Analysis of Shear Strength Enhancement by Bolt Active and Passive Actions
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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| Material | Drilling Diameter/mm | Bolt Diameter/mm | Elastic Modulus/GPa | Poisson’s Ratio | Yield Strength/MPa | Tensile Strength MPa |
| HRB335 | 32 | 20 | 200 | 0.3 | 335 | 455 |
| Aluminum-Magnesium Alloy | 4 | 2.5 | 69.3 | 0.33 | 195 | 230 |
| Material | Compressive Strength/MPa | Tensile Strength/MPa | Elastic Modulus/GPa | Poisson’s Ratio | Cohesion/MPa | Friction Angle/° |
| Anchoring Agent | 28.25 | 4.38 | 1.78 | 0.12 | 6.40 | 16.5 |
| Material | Compressive Strength/MPa | Tensile Strength/MPa | Elastic Modulus/GPa | Poisson’s Ratio | Cohesion/MPa | Friction Angle/° |
| Sandstone | 20~170 | 2~25 | 3~35 | 0.1~0.3 | 1~40 | 25~60 |
| Rock-like Material | 1.67~14.17 | 0.17~2.08 | 0.25~2.92 | 0.1~0.3 | 0.0833~3.33 | 25~60 |
| Gypsum Specimen | 13.12 | 1.82 | 1.87 | 0.28 | 0.085 | 48 |
| Material | Bulk Modulus / GPa | Shear Modulus / GPa | Cohesion / MPa | Friction Angle / ° | Tensile Strength / MPa | Yield Strength / MPa |
| Sandstone | 15.6 | 12.7 | 11 | 43 | 5 | - |
| Grout | 6.9 | 5.6 | 12 | 30 | 6 | - |
| Bolt | 166.7 | 76.9 | - | - | 455 | 335 |
| Bearing Plate | 166.7 | 76.9 | - | - | 455 | 335 |
| Plastic Shear Strain | 0 | 5e-4 | 1e-3 | 5e-2 | 1e-1 |
| Cohesion / MPa | 12 | 6 | 1 | 0.1 | 0.05 |
| Internal Friction Angle / ° | 30 | 30 | 28 | 28 | 28 |
| Plastic Shear Strain | Normal Stiffness / (GPa·m⁻¹) | Shear Stiffness / (GPa·m⁻¹) | Cohesion / MPa | Friction Angle / ° |
| Rock joints I | 2,000 | 2,000 | 0.1 | 20 |
| Rock joints II | 2,000 | 2,000 | 0.1 | 20 |
| Rock-Grout | 9,578 | 9,578 | 8 | 30 |
| Bolt-Grout | 9,578 | 9,578 | 10 | 30 |
| Bolt-Plate | 21,688 | 21,688 | 10 | 32 |
| Plate-Rock | 60,000 | 60,000 | - | - |
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