Determining Digital Representation and Representative Elementary Volume Size of Broken Rock Mass Using the Discrete Fracture Network–Discrete Element Method Coupling Technique
Abstract
:1. Introduction
2. Characterization of Random Fracture Networks in Broken Rock Masses
2.1. On-Site Research of Structural Surface
2.2. Mathematical Description of Stochastic Model for Geometric Parameters of Structural Surfaces
2.2.1. Shape and Size of Structural Surfaces
2.2.2. Occurrence of Structural Planes
2.2.3. Density of Structural Planes
2.2.4. Center Point and Vertex of a Rectangular Structural Surface
2.2.5. Degree of Aperture of a Structural Plane
2.3. Generation of Random Fracture Network Model
3. Modeling of Broken Rock Masses Based on the Coupled DFN–DEM Approach
3.1. Statistics of Structural Plane Geometric Parameters
3.2. Construction of Discrete Fracture Networks
3.3. Construction of Equivalent Rock Mass Models Using DFN–DEM Coupling Technique
4. REV Size of Broken Rock Mass
4.1. Establishment of Numerical Models
4.2. Determination of REV
5. Conclusions
- (1)
- The average and variance values of the structural plane in the surrounding rock of the main powerhouse are 4.30 m and 3.45 m2, respectively, and the average and variance of the structural plane dip angles are 51.42° and (27.93°)2, respectively. The count and length of fractures per unit area of the rock masses are 0.23 and 0.97 m−1, respectively; the number of fractures per unit length of the rock is 0.58 m−1; and the fracture area per unit length is 1.87 m−1.
- (2)
- The mechanical parameters evaluated from five cylindrical models generated using the proposed approach are quite close, which suggests good stability and effectiveness of the method.
- (3)
- The REV size of the rock masses determined using the proposed approach is 5 m × 10 m for the cylindrical rock models. This result is consistent with the REV size estimated by the RMSI method using cubic rock models, which demonstrates the validity of using cylindrical models to evaluate the REV size of broken rock masses.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Distribution Type | Probability Density Function | Random Numbers | Fissure Applications |
---|---|---|---|
Uniform distribution | Midpoint location | ||
Negative exponents distribution | Trace length | ||
Fisher distribution | Dip angle | ||
Log-normally distributed | Trace length/Aperture | ||
Poisson distribution | Density | ||
Normal distribution | Aperture |
Geologic Statistics Window Locations | Roof Arch | Upstream Wall | Downstream Wall | Average |
---|---|---|---|---|
Number of structural faces/strips | 1049 | 1238 | 1421 | 1236 |
Average trace length of fractures/m | 4.99 | 3.76 | 4.15 | 4.30 |
Trace length variance/m2 | 4.00 | 2.85 | 3.50 | 3.45 |
Fracture average dip angle/° | 43.26 | 56.32 | 54.69 | 51.42 |
Dip angle variance/(°)2 | 29.76 | 27.01 | 27.02 | 27.93 |
Quantity areal density (number of fractures per unit area)/m−2 | 0.15 | 0.29 | 0.26 | 0.23 |
Fracture density (length of fracture per unit area)/m−1 | 0.75 | 1.07 | 1.10 | 0.97 |
Fracture line density (number of fractures per unit length)/m−1 | 0.31 | 0.87 | 0.55 | 0.58 |
Three-dimensional fracture density (fracture area per unit volume)/m−1 | 2.40 | 1.22 | 1.99 | 1.87 |
Density /g·cm−3 | Bulk Modulus /GPa | Shear Modulus /GPa | Cohesion /MPa | Internal Friction Angle/° | Tensile Strength /MPa |
---|---|---|---|---|---|
2600 | 24.6 | 12.5 | 11.3 | 50 | 3.58 |
Normal Stiffness/GPa | Tangential Stiffness/GPa | Tensile Strength/MPa | Cohesion/MPa | Tensile Strength /MPa |
---|---|---|---|---|
30 | 15 | 0.3 | 1.1 | 30 |
Density/g·cm−3 | Bulk Modulus/GPa | Shear Modulus/GPa |
---|---|---|
7800 | 300 | 250 |
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Huang, X.; Li, S.; Jin, J.; Shi, C. Determining Digital Representation and Representative Elementary Volume Size of Broken Rock Mass Using the Discrete Fracture Network–Discrete Element Method Coupling Technique. Appl. Sci. 2024, 14, 606. https://doi.org/10.3390/app14020606
Huang X, Li S, Jin J, Shi C. Determining Digital Representation and Representative Elementary Volume Size of Broken Rock Mass Using the Discrete Fracture Network–Discrete Element Method Coupling Technique. Applied Sciences. 2024; 14(2):606. https://doi.org/10.3390/app14020606
Chicago/Turabian StyleHuang, Xiao, Siyuan Li, Jionghao Jin, and Chong Shi. 2024. "Determining Digital Representation and Representative Elementary Volume Size of Broken Rock Mass Using the Discrete Fracture Network–Discrete Element Method Coupling Technique" Applied Sciences 14, no. 2: 606. https://doi.org/10.3390/app14020606
APA StyleHuang, X., Li, S., Jin, J., & Shi, C. (2024). Determining Digital Representation and Representative Elementary Volume Size of Broken Rock Mass Using the Discrete Fracture Network–Discrete Element Method Coupling Technique. Applied Sciences, 14(2), 606. https://doi.org/10.3390/app14020606