# Improved FraSegNet-Based Rock Nodule Identification Method and Application
## 3 Evaluation Methods
### Barton-Bandis Parameter Mapping
#### 3.3.1 Parameter Mapping Formula  
To automate the conversion of fracture characteristics into rock mass mechanical parameters, a mapping relationship is created based on the Barton-Bandis theory and experimental analysis:  
1. Density: Density decreases as fracture density increases, and this is shown by the following equation: \[\rho=\rho_{0}\cdot\exp\;(-\alpha\cdot\mathrm{D})\] (6) where \(\rho\): The density of the fractured rock mass (kg/m\({}^{3}\)). \(\rho_{0}\): The density of the intact rock (kg/m\({}^{3}\)), i.e., the original rock without fractures. \(\mathrm{D}\): The fracture density, typically defined as the total length of fractures per unit area (m/m\({}^{2}\)). \(\alpha\): The density decay coefficient quantifies the effect of fracture density on the overall rock mass density. 2. The formula for the cohesion (C) of a fractured rock mass, considering fracture density and area, is usually written as follows: \[\mathrm{C}=\mathrm{C}_{0}\cdot\exp\;(-\mathrm{k}\cdot\frac{\mathrm{A}}{\mathrm{ JCS}})\] (7)where  
C: The cohesion of the fractured rock mass (in MPa). C\({}_{0}\): The cohesion of the intact rock (in MPa). A: The fracture area (in m\({}^{2}\)), representing the total area of fractures in a given volume or unit area of rock. D: The fracture density (in m/m\({}^{2}\)), defined as the total length of fractures per unit area. k: The weakening coefficient quantifies the reduction in cohesion caused by the presence of fractures. JCS: The peak normal stress on the fracture surface, related to the fracture's resistance to shear along the fracture plane (in MPa). (3) The formula for the friction angle (\(\varphi\)) of a fractured rock mass, affected by the fracture dip angle (\(\theta\)), is usually written as follows:  
\[\phi=\phi_{0}-\frac{\text{JRC-lg ($\sigma_{\text{n}}$/JCS)}}{1+\theta/\text{k}_{\phi}} \tag{8}\]  
where  
\(\Phi\): The friction angle of the fractured rock mass. \(\Phi_{0}\): The initial friction angle of the intact rock. JRC: The Joint Roughness Coefficient represents the roughness of the fracture surface. \(\sigma_{\text{n}}\): The normal stress on the fracture surface (in MPa). \(\theta\): The dip angle of the fracture relative to the horizontal (in degrees). \(\text{k}_{\phi}\): The influence coefficient accounts for the effect of fracture characteristics (such as roughness and orientation) on the friction angle. Equations (7) and (8) describe in detail the effect of cohesion and friction angle on rock cohesion, and these parameters are the core part of the definition in the Coulomb-Mohr criterion. (4) The formula for the elastic modulus (E) of a fractured rock mass, considering fracture density (D) and fracture width (W), is usually written as follows:  
\[\text{E}=\text{E}_{0}\cdot\text{exp (1-k}_{\text{E}}\cdot\frac{\text{D}}{1+\text{W}/ \text{W}_{\text{C}}}) \tag{9}\]  
where  
E: The elastic modulus of the fractured rock mass. E\({}_{0}\): The elastic modulus of the intact rock. D: The fracture density, usually expressed as the total length of fractures per unit area (fracture length density). W: The average fracture width. W\({}_{\text{C}}\): The critical width of the fractures at which they close and the elastic modulus returns to that of the intact rock. k\({}_{\text{E}}\): The elastic modulus attenuation coefficient represents the rate at which the elastic modulus decreases as the fracture density increases. The fracture closure critical width (W\({}_{\text{C}}\)) is the threshold width at which fractures start to close, and the material behavior returns to that of the intact rock.