# Deterministic Discrete Fracture Network Model and Its Application in Rock Mass Engineering
## 2 Acquisition of Structural Surface Parameters
### Structural 3D Modeling of Rock Mass  
This section employs a deterministic method for modeling, characterizing joints, layers, and faults with different models. Joints are represented by disk models, which require parameters including the disk's orientation, central coordinates, and persistence. The calculation of persistence and central coordinates follows: Previous studies have accurately described the relationships among spacing, surface density, volumetric density, and the persistence of structural planes. In the previous step, we extracted the spacing, while surface density and volumetric density can be directly calculated from the number of structural planes. Combining this information with prior research allows us to estimate the persistence of the structural planes. Based on this, geometric knowledge is utilized to deduce the relationship between persistence, trace length, orientation, and the central coordinates of the structural planes, thereby obtaining the 3D central coordinates of the structural planes. Layer and fault models are characterized using the flat plate model, where the model parameters include the coordinates of a point on the model and its orientation. The coordinates of a point can be replaced by the trace center, thus eliminating the need for additional calculations. For the rock mass model, it is necessary to continuously adjust its volume range to avoid edge effects. After calculating the parameters of each model, the DFN model can be obtained by combining these models, as shown in Figure 2 below. (1) Joint Disk Model:  
Joint fractures typically do not penetrate through the entire rock mass region, so a disk model is chosen to represent them. The data required for the disk model in 3D space include the normal vector of the disk plane, the center coordinates of the disk, and the persistence of the disk. The normal vector can be calculated from the dip direction and dip angle of the plane. What needs to be calculated are the persistence and center coordinates. The 3D form of the joint model, along with the structural plane parameters it contains, is illustrated in Figure 3.  
Figure 3: The distribution of the 3D joint model. Figure 2: Estimation of the 3D Distribution Morphology of Integral Structural Surfaces. \(\dagger\) Calculation of Disk Persistence:  
As mentioned in previous research, the study object of this experiment is large planes with good influence; smaller, fragmented structural planes have been excluded. Since these structural planes are within a small-scale rock mass and their 3D distribution characteristics do not differ significantly, we decided to use the average persistence as the size of the disk model for the study. In Ref. [26], the authors constructed 77 fracture network models with different lengths (D) and spacings (C) based on the rock mass fracture classification table from the International Society for Rock Mechanics (ISRM, 1978) (Table 1). Refs. [27; 28] proposed that when the structural surface representation model is a disk model, the persistence in Table 1 can be approximated as the model size. The relationship between persistence, spacing, and volumetric density is shown in Table 1.  
In Table 1, VCS represents Very Close Spacing; M represents Moderate; W represents Wide; HP represents High Persistence; and L represents Light. The first row is the classification based on spacing, the first column is the classification based on structural plane size, and the middle section represents the corresponding bulk density. The calculation formula for the trace line density \(\rho_{m}^{(k)}\) is as follows:  
\[\rho_{m}^{(k)}=\frac{N^{(k)}}{W^{2}} \tag{1}\]  
\(W\) represents the side length of the sampling window, \(N^{(k)}\) represents the number of trace lines, and \(k\) represents the number of groups of structural planes.