## 3 Modeling of Broken Rock Masses Based on the Coupled DFN-DEM Approach
### Construction of Discrete Fracture Networks  
Based on relevant theories in structural statistics of rock masses, this research develops a tool named \"Random Fracture Network Simulation Program for Fractured Rock Masses\". This program encompasses a fracture data input module, a fracture network generation module, and a fracture network output module, offering the following features and advantages: (1) Real-time selection of parameter distribution functions and generation of fracture networks based on the input geometric parameters of structural surfaces. (2) The output result file can be inputted into some other software for further analysis, providing ease of connection with program interfaces. (3) A user-friendly interface that requires minimal compilation of data files, effectively reducing the likelihood of errors. The existing approaches for simulating broken rock masses generally require numerical simulations to obtain the probabilistic distributions of the structural surfaces' geometric parameters [30]. In the proposed method, the optimal probabilistic distribution functions for the geometric parameters can be automatically acquired without additional simulations, which can significantly accelerate the simulation process.  
The simulation process of the program is illustrated in Figure 8. Initially, within the fracture data input module, a database of geometric parameters for structural surfaces is established. The number of structural plane groups, as well as the probability distribution forms for the geometric parameters of each structural plane group, can thus be determined. Next, employing the Monte Carlo principle, the program calculates the center point, vertex coordinates, and geometric parameters for each fracture to complete the simulation for each group of structural surfaces. To optimize the structural plane network, fractures that are in close proximity or have very small angles are merged or deleted; fractures beyond the model dimensions are truncated and removed. Finally, after completing the simulation of the structural surface network, the program outputs result in required formats.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Geologic Statistics Window Locations** & **Rood Arch** & \
\begin{tabular}{c} **Upstream** \\ **Wall** \\ \end{tabular} &
\begin{tabular}{c} **Downstream** \\ **Wall** \\ \end{tabular} & **Average** \\ \hline 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/m\({}^{2}\) & 4.00 & 2.85 & 3.50 & 3.45 \\ Fracture average dip angle/\({}^{\circ}\) & 43.26 & 56.32 & 54.69 & 51.42 \\ Dip angle variance/(\({}^{\circ}\))\({}^{2}\) & 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 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Analysis results of geological statistical window of surrounding rock of main powerhouse.