## 3 Methodology
### Numerical Simulation  
In this study, PFC\({}^{\text{3D}}\) 5.0 discrete element software was employed to reveal the formation mechanisms of the Conaxue Co landslide dam. A three-dimensional (3D) analysis was conducted to examine particle migration under seepage conditions, while a two-dimensional analysis was performed to investigate the distributions of seepage field and force chains under water flow conditions. The topographic data of the landslide dam (12.5 m DEM data from [[https://search.asf](https://search.asf)]([https://search.asf](https://search.asf)). alaska.edu/#/, accessed on 12 December 2024) were first converted into grid format and subsequently imported into Rhinoceros 8 software. To simulate the mechanical behavior of the landslide, advanced numerical techniques were employed in the literature, in line with recent developments in slope stability analysis [21; 22; 23]. Subsequently, the boundaries of the dam body and bedrock were precisely delineated, and their geometric configurations were defined based on the topographic data. Given that field investigations demonstrated distinct inverse grading structure for the Conaxue Co landslide dam, the coarse-grained and fine-grained layers were differentiated during the modeling process. Rigid spherical particles were generated for each layer based on the particle size distribution obtained through field investigation and laboratory sieving. Layer 1 exhibited a porosity of 0.55, while Layer 2 had a porosity of 0.35. Given computational limitations, a total of 16,403 spherical particles were generated in the model, including 3380 in the coarse-grained layer and 13,023 in the fine-grained layer. As the Conaxue Co landslide dam originated from a high-speed and long-distance landslide deposit, the interparticle contact behavior was modeled using the Mindlin-Hertz contact model in PFC. With reference to previous model parameters [24], contact parameters were determined through trial-and-error methods and numerical tests. The finalized parameters are listed in Table 1, and the 3D particle flow model is illustrated in Figure 5. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Dam** & **Elastic Modulus** & **Poisson’s** & **Friction** & **Coefficient of** & **Particle Density** & **Anti-Rotation** \\
**Structure** & **E (MPa)** & **Ratio** & **Coefficient** & **Restitution** & \(\rho\) (kg\(\cdot\)m\({}^{-3}\)) & **Coefficient** \(\mu r\) \\ \hline Layer 1 & 200 & 0.5 & 0.5 & 0.3 & 2650 & 0.1 \\ \hline Layer 2 & 100 & 0.3 & 0.4 & 0.3 & 2350 & 0.1 \\ \hline \end{tabular}
\end{table} 
Table 1: Micromechanical parameters of particles and contacts used in the 3D model. Figure 4: The method for determining the structure of Conaxue Co landslide dam. **(A)**—A typical profile of Conaxue Co landslide dam; **(B)**—a square area was selected to determine the distribution of particles larger than 100 mm; **(C)**—sampling and sieving were conducted in the laboratory to determine the distribution of particles smaller than 100 mm. To develop the 2D model, the typical longitudinal profile of the dam body and bedrock was initially created in software CAD 2024 using elevation data. The dam body was subsequently divided into a coarse-grained layer and a fine-grained layer. The outlined profiles of both dam body and bedrock were saved in STL format and imported into PFC\({}^{\text{2D}}\) software to establish the dam's geometry. Rigid spherical particles were also generated for the coarse-grained layer and fine-grained layer based on the particle size distribution obtained from field investigation and laboratory sieving. The porosity was calculated by substituting the 2D porosity of the landslide dam into Equation (1) [25]. \[n_{2D}=0.42\times n_{3D}^{2}+0.25\times n_{3D} \tag{1}\]  
where \(n_{2D}\) is the 2D porosity of the landslide dam, and \(n_{3D}\) is the 3D porosity of the landslide dam. The porosities of the coarse-grained and fine-grained layers are 0.265 and 0.139, respectively.