## 4 Simulation Results and Discussions
### The Influence of Particle Size Distribution  
The section includes numerical experiments conducted on continuous gradation soil, which are identical to the previous numerical experiments involving high groundwater levels. Therefore, the focus is solely on presenting the computational results for discontinuous gradation soil and conducting a comparative analysis with the findings obtained from the continuous gradation soil calculations. At 5000 simulation steps, the computational model with 12 layers of particles exhibits not obvious displacement, as shown in Figures 16a and 22. The boundaries between adjacent layers remain distinct, and only a few particles near the damaged section of the lower pipe have escaped, indicating the system's stability. However, as the simulation progresses to 400,000 steps, the continuous gradation soil experiences substantial downward displacement in the central region, leading to evident surface subsidence. Particle loss has occurred in all layers above the leakage point, with the 9 th layer being displaced to the leakage point. Despite varying displacement between layers, clear boundaries persist, and there is no apparent mixing of particles among different layers. In contrast, the gradation soil shows a similar pattern of significant displacement in the central region. However, due to the presence of larger-sized particles, the soil arching effect becomes more pronounced near the leakage point. As a result, only the bottom four layers of particles have leaked out, disrupting the boundaries between layers. Smaller particles migrate more extensively downward along the interstices between the skeleton particles, particularly noticeable near the leakage point. As shown in Figure 23.  
Figure 21: The internal force chains within the subsurface at 400,000 simulation steps. Figure 22: The subsurface displacements at 5000 simulation steps. Figures 18a and 24 show that both soil under different gradations initially remain stable during the simulations. However, near the leakage point, a small area experiences particle displacement. Continuous gradation particles exhibit a larger variation in displacement area compared to discontinuous gradation particles. Specifically, continuous gradation particles show more even displacement throughout the area, while discontinuous gradation particles primarily experience displacement around the larger particles near the leakage point, resulting in a smaller overall displacement area. As the simulations progress to 400,000 steps, continuous gradation particles display a larger overall displacement area, and the displacement values on both sides of the leakage point axis become more symmetrical. This observation highlights a significant correlation between particle displacement and the distance from the leakage point, with displacement diminishing as the distance increases, resulting in mostly stationary particles in the edge region. In contrast, Figure 25 demonstrates the displacement of discontinuous gradation particles lacks the axis symmetry observed in continuous gradation particles. The occurrence and magnitude of particle displacement become more unpredictable. As particles in the vicinity of the leakage point and central region experience overall displacement, fine particles at the edge region also undergo displacement, providing numerical evidence that the finer particles are transferring through the channels formed between the skeleton particles. When particle contacts are loose, particles are prone to sliding under external forces. Conversely, densely packed particles form stable force chains through close interlocking and mutual compression. At the beginning of the simulations, continuous gradation particles have more force chains due to their smaller size, resulting in a denser arrangement. However, As shown in Figure 26. These force chains are relatively short and weaker compared to those formed by discontinuous gradation particles. As the simulations progress  
Figure 23: The subsurface displacements at 400,000 simulation steps.