## 4 Simulation Results and Discussions
### The influence of Particle Friction Coefficient  
The particle friction coefficient refers to the resistance between two particles when they come into contact due to the interaction between their surfaces. It determines the resistance magnitude when particles slide or attempt to slide relative to each other. As shown in Figure 10. At the initial computation stage, the soil with friction coefficients of 0.3 and 0.6 showed minimal changes, and each soil layer had an orderly arrangement with clear boundaries. Importantly, no significant particle loss occurred in the bottom layer of the soil. However, as the computation progressed, Figure 11 illustrates both soil types experienced particle loss from the damaged pipeline section. Specifically, the soil with a friction coefficient of 0.3 lost particles from six layers above the damage site, while the soil with a friction coefficient of 0.6 only lost particles from four layers above. This particle loss caused a funnel-shaped deformation in the lower soil layers, with smaller friction coefficients associated with narrower funnel openings. Additionally, it is worth noting that neither soil type experienced surface settlement, regardless of their different friction coefficients.  
The particle displacement contour map reveals that different particle friction coefficients result in varying ranges of particle displacement within the soil, even under the same computation duration. In Figure 12, during the initial stage, both friction coefficients of 0.3 and 0.6 exhibit similar influences on soil displacement, with the numerical values falling within a comparable range. However, as the simulation progresses to 400,000 steps (Figure 13), the soil with a friction coefficient of 0.3 experiences a greater range of particle displacement compared to the soil with a friction coefficient of 0.6. Despite this difference, the numerical values of displacement for both cases still remain approximately within the same range, and there is no observed displacement of soil particles on either side of the model.  
Figures 14 and 15 display force chain patterns in two types of soil with varying friction coefficients, both at the beginning and end of the computation. While their forms show no significant differences, the disparity lies in the magnitude of force chain values, with higher friction coefficients leading to stronger force chains among particles. This effect becomes more pronounced as the computation steps increase. F  
Figure 11: The subsurface displacements at 400,000 simulation steps.  
Figure 10: The subsurface displacements at 5000 simulation steps.  
Based on the analysis of the computational results presented earlier, the specific effects of particle friction coefficient on the process of soil particle slip and discharge can be summarized in the following three points:  
(1) Sliding Resistance: Higher friction coefficients result in increased frictional resistance between soil particles, hindering relative motion.  
(2) Stability of Water and Soil Particles: A higher particle friction coefficient counteracts water's wetting effect on soil particles, improving soil stability.  
(3) Critical Slope: The particle friction coefficient influences the critical slope at which soil begins to slide. Larger friction coefficients correspond to higher critical slopes, providing greater stability even at steeper angles.