## 2 CFD Model
### Geometric Model and Boundary Conditions  
Once the falling debris detaches from the lining surface, it leaves behind a pit hole that conforms to the shape of the fallen debris, as illustrated in Figure 2a. To accurately capture the true geometric characteristics of high-speed railway lining debris, on-site scanning of the resulting potholes was conducted within a railway tunnel in China. The scanning process employed a Leica P50 three-dimensional laser scanner. Given the limited vault height of the high-speed railway tunnel (approximately 10 m), the scanning distance was set to the instrument's minimum allowable value of 120 m. The corresponding scanning rate was configured at 1,000,000 points/s, and a scanning resolution of up to 0.8 mm@10 m was chosen to capture intricate surface details. Following the completion of on-site scanning, the three-dimensional point cloud data representing the lining stripping hole was imported into CloudCompare. This facilitated the extraction of the geometric shape of the falling debris, with subsequent smoothing of the lining surface to a certain degree. Figure 2b showcases the geometry of the lining falling debris obtained through field scanning. The dimensions of the debris are specified as follows: length--30.6 cm, width--27.1 cm, and height--5.5 cm, with a corresponding mass of 1.5 kg, located at the tunnel vault. In the figure, the coordinate axes are defined with the \(X\) axis parallel to the train's forward direction, the \(Y\) axis opposite to the falling direction of the debris, and the  
\(Z\) axis in the horizontal direction. The top surface of the falling debris, connected to the original tunnel lining structure, exhibits a rough and uneven texture, while the bottom surface represents the lining surface before debris stripping, characterized by its smoothness. Additionally, the lengths in each direction of the falling debris, as obtained from this scan, are compared with reported actual accidents or research-based falling debris sizes. The length of each direction of the lining falling debris is within the range of the actual falling debris reported, suggesting its representativeness in this research [5,33]. Moreover, by adjusting the shape factor and rotational inertia matrix of the debris, the impact of their asymmetry on the motion trajectory is accurately captured. Figure 3 illustrates the numerical simulation of the entire area, comprising two atmospheric domains and an intermediate tunnel section. The atmospheric domain is represented by a semi-cylinder with a length of \(11.56L\) and a radius of \(31.23W\). The tunnel is a standard single-hole double-line tunnel covering \(100\) m\({}^{2}\) with a length of \(15.41L\). The train model utilized is a typical 8-marshalling train featuring CRH380B in China, accounting for the bogie/s influence on the flow field structure while disregarding the effects of windows and pantographs. The head train measures \(25.965\) m in length (\(L\)), \(3.202\) m in width (\(W\)), and \(3.722\) m in height (\(H\)), while the middle train's length is \(0.96L\). Initially, the nose tip of the head train is positioned \(2L\) from the tunnel entrance, with falling debris situated at the tunnel's midpoint. To ensure the complete development of the gap flow field between the falling debris and the tunnel wall, a \(2\) cm separation from the tunnel wall is maintained at the top. Both the magnitude and rate of pressure change are most pronounced when the head train reaches specific locations. This phenomenon most readily triggers crack propagation and lining detachment incidents. Consequently, debris detachment is modeled to occur when the train's nose tip arrives at the designated position by activating the dynamic fluid body interaction (DFBI) module in Simcenter STAR-CCM+2306 [34].