## 2 FE Model Validation
### Numerical Model
#### 2.2.4 Contact and Boundary Conditions  
To simulate the fixed boundary conditions at the bottom of the column in the actual test, the base in Figure 5 is defined as a rigid body, with its six degrees of freedom (DOFs) completely constrained (\(U_{\text{x}}=UR_{\text{x}}=0\), \(U_{\text{y}}=UR_{\text{y}}=0\), \(U_{\text{z}}=UR_{\text{z}}=0\)); the impactor is fixed at five DOFs (\(UR_{\text{y}}=0\), \(U_{\text{x}}=UR_{\text{x}}=0\), \(U_{\text{z}}=UR_{\text{z}}=0\)) and allowed to move only in the direction of DOF \(U_{\text{y}}\). In the predefined field, the impactor is given an initial velocity in the \(U_{\text{y}}\) direction, with the velocity property defined as \"Translational Only\", which means that the impactor can only move along a straight line at a constant velocity. The top steel plate is also defined as a rigid body, but its DOFs are not constrained.  
A surface-to-surface contact is established between the steel backing plate and the top surface of the column cap of the specimen. The contact surface has a property of a \"hard\" contact in its normal direction, which only transfers the force in the normal direction of the contact surface and allows for the separation of the steel backing plate element from the concrete element; the contact force is zero when separation occurs.  
The nodes are connected for the axial force application device composed of the top plate, the prestressing bars, and the base, as shown in Figure 7. Taking the method of connection between the top plate and the prestressing bars as an example, a reference point is established at each of the two connections, the top plate and the reference point are constrained by point-surface coupling, and the reference point and the top point of the prestressing bar are constrained by a point-point MPC tie. The same nodal connection method is adopted between the lower prestressing bars and the base.  
The initial position of the loading head method under a static load is different from those under impact. Under a static load, the initial gap between the loading head and the concrete surface is set to 0. After the prestress is applied by the cooling method in Step 1 (with an analysis time of 1 s), a linearly varying horizontal displacement is applied to the loading head only when Step 2 starts, and the other five DOFs (i.e., except the horizontal DOF) are constrained. In comparison, under a horizontal impact, since the initial velocity needs to be predefined in the \"Predefined field\" in the initial step \"Initial\", the initial gap between the loading head and the concrete surface is set to s = \(v_{0}\)t (where \(v_{0}\) is the impact  
Figure 6: Applied prestress by cooling method.  
Figure 7: Connection method between the top plate and prestressing bars.  
velocity of the loading head and t is the time of Step 1, i.e., 1 s). When Step 1 starts, the prestressing bars cool down and contract according to the cooling curve, while the loading head moves horizontally at an initial velocity \(v_{0}\) with the same boundary constraints as those under a static load. When the analysis step time reaches 1 s, the calculation in Step 1 is ended, and at this time, the application of the axial force has been completed and the loading head moves exactly to the surface of the column cap of the specimen, enabling the two to contact and impact one another as soon as Step 2 starts.