# Safety Performance Evaluation of Ultra-High-Performance Concrete Semi-Assembled Barrier
## 5 Analysis of the Crash Simulation Results
### Buffering Function  
The buffer function of the barrier is primarily evaluated based on the acceleration and speed of the center of gravity of a 1.5-t car. The key indicators include the occupant ride-down acceleration (ORA) and occupant impact velocity (OIV). Acceleration during a vehicle collision is crucial for directly evaluating driver safety. Effective energy absorption and buffering by the barrier can reduce speed changes during collisions, thereby enhancing vehicle safety. According to the Standard for Safety Performance Evaluation of Highway Barriers (JTG B05-01-2013) [25], the longitudinal and lateral ORA at the driver's position should be less than 200 m/s\({}^{2}\). Moreover, the longitudinal and lateral OIV of occupant collisions should be less than 12 m/s. The ORA can be directly obtained using post-processing software. OIV refers to the instantaneous speed at which an occupant collides with the barrier inside a vehicle during a small vehicle collision. This can be calculated using the following formula:  
\[OIV_{x}=\int_{0}^{t_{0}}a_{x}dt \tag{14}\]  
\[OIV_{y}=\int_{0}^{t_{0}}a_{y}dt \tag{15}\]  
where  
\(OIV_{x}\)--X direction component of occupant impact velocity;  
\(OIV_{y}\)--Y direction component of occupant impact velocity;  
\(a_{x}\)--Vehicle acceleration in the X direction;  
\(a_{y}\)--Vehicle acceleration in the Y direction;  
\(t_{0}\)--The moment of impact, determined as the smaller of \(t_{x}\) and \(t_{y}\), which are calculated by the following equations when an occupant comes into contact with the interior of the vehicle:  
\[\int_{0}^{t_{x}}dt\int_{0}^{t_{x}}a_{x}dt=0.6 \tag{16}\]  
\[\int_{0}^{t_{y}}dt\int_{0}^{t_{y}}a_{y}dt=0.3 \tag{17}\]  
Figure 14: Barrier section after collision. Ora  
Post-processing software was used to extract the ORA in the X and Y directions at the center of gravity of a 1.5-ton car during a collision, as illustrated in Figure 15a,b. In the finite element simulation, the peak acceleration of the occupant in the X direction was 93.2 m/s\({}^{2}\), and in the Y direction it was 172.7 m/s\({}^{2}\). These values were compared with data obtained from a full-scale vehicle crash test, where the peak acceleration in the X direction was 88.5 m/s\({}^{2}\), and in the Y direction it was 170.9 m/s\({}^{2}\). The relative errors between the simulation and the actual peak acceleration in the X and Y directions were 5.3% and 1.0%, respectively, both meeting the specification requirements as they were less than 200 m/s\({}^{2}\). The errors were within a reasonable range. Thus, it can be concluded that the ORA in the simulation results aligns well with the ORA obtained in the real vehicle collision test. 2. OIV  
According to Equations (16) and (17), the theoretical displacement curves of the occupant's head in the X and Y directions during the vehicle collision in the numerical simulation can be obtained (as shown in Figure 16), with \(t_{x}\) = 0.142 s and \(t_{y}\) = 0.099 s. Therefore, the occupant collision time \(t_{0}\) is taken as 0.099 s. Using Equations (14) and (15), the acceleration curves are integrated, yielding the occupant collision speeds in the X and Y directions in the numerical simulation, which were subsequently compared with the results of the real vehicle collision test (Figure 15c,d). Figure 15: Acceleration test and simulation results. In the finite element simulation, when \(t_{0}=0.099\) s, \(OIV_{x}=6.89\) m/s, and \(OIV_{y}=8.09\) m/s. In the full-scale vehicle crash test, the measured collision times \(t_{0}=0.133\) s, \(OIV_{x}=8.50\) m/s, \(OIV_{y}=9.60\) m/s. The relative errors between the simulation and the actual peak acceleration in the X and Y directions were 18.9% and 15.7%. The simulation results were less than 12 m/s and met the specification requirements.