## 5 Parameters Study
### Influence of Pavement Roughness  
#### 5.7.1 Pavement Surface Roughness Generation Method  
There are several methods available for simulating pavement unevenness, with the power spectral density (PSD) method being the most common. According to ISO-8608 [28], the general form of the PSD function \(G_{q}(n)\) is as follows:  
\[G_{d}(n)=G_{d}(n_{0})\left(\frac{n}{n_{0}}\right)^{-n} \tag{12}\]  
where \(n\) denotes the spatial frequency per meter. \(n_{0}\) is the reference spatial frequency, and \(n_{0}\) = 0.1 cycles/m. \(w\) denotes the exponent of the fitted PSD function. Given the power density of the pavement, harmonic superposition can be used to generate different grades of uneven pavement. \[r(x)=\sum_{i}d_{i}\cos(n_{S,i}+\theta_{i}) \tag{13}\]  
\[d=\sqrt{2G_{d}(n)\Delta n} \tag{14}\]  
where \(\Delta n\) is the sampling interval of the spatial frequency, \(d\) is the amplitude of each class of pavement, and \(\theta\) is a randomly assigned phase angle. In ISO-8608 [28], the recommended \(G_{q}(n)\) values for grades A, B, and C of road surfaces were 16 \(\times\) 10\({}^{-6}\) m\({}^{3}\), 64 \(\times\) 10\({}^{-6}\) m\({}^{3}\), and 256 \(\times\) 10\({}^{-6}\) m\({}^{3}\), and 10 \(\times\) 10\({}^{-6}\) m\({}^{3}\), respectively. To assess the influence of various parameters on simulating road surface unevenness, three representative pavement models were selected for comparison. The parameters of these models were sourced from [PERSON] [29], [PERSON] [27], and [PERSON] [30], and they are referred to as Model 1, Model 2, and Model 3, respectively. [PERSON] et al. [29] considered the vehicle frequency and the first three-order bridge frequency within the 0-40 Hz range. The range of the n value was 1-100 cycles/m. In contrast, [PERSON] [27] focused on the bridge frequency within the 0-2 Hz range, selecting a spatial frequency range of 0.06-3 cycles/m. [PERSON] [30] focused on the acceleration corresponding to road unevenness, without considering frequency identification. The road surface unevenness coefficient adopted values from ISO-8608 [28], and the selected spatial range was 0.01-5 cycles/m. The influence of various parameters in the PSD function were further analyzed by considering a case study of a 30 m span bridge. The geometry and material parameters were the same as those provided in [PERSON] et al. [29]. In the FE model, a high shear stiffness value of 5 \(\times\) 10\({}^{7}\) MPa was assigned, implying a state of near-perfect bonding within the structure. The material and geometrical properties were the length of the simply supported beam \(L\) = 30 m, cross-sectional area equals 2.0 m\({}^{2}\), the moment of inertia \(I\) = 0.175 m\({}^{4}\), mass per unit length \(m=1000\) kg/m, and elastic modulus \(E=27.5\) GN/m\({}^{2}\). The mass of the vehicle \(m_{v}=1000\) kg, spring stiffness \(k_{v}=170\) kN/m, and a zero damping was assumed. The road surface profiles generated using these three pavement roughness models are depicted in Figure 19. The road surface generated by Model 1 exhibited relatively dense spacing between the peaks, resulting in minor fluctuations across the entire bridge length. In contrast, the road surface profiles produced by the other two models showed relatively sparse peaks and larger fluctuations throughout the entire length. This difference can be attributed to the fact that Model 1 lacks small frequencies within the range of 0.01-1 Hz, which implies the absence of longer road surface waves. In the case of a smooth road surface without unevenness, the various frequencies can be clearly identified, as shown in Figure 20. Among them, 0.07 Hz represents the vehicle driving frequency (\(\
u/L\)), 2.07 Hz represents the vehicle's natural frequency, and the first three natural frequencies of the bridge are 3.87 Hz, 15.27 Hz, and 33.33 Hz, respectively. Due to the small driving frequency, the bifurcation effect at the peak of the acceleration spectrum was not prominent, and it can be approximated as a single main peak.