## 3 Wind Load Description  
### Turbulent Wind Field Simulation  
To accurately simulate the turbulent wind loads acting on the cable-stayed bridge in real environmental conditions, the wind field at the bridge site was simplified into eight independent 1D multi-variable stochastic wind processes. As shown in Figure 7, a total of 190 wind field simulation points were evenly distributed along the traffic direction on the main girder at 15 m intervals. Additionally, 70 wind field simulation points were arranged along the height of each pylon (left and right banks), and 196 wind field simulation points were set at the midpoints of all the stay cables. The turbulent wind on the auxiliary pier and the stay cable inside the pylon was not considered.  
According to _the Wind-Resistant Design Specifications for Highway Bridges_[22], the spatial turbulent wind field was simulated using the harmonic superposition method [23; 24], generating 526 spatially correlated wind speed time histories for all the structural components. The mean wind speed at the deck height ranged from 20 m/s to 52.7 m/s, with a simulated duration of 1000 s. It is critical to set the cutoff frequency at 2.5 Hz to avoid frequency aliasing, ensuring the sampling interval \(\Delta t\) satisfies \(\Delta t\leq 1/2f_{u}\), where \(f_{u}\) denotes the upper cutoff frequency of the turbulent wind. The parameters for turbulent wind field simulation are listed in Table 2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **Value** & **Item** & **Value** \\ \hline Simulated points & 526 & Cutoff frequency & 2 Hz \\ Time span & 1000 s & Frequency segmentation & 2000 \\ Time step length & 0.25 s & Surface roughness Coefficient & 0.16 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters for turbulent wind field simulation.  
Figure 6: Stay cable force comparison of two schemes.  
Figure 7: Target locations for wind field simulation.  
The horizontal and vertical target turbulent wind spectra were defined as the Kaimal spectrum and the Panofsky spectrum, respectively, with their equations provided in Equations (2) and (3).  
\[\frac{nS_{u}(Z,n)}{(u^{*})^{2}}=\frac{200f}{(1+50f)^{5/3}} \tag{2}\]  
\[\frac{nS_{w}(Z,n)}{(u^{*})^{2}}=\frac{6f}{(1+4f)^{2}} \tag{3}\]  
where \(S_{u}(Z,n)\) and \(S_{w}(Z,n)\) represent the horizontal and vertical turbulent wind PSD functions, respectively; \(n\) is fluctuation frequency of the wind; \(u^{*}\) is shear velocity of the oncoming flow; \(f=nZ/U(Z)\) is the similarity coordinate, and \(U(Z)\) is the mean wind speed at height \(Z\).  
The cross-power spectral density function is as follows:  
\[S_{u_{1}u_{2}}^{c}(r,n)=\sqrt{S(Z_{1},n)S(Z_{2},n)}\cdot e^{-r} \tag{4}\]  
where  
\[r=\frac{2n\left[C_{z}^{2}(Z_{1}-Z_{2})^{2}+C_{y}^{2}(y_{1}-y_{2})^{2}\right]^{ 1/2}}{\left[U(Z_{1})+U(Z_{2})\right]} \tag{5}\]  
where \(C_{z}\) and \(C_{y}\) is dependent on the ground surface roughness. In this paper, \(C_{z}\) and \(C_{y}\) are taken as 10 and 16, respectively. The typical time histories of wind turbulence are given in Figure 8, and the wind spectra obtained from the simulated turbulence histories are presented in Figure 9.  
Figure 8: Simulated \(u(t)\) and \(w(t)\) at the middle span of the main girder.  
Figure 9: Wind spectra: (**a**) horizontal direction; (**b**) vertical direction.  
The horizontal and vertical turbulent wind velocity power spectra of the turbulent wind field generated by the program exhibited excellent agreement with the target spectra. This validates the fidelity of the simulated wind field for dynamic analysis of structures under turbulent wind conditions.