# Reliability Analysis of the Main Pier during the Construction Period of HLCR Bridges
## 2 Theoretical Foundation
### Load Probability Modeling
#### 2.4.3 Wind Load  
According to the specification in [35], the basic wind speed probability distribution is selected in this paper to be consistent with the generalized Pareto distribution model, with the following parameter values:  
\[f(x)=\frac{1}{\alpha e^{(1-k)y}} \tag{28}\]  
\[F(x)=1+\frac{1}{e^{y}} \tag{29}\]  
Here, \(\alpha\) is the scale parameter with a value of 5.5; \(k\) is the shape parameter and its value is 0.58; \(\zeta\) is the position parameter with a value of 8.27; \(y\) is the function describing the relationship between the parameters  
where \(U_{d}\) is the design reference wind speed at the reference height of the bridge or member (m/s); \(k_{f}\) is the wind resistance risk factor, which can be selected as 1.02 according to the specification in [35]; \(k_{t}\) is the terrain condition factor, taken as 1 for flat and open terrain; \(k_{h}\) is the surface category conversion and wind speed height correction factor (1.53 for the main girders and 1.51 for the piers); \(W_{y}\) is the fundamental wind speed, which as described earlier, is consistent with the generalized Pareto distribution (m/s). The design wind speed for the construction phase can be calculated by the following equation:  
\[U_{sd}=k_{sf}U_{d} \tag{31}\]  
where \(U_{sd}\) is the design wind speed during the construction phase (m/s), and \(k_{sf}\) is the risk factor of wind resistance during the construction period, which can be taken as 0.84 according to the specification in [35]. The equivalent static gust wind speed during the construction phase of a bridge or member can be calculated by the following equation:  
\[U_{sg}=G_{V}U_{sd} \tag{32}\]  
where \(U_{sg}\) is the equivalent static gust wind speed during the construction phase of a bridge or member (m/s), and \(G_{V}\) is the equivalent static gust wind coefficient, which can be taken as 1.25 for the main girders and 1.16 for the piers according to the specification in [35]. The equivalent static gust wind load per unit length of the main girder under a cross-bridge wind is calculated as follows:  
\[F_{g1}=\frac{1}{2}\rho U_{sg}^{2}C_{H}D \tag{33}\]  
where \(F_{g1}\) is the equivalent static gust wind load acting on the unit length of the main beam (kN/m); \(\rho\) is the air density (kg/m\({}^{3}\)), which can be taken as 1.25 kg/m\({}^{3}\); \(C_{H}\) is the transverse force coefficient of the main beam, which can be taken as 1.3 according to the specification in [35]; \(D\) is the characteristic height of the main beam (m). The calculation gives \(F_{g1}=2.66W_{y}D\). The equivalent static gust wind loads on the bridge piers, under wind loads in the cis-bridge direction, are calculated as follows:  
\[F_{g2}=\frac{1}{2}\rho U_{sg}^{2}C_{D}A_{n} \tag{34}\]  
where \(F_{g2}\) is the equivalent static gust wind load acting on a unit length of the bridge pier (kN/m); \(\rho\) is the air density (kg/m\({}^{3}\)), which can be taken as 1.25 kg/m\({}^{3}\); \(C_{D}\) is the resistance coefficient of the bridge pier, which can be taken as 1.6 according to the specification in [35]; \(A_{n}\) is the area projected downwind on the unit length of the member (m\({}^{2}\)/m). The calculation gives \(F_{g2}=3.00W_{y}A_{n}\).