# Reliability Analysis of the Main Pier during the Construction Period of HLCR Bridges
## 2 Theoretical Foundation
### Analysis of Indeterminate Factors Affecting the Resistance of the Main Pier in Cradle Construction  
Research by domestic and foreign scholars shows that there are many factors affecting the resistance of bridge structures, and the lack of resistance of structural members during the construction period is an important cause of bridge structure failure. Therefore, when conducting a reliability analysis of the main pier during the construction period of the bridge structure, the factors affecting the resistance of the pier should be reasonably analyzed first.  
Factors affecting the structural resistance \(R\) of bridges are usually considered from the following three aspects: the uncertainty of material properties \(K_{M}\), the uncertainty of geometric parameters \(K_{A}\) and the uncertainty of the computational model \(K_{P}\)[30]. Since these factors are generally random variables, the resistance of a structure or member is often a function of multiple random variables. In determining the statistical characteristics of the resisting force, the statistical parameters of each influencing factor are usually determined first, and then the statistical parameters and probability distribution types of the resisting force are deduced according to the functional relationship between the resisting force and the relevant factors. According to the results of a large number of studies, the uncertainty of geometric parameters in practical engineering is small [1], so its variation has little influence on the reliability index. For the convenience of calculation, this paper mainly considers the influence of the uncertainty of material properties \(K_{M}\) and calculation mode \(K_{P}\) on the uncertainty of the pier's body resistance.  
The uncertainty of the material properties of structural members mainly refers to the variability of the material properties in the members due to the quality of the material and the fabrication process caused by the loading condition, shape and size, environmental conditions and other factors. This uncertainty can be expressed in \(K_{M}\)[30]:  
\[K_{M}=\frac{f_{st}}{\omega_{0}f_{k}} \tag{14}\]  
where \(f_{st}\) represents the actual material property values in the structural elements, \(f_{k}\) the standard value of the material properties of the specimen as specified in the specification and \(\frac{1}{\omega_{0}}\) is the coefficient reflecting the difference between the material properties of the structural elements and the material properties of the specimens.  
The uncertainty of the component resistance calculation model mainly refers to the variability caused by the approximation of certain basic assumptions made in the process of resistance calculation and by the imprecision of the calculation formula, which can be expressed by the random variable \(K_{P}\)[30]:  
\[K_{P}=\frac{R_{s}}{R_{j}} \tag{15}\]  
where \(R_{s}\) is the actual resistance value of the component, which can generally be measured in the test or accurately calculated; \(R_{j}\) is the resistance value calculated according to the specification formula, and the measured values of material properties and geometric dimensions are used for calculation.  
The statistical analysis of \(K_{M}\) and \(K_{P}\) leads to the mean value \(\mu\) with the coefficient of variation \(\delta\). The commonly used statistical parameters for the uncertainty \(K_{M}\) of the material properties of reinforced concrete structures and the uncertainty \(K_{P}\) of the calculation mode of the members can be selected from the reliability design specification for highway engineering [30].