# Research on the Reliability of Bridge Structure Construction Process System Based on Copula Theory
## 1 Introduction
Copula theory has been gradually used in the analysis of structural system reliability in recent years [17]. [PERSON] et al. first applied the Copula function to structural reliability analysis, and pointed out that the essence of the Nataf transform is to use the Gaussian Copula function to construct the joint distribution function among variables [18]. [PERSON] [19] used Copula theory to investigate the correlation between peak structural displacements and permanent displacements due to seismic loads. [PERSON] and [PERSON] [20; 21] used Copula function to describe the spatial dependence structure of continuous random field and discrete random field in geostatistics, provided three methods of spatial interpolation of geomechanical parameters based on Copula function, and, on this basis, proposed to consider the prior distribution of model parameters using Bayesian theory. [PERSON] [22] achieved the time-varying reliability analysis of multivariate structural systems by studying multivariate random variable Copula functions. By considering the correlation of failure modes of structural systems, [PERSON] [23] proposed a reliability analysis method of structural systems based on the hybrid Copula model; the nonlinear correlation between the failure modes of binary and multivariate structural systems was reasonably analyzed, and the time-varying reliability of the structures was reasonably predicted with corrections based on the analysis results, which provides a new method for the reliability analysis of structural systems. [PERSON] et al. [24] applied the Copula function into the reliability analysis of geotechnical structural systems and discussed the difference of failure probabilities of geotechnical structural systems calculated by different Copula functions, reflecting the necessity of making the optimal Copula function selection. [PERSON] [25] applied Copula theory to the time-varying reliability analysis of bridge structures; the reliability of bridge structures during long-term operation was analyzed, and the reliability of bridge structures was predicted and analyzed based on Bayesian dynamic model, which provides a reference for the operation management of bridge projects. [PERSON] [26], by applying Copula theory into the time-varying reliability analysis of existing small- and medium-span bridges, and proposing a bridge system reliability assessment method that considers multiple failure criteria based on the Copula function and AHP-EW (analytic hierarchy process-entropy weight) decision method, further improved the rationality of the bridge system reliability assessment. [PERSON] [27], using Copula theory to analyze the stability reliability of concrete dams, laid the foundation for the joint reliability analysis of engineering instances with few test data and where the joint distribution model cannot be determined. Copula theory is simple to calculate and easy to understand, and it is not limited by the amount of data. Copula theory is introduced into the reliability analysis of structural systems, which overcomes the problems of cumbersome calculation of traditional system reliability analysis methods and inadequate consideration of failure mode correlation. Although scholars at home and abroad have conducted a series of studies on the Copula function, the research on the Copula function is mainly focused on the theoretical level, and the research on structural reliability analysis based on Copula theory is still in the primary stage. Most of the existing structural system reliability analysis theories are focused on the bridge operation stage, and there are relatively few studies on the reliability of bridge system in the construction stage. Therefore, this paper proposed using Copula theory to analyze the reliability of the bridge system construction process. Based on Copula function theory, this paper analyzed the reliability of structural systems during bridge construction. Four different Copula functions were used to establish the correlation between failure modes.