# Random Field-Based Time-Dependent Reliability Analyses of a PSC Box-Grider Bridge
## 1 Introduction  
The serviceability and durability of bridges are gradually reduced due to the influence of various deterioration factors during service, which may even lead to accidents involving safety [1; 2]. Therefore, to provide the scientific basis for diagnosis of structural health and maintenance decisions to ensure the safe operation of bridges, it is necessary to evaluate the service status of bridges throughout their whole service lives. Factors, such as material properties, load conditions, geometric characteristics, and steel corrosion, etc., show considerable randomness and have significant influence on the mechanical properties of prestressed concrete (PSC) bridges. Therefore, probabilistic methods have been used to evaluate the structural state in order to obtain rational results [3; 4; 5]. Based on the first-order reliability method (FORM), [PERSON] [6] studied the reliability of several typical PSC beams, such as rectangular beams, T-beams, and \(\pi\)-beams, in American Concrete Institute (ACI) code and discussed the effects of secondary moment, eccentricity, and area of prestressed tendons on structural reliability. [PERSON] [7] analyzed the influence of steel corrosion on the reliability of the flexural bearing capacity of PSC bridges (T-type)during the whole service process. [PERSON] [8] proposed a life-cycle performance evaluation method based on the structural reliability of PSC bridges. [PERSON] [9] applied the Monte Carlo method to evaluate the reliability of high-performance PSC elements, including box girders, I-girders, and double-T girders. [PERSON] [10] compared the reliability levels of precast PSC bridges designed by three different codes: The Spanish Norma IAP-98 code, the Eurocode, and the AASHTO LRFD code. [PERSON] [11] also carried out some related studies. In addition, the time-dependent effects caused by concrete shrinkage and creep present a high degree of uncertainty due to the influences of various random factors. [PERSON] [12] presented the time-dependent reliability of a PSC box-girder bridge by using the stochastic finite element method, in which the combined effects of creep, shrinkage, and steel corrosion were taken into account. [PERSON] [13] also proposed a hybrid method to analyze the time-variant deflection reliability of a high-speed railway PSC bridge, and the research results could provide theoretical guidance for maintenance and rehabilitation of similar bridges. In the aforementioned reliability analysis of PSC bridges, structural parameters are usually treated as uncorrelated random variables. In fact, the stiffness, distributed load, and material characteristics of bridge structures may change randomly with their locations, resulting in their probability distribution being described by the random field models. [PERSON] [14] proposed a simple and practical procedure of stochastic finite element analysis to obtain the statistical characteristics of the deformation of structural members whose material properties vary randomly along their axes. For concrete structures, [PERSON] [15] presented a probabilistic analysis method that took into account the material uncertainties modeled by means of random fields and failure due to cracking. [PERSON] [16] developed a stochastic meshless method for reliability analysis of linear-elastic structures with spatial variability of material properties, and the effectiveness of the developed method was verified by numerical examples. [PERSON] [17; 18] studied the influence of the spatial variability in the local corrosion of steel on the reliability and vulnerability of reinforced concrete (RC) structures. The results show that spatial variability has a great effect on the failure probability of RC structures. However, few studies have considered the influence of random fields on the time-dependent reliability of PSC bridges. [PERSON] [19] presented a random field-based reliability methodology for a PSC box-girder bridge in which the inertia moment and live load were modeled as random fields and discretized by the midpoint method.