## 1 Introduction  
As the key node of interoperability of traffic systems, the bridge is a vital guarantee for the development of the economy and social safety [1]. However, the problem of deterioration of bridge structures has become acute as time goes on [2; 3; 4]. According to the Federal Highway Administrationreport, nearly 40% of the 61,5002 bridges in the United States have been in service for more than 50 years by the end of 2017, and 54,560 bridges are defective [5]. The capital requirement for repairing these bridges is over $123 billion. Similarly, the safety situation of bridges in China is not optimistic. At present, about 13% of bridges in China have serious problems caused by structural damage and natural deterioration [6]. Steel corrosion is recognized as one of the most severe deterioration factors that affect the durability of reinforced concrete (RC) bridges. Thus, the research on bearing capacity time-varying evolution of corroded structures is of great scientific significance and engineering application value in order to determine the operation status of existing bridges, as well as reduce the maintenance costs. The multiple effects of reinforcement corrosion on structures mainly include three aspects, that is, the deterioration of reinforcement performance [7], the concrete cover cracking and spalling [8], and the failure of the bonding mechanism between concrete and reinforcement [9]. Many studies have taken into account the above effects on the capacity assessment, such as nondestructive testing methods, which can use direct approaches, e.g., [PERSON] et al. [10] and [PERSON] et al. [11] investigated the correlation between corrosion-induced surface crack width and level of internal corrosion; or indirect methods, e.g., [PERSON] et al. [12] examined the corrosion effects on the seismic capacity of reinforced concrete structures, which often requires a transition from material damage to structural performance degradation. In bridge structures, eccentric compression members such as piers and main arches often act as the crucial bearing units. The damage of these eccentric compression members is often more unacceptable than that of other components. AASHTO 2011 (American code) [13] and JTG/T J21-2011 (Chinese code) [14] provide the evaluation methods for existing bridges, which are introduced briefly in Appendices A and B. However, in the methods provided, the deteriorated resistance of serving RC bridges is simulated as a product of initial resistance and deterioration coefficients. The deterioration coefficients depend on detection data, which reflect the geometric characteristics, damage status and state parameters. Although the deterioration coefficients are quantified by a fixed rating table, the calculation process is still descriptive. The calculation results inevitably include the effects of the subjectivity of state rating and uncertainty of weight division. There is still a certain gap between the descriptive assessment and quantitative evaluation in the practical engineering application. To quantitatively evaluate the time-varying characteristics of the corroded RC columns bearing capacity, experimental research [15; 16; 17] has been carried out. Moreover, the bearing capacity models of corroded RC columns have been developed, which can be generally classified into two categories. One is the piecewise calculation method, which divides RC eccentric compression columns into an axial column, small eccentric compression column and large eccentric compression column. According to the different stress state of the components, the formulas for calculating the bearing capacity of corroded RC columns are segregated. For example, [PERSON] et al. [18] examined the relationships between the average cross-sectional area loss of the steel bar, the average and maximum crack widths of concrete cover, and the strength loss of the RC columns, and proposed the load-carrying capacity model of large eccentric and small eccentric columns, respectively. [PERSON] et al.