## 1 Introduction  
Reinforced concrete circular columns are widely used for infrastructure construction. The columns exposed to the marine environment without added protection are continuously affected by chloride corrosion [1]. Corrosion activates the degradation of materials, causing loss of the bearing capacity of the column. The existing literature reported that a large cost of repair and replacement of US bridges every year are due to corrosion [2]. For the purpose of reducing the economic loss and insuring service security, predicting the chloride concentration on the surface of rebar during long-term servicing accurately using a reliable diffusion model is crucial. [PERSON] et al. [3] first used the one-dimensional (1D) [PERSON]'s second law to obtain a chloride diffusion solution considering a constant diffusion coefficient. [PERSON] and [PERSON] [4] found a power law relationship between the diffusion coefficient and concrete age. They considered the diffusion coefficient as variable with time, updating and improving the 1D diffusion mathematic model. On the basis of this new diffusion model, several modified diffusion models are currently applied for the estimation of chloride penetration. For example, in the Duracrete report, a simplified 1D diffusion mathematical model considering the environment, test, and execution factors into diffusion coefficients was adopted as the basic model in durability design [5]. This diffusion model in the Duracrete report is also widely used to predict the time to corrosion initiation of RC structure subject to chloride corrosion [6; 7]. [PERSON] and [PERSON] [8] modified the model considering the surface chloride concentration as time-dependent parameter. [PERSON] et al. [9] also developed the model considering the effect of concrete skin on diffusion mechanism. Obviously, numerous slab diffusion models based on 1D coordinates are available. However, in recent years, researchers are continuously clarifying the impact of the surface geometry element on chloride diffusion. [PERSON] and [PERSON] [10] employed finite difference (Crank-Nicolson) based on the two-dimensional (2D) [PERSON]'s second law to calculate the probability of corrosion initiation in each bar inside a rectangular cross-section. The developed computer program replaces the difficult metathetic solution method with finite element analysis (FEA), which is effective in simulating chloride diffusion in an irregular section. [PERSON] et al. [11] adopted the FEA to describe chloride diffusion in a rectangular cross-section, obtaining the non-uniform corrosion state of rebar encased in concrete. [PERSON] et al. [12] estimated the corrosion initiation time of rebar in an RC circular column with three-dimensional (3D) coordinates using the same analysis method. [PERSON] et al. [13] used the FEA to calculate the chloride concentration distribution of prestressed T-beam. For an RC structure, the achieved construction quality usually involves high scatter and variability. Meanwhile, the surrounding environment affects chloride penetration through concrete steadily. A probability-based estimation of the chloride diffusion process is necessary. Compared with FEA, a concise mathematical diffusion model is more convenient in achieving this. For a circular section, [PERSON] and [PERSON] [14] proposed a circular diffusion formulation dependent on [PERSON]'s second law with polar coordinates, assuming a constant diffusion coefficient. The results showed that for a circular RC section, the chloride concentration estimated by the circular diffusion model is higher than that estimated by the slab model for the same position. Nevertheless, the earlier experimental study has revealed that the diffusion coefficient was a time-dependent variable [15]. [PERSON] et al. [16] gave a detailed explanation about the character of the diffusion coefficient in term of long-term transport processes. [PERSON] et al. [17] pointed out that the diffusion coefficient decreases with time because of further hydration of the cement.