## 5 Conclusions  
In this paper, the lack of unified consensus for a quantitative assessment of corroded reinforced concrete pier columns is verified, and it is found that existing codes are not able to provide the quantitative calculation of corroded RC eccentric compression members. To address this deficiency, the interpolation and Fourier fitting model are employed to construct the M-N curve, and are validated by the existing test data and models. Some concluding remarks can be summarized as follows.  
(1) The traditional method needs to determine the eccentric compressive properties (large or small eccentricity) first, and then calculate the bearing capacity according to different formulas. The stress state of compressed steel bars also needs to be judged, which makes the traditional method cumbersome and inconvenient in engineering applications. In addition, the inconsistency between the formulas for calculating the bearing capacity of compression members with large and small eccentricity makes the derivatives at the balanced failure point unequal. A cusp appears on the M-N curve, and the curve is not smooth. To resolve the above imperfections, this paper proposes a new construction method for the M-N curve. The proposed model connects bending, eccentric compression and axial compression by a unified formula, and achieves a better interpretation of the continuous transition of the adjacent stress state with simple calculations and less computational complexity.  
(2) Comparison results based on the experimental data from forty-five corroded eccentric compression columns demonstrated that the prediction performance of the proposed method is satisfactory with an average ratio of predicted results to test results of 1.06 and a standard deviation of 0.14; the satisfactory results are also obtained from comparison with the existing models.  
(3) The unified model provides a new feasible method for the construction of the M-N curve used for bearing capacity evaluation of deteriorated RC members. The theories are well designed and established, and the prediction result is more comprehensive which can intuitively reflect the effect of corrosion on the bearing capacity under different mechanical conditions.  
In this work, the relationship between the decrease in bearing capacity and corrosion rate is established. To predict the time-varying bearing capacity of actual bridge structures, the model of corrosion initiation time and corrosion rate under different environments should be analyzed for further study.  
Figure 9: Calculated values of basis points under different parameter combinations.  
**Author Contributions:** [PERSON] conceived and wrote this paper. [PERSON] offered useful suggestions for the preparation and writing the paper. [PERSON] collected the data. [PERSON] advised on the data analysis and paper organization. [PERSON] involved in paper writing.  
**Funding:** This work was supported by the National Key Research and Development Program of China (2017 YFC0806007), the National Science Fund for Distinguished Young Scholars (51425801), the Technology Innovation and Application Demonstration Project of Chongqing (gctc2017 rgzn-zdyfX0018, csc2018 gcx-mszdX0084), the Science and Technology Planning Project of Yunnan Province of China (2017 IB025), and the State Key Laboratory Base of the Mountain Bridge and Tunnel Engineering(Chongqing Jiaotong University: CQSLBF-Y14-1).  
**Conflicts of Interest:** The authors declare no conflict of interest.