## 3 Model Validation
### Validation by Existing Models  
In this section, the performance of this proposed method is further demonstrated on a numerical example in [22; 26], referring to a column suffering from corrosion attack. As shown in Figure 7, the column has a square cross-section of side 610 mm. The longitudinal reinforcement is constituted by four 28-mm bars for each side, with a cover of 28 mm. The stirrups are constituted by 12-mm bars with a pitch equal to 250 mm. The reinforcement ratio is 1.98%. All longitudinal reinforcements and stirrups have the same corrosion rate. Table 1 gives the mathematical model of the moment-axial force interaction diagrams established by the proposed method. As can be seen from Table 1, the Fourier model fitting to interpolating points has high accuracy with a goodness of fit close to 1, which can meet the need of constructing a smooth M-N curve. Figure 6: Comparison between the predicted values and experimental data. As can be seen from Figure 7, the proposed method is in good agreement with the M-N curves calculated by [22] (numerical model) and [26] (simplified model with three branches and four points). Taking data in [22] as the reference value, the maximum relative percentage error of axial compression point, pure bending point and balanced failure point is only 7.9% under the no corrosion condition. For a corrosion rate of 50%, the scatter is only in the range of 3.8% for compression. Figure 7 also shows that the bearing capacity of reinforced concrete members is significantly reduced with an increase in corrosion degree. When the corrosion rate increases from 10% to 50%, the bearing capacity of the axial compression point degenerates from 31.4% to 45.2%, while the decrease rate in pure bending point ranges from 25.4% to 77.4%. The balanced failure point moves down and to the left and the critical eccentricity at this point increases first and then decreases with an increase in corrosion degree. When the corrosion rate increases from 10% to 50%, the axial force of the balanced failure point decreases from 48.0% to 67.6%, while the bending moment decreases from 30.3% to 65.9%. In addition, as it directly connects three kinds of mechanical states: pure bending, eccentric compression and axial compression, the proposed model could better explain the continuous transition of the adjacent stress state. Compared with the above two models, the model proposed in this paper is smoother and has less computational complexity with only three characteristic points needing to be calculated. Furthermore, this paper discusses the effects of different deterioration factors on the degradation of bearing capacity under different loading conditions. For instance, Figure 8 shows the strength contributions of the four parts \(A_{1\text{c}}\), \(A_{2\text{c}}\), \(A_{3\text{c}}\) and \(A_{1\text{red}}\) on the axial compression bearing capacity under different corrosion levels. As seen from Figure 8, with the increase in the corrosion rate, the contributions from \(A_{1\text{c}}\) and \(A_{2\text{c}}\) decrease significantly because of the tremendous influence of concrete cracking, which accounts for 80% of the total decline when the corrosion rate is 10%, while for a corrosion rate of 50%, the decrement proportion is 73%; the contribution reduction of \(A_{1\text{red}}\) comes second; and \(A_{3\text{c}}\) changes least. Thus, among the several factors of deterioration in axial compression, concrete cracking predominates.