**5. Spatial Diffusion Model of Corrosion Factors**

Based on the analysis results above, the spatial diffusion model of corrosion factors in the cable can be established under various tilt angles, temperatures, humidity, corrosion periods, and defect areas, divided into upper and lower cable sections for display. Firstly, the spatial diffusion model of corrosion factors in the square hole defective cable is exhibited. The results are shown below.

(1) The spatial diffusion model of corrosion factors in the A1 cable segment.

$$\begin{cases} \mathbf{C}\_{5} = 0.387 \cdot \left( t \right)^{0.32} \cdot \left( h \right)^{0.08} \cdot \left( T\_{1} \right)^{0.12} \cdot \left( W \right)^{0.52} \cdot \left( \cos \theta \right)^{0.43} + 0.216\\ D = \left[ 11.42 \cdot \left( t \right)^{0.23} \cdot \left( h \right)^{0.05} \cdot \left( T\_{1} \right)^{0.11} \left( W \right)^{0.54} \cdot \left( \cos \theta \right)^{0.41} + 1.231 \right] \times 10^{-10} \right. \\ C(x, y, z) = \mathbf{C}\_{S} \times \left( 1 - \operatorname{erf} \frac{x}{2 \sqrt{D \times t}} \times \operatorname{erf} \frac{y}{2 \sqrt{D \times t}} \times \operatorname{erf} \frac{z}{2 \sqrt{D \times t}} \right) \end{cases} \tag{16}$$

(2) The spatial diffusion model of corrosion factors in the B1 cable segment.

$$\begin{array}{l} \mathbf{C}\_{s} = \eta\_{1} \left[ 0.387 \cdot (\boldsymbol{h})^{0.32} \cdot (\boldsymbol{h})^{0.08} \cdot (\boldsymbol{T}\_{1})^{0.12} (\boldsymbol{W})^{0.52} \cdot (\cos \boldsymbol{\theta})^{0.43} + 0.216 \right] \\ D = \eta \left[ 11.42 \cdot (\boldsymbol{t})^{0.23} \cdot (\boldsymbol{h})^{0.05} \cdot (\boldsymbol{T}\_{1})^{0.11} (\boldsymbol{W})^{0.54} \cdot (\cos \boldsymbol{\theta})^{0.41} + 1.231 \right] \times 10^{-10} \\ \mathbf{C}(\mathbf{x}, \boldsymbol{y}, \boldsymbol{z}) = \mathbf{C}\_{S} \times \left( 1 - \boldsymbol{erf} f \frac{\mathbf{x}}{2\sqrt{D \times t}} \times \boldsymbol{erf} f \frac{\mathbf{y}}{2\sqrt{D \times t}} \times \boldsymbol{erf} f \frac{\boldsymbol{z}}{2\sqrt{D \times t}} \right) \end{array} \tag{17}$$

Among them, the values of *η*<sup>1</sup> and *η* under different tilt angles are shown in Table 5. The spatial diffusion model of corrosion factors within the annular defect cable can be depicted as follows using the approach described above.

(1) The spatial diffusion model of corrosion factors in the C1 cable segment.

$$\begin{array}{l} \mathsf{C}\_{s} = 0.393 \cdot (t)^{0.24} \cdot (h)^{0.12} \cdot (T\_{1})^{0.16} (\mathsf{W})^{0.57} \cdot (\cos \theta)^{0.46} + 0.413\\ D = \left[13.32 \cdot (t)^{0.26} \cdot (h)^{0.06} \cdot (T\_{1})^{0.13} (\mathsf{W})^{0.63} \cdot (\cos \theta)^{0.47} + 1.572 \right] \times 10^{-10} \end{array} \tag{18}$$
  $\mathsf{C}(x, y, z) = \mathsf{C}\_{S} \times \left(1 - \mathrm{erf} \frac{x}{2\sqrt{D \times t}} \times \mathrm{erf} \frac{y}{2\sqrt{D \times t}} \times \mathrm{erf} \frac{z}{2\sqrt{D \times t}} \right)$ 

(2) The spatial diffusion model of corrosion factors in the D1 cable segment.

$$\begin{cases} \mathbf{C}\_{s} = \eta\_{2} \left[ 0.393 \cdot (t)^{0.24} \cdot (h)^{0.12} \cdot (T\_{1})^{0.16} (\mathcal{W})^{0.57} \cdot (\cos \theta)^{0.46} + 0.413 \right] \\ D = \eta\_{3} \left[ 13.32 \cdot (t)^{0.26} \cdot (h)^{0.06} \cdot (T\_{1})^{0.13} (\mathcal{W})^{0.63} \cdot (\cos \theta)^{0.47} + 1.572 \right] \times 10^{-10} \\ \mathbf{C}(x, y, z) = \mathbf{C}\_{\mathcal{S}} \times \left( 1 - \operatorname{erf} \frac{x}{2\sqrt{D \times t}} \times \operatorname{erf} \frac{y}{2\sqrt{D \times t}} \times \operatorname{erf} \frac{z}{2\sqrt{D \times t}} \right) \end{cases} \tag{19}$$

Among them, Table 5 shows the values of *η*<sup>2</sup> and *η*<sup>3</sup> under various tilt angles. The concentration of corrosion factors at each spatial position of the cable was calculated using this model to verify the accuracy of the model above. The calculated results were compared with the measured results, as shown in Figures 11–14. The findings demonstrate that the prediction results of the model are lower than the experimental test results, and the relative error between the two is within 15%, illustrating that the prediction model proposed in this article has a certain accuracy.

**Figure 11.** Comparison results of the A1 segment cable (defect size is 2 cm × 2 cm): (**a**) tilt angle 30◦; (**b**) tilt angle 45◦.

**Figure 12.** Comparison results of the B1 segment cable (defect size is 2 cm × 2 cm): (**a**) tilt angle 30◦; (**b**) tilt angle 45◦.

**Figure 13.** Comparison results of the C1 segment cable (defect size width is 3 cm): (**a**) tilt angle 0◦; (**b**) tilt angle 30◦.

**Figure 14.** Comparison results of the D1 segment cable (defect size width is 3 cm): (**a**) tilt angle 0◦; (**b**) tilt angle 30◦.
