# Dynamic Simulation of Underground Cable Laying for Digital Three-Dimensional Transmission Lines
## 4 Engineering Examples and Analysis of Results
### Safety Survey and Hazard Analysis  
#### 4.2.1 Analysis of Axial Tension During the Initial Traction Period  
The maximum permissible traction cable is generally based on the cable-bearing steel tensile strength of one-quarter of the determination, that is, according to the tensile strength multiplied by the cross-sectional area of the steel for the maximum traction. However, due to the differences in traction, the general cable maximum allowable traction is calculated as follows:  
\[T_{m}=K\delta S \tag{11}\]  
where \(K\) is the correction factor, the power cable takes 1, the control cable takes 0.6; \(\delta\) is the allowable tensile strength of the material, N/mm\({}^{2}\) (specific values refer to Table 4); S is the cross-sectional area of the material, mm\({}^{2}\).  
Taking the cable laying system shown in Figure 8 as an example, the maximum allowable cable traction force is calculated to be 56 kN. The following figure shows the axial traction force of the cable micro-section during cable laying.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Stressed Material** & \
\begin{tabular}{c} **Tensile Strength/** \\ **(N/mm\({}^{2}\))** \\ \end{tabular} &
\begin{tabular}{c} **Applicable Traction** \\ **Methods** \\ \end{tabular} \\ \hline Copper conductor & 70 & traction head \\ Aluminum conductor & 40 & traction head \\ Polyethylene sheath & 7 & hauling net cover \\ Cross-linked polyethylene sheath & 6 & hauling net cover \\ \hline \hline \end{tabular}
\end{table}
Table 4: Maximum allowable traction strength of power cable.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Cable Location** & **Real Value/N** & **Simulation Value/N** & **Error** \\ \hline
1 & & 12,200.36 & 5.4\% \\
9 & & 12,290.10 & 4.7\% \\
17 & & 12,590.64 & 2.4\% \\
89 & & 12,770.32 & 1.1\% \\
121 & & 13,000.25 & 0.8\% \\
197 & & 13,100.22 & 1.5\% \\
237 & & 13,150.98 & 1.9\% \\
379 & & 13,440.74 & 4.2\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: The error between the real value and simulation value.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Mean Error** & **Max Error** \\ \hline Reference [4] & 3.89\% & — \\ Reference [5] & 3.21\% & 8.9\% \\ Reference [7] & 3.18\% & 6.3\% \\ This paper & 2.75\% & 5.4\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of error in the paper and Refs. [4,5,7].  
Figure 10 presents that in the initial traction cable, the cable axial tension increases instantaneously and then slowly fluctuates to a stable value of about 13 s. The cable laying process of axial tension gradually stabilized at about 13 kN in the cable within the maximum permissible traction force, which is in line with the requirements of construction safety.  
In the initial stage of the traction axial force, changes in movement make the cable axial tension suddenly increase, followed by a gradual stabilization of its axial tension up to 49 kN. The cable can withstand a maximum of 56 kN; therefore, at the beginning of the laying of the cable, the traction speed should be controlled, and the traction force should gradually be increased, minimizing the transient tension to ensure the safety of construction.