## 4 Analysis of Pipeline Overvoltage under the Action of Multi-Tower Flow
### The Influence of Soil Resistivity  
In order to investigate the impact of soil resistivity on the overvoltage of natural gas pipelines at the cross-crossing during lightning strikes, several parameters were set as follows: the lightning peak current (I\({}_{0}\)) was fixed at 50 kA, the distance between the \"tube-line\" (\(d_{\mathrm{gp1}}\)) was set to 40 m, and the cross angle of the \"tube-line\" (\(\beta\)) was 0\({}^{\circ}\). The soil resistivity (\(\rho\)) was varied, with values of 200 \(\Omega\cdot\)m, 500 \(\Omega\cdot\)m, 800 \(\Omega\cdot\)m, 1000 \(\Omega\cdot\)m, 1200 \(\Omega\cdot\)m, and 1500 \(\Omega\cdot\)m being selected sequentially. The current waveform of the lightning current passing through the T\({}_{0}\) and T\({}_{\mathrm{R1}}\) tower grounding grid under different soil resistivity conditions is shown in Figure 6. The resulting lightning overvoltage amplitude of the natural gas pipeline at the cross-crossing is presented in Figure 9. Additionally, Figure 10 illustrates the potential distribution of the tower grounding grid and the natural gas pipeline at the cross-crossing for different soil resistivity values. Figure 9: The influence of soil resistivity on overvoltage of natural gas pipeline at cross-crossing. (**a**) Induced voltage amplitude of metal layer and insulation layer of pipeline. (**b**) Voltage amplitude of pipeline insulation layer. According to Figure 9a, it can be observed that the induced voltage of the metal layer and insulation layer of the natural gas pipeline increases as the soil resistivity increases. When the soil resistivity increases from 200 \(\Omega\cdot\)m to 1500 \(\Omega\cdot\)m, the induced electric potential amplitude of the natural gas pipeline and the induced voltage amplitude of the insulation layer increase from 9.68 kV and 13.07 kV to 59.63 kV and 64.80 kV, respectively. This represents an increase of 516.01% and 395.79% for the induced electric potential amplitude and induced voltage amplitude, respectively. The results in Figure 9b demonstrate that as soil resistivity increases, the pressure resistance of the pipeline insulation layer gradually increases. However, after reaching a certain point, the increase in pressure resistance becomes less pronounced. For instance, when the soil resistivity increases from 200 \(\Omega\cdot\)m to 1000 \(\Omega\cdot\)m, the withstand voltage of the insulating layer increases from 4.25 kV to 7.23 kV, representing a 70.12% increase. On the other hand, when the soil resistivity increases from 1000 \(\Omega\cdot\)m to 1500 \(\Omega\cdot\)m, the withstand voltage of the insulating layer only increases from 7.23 kV to 7.35 kV, resulting in a mere 1.66% increase. The reason for studying the variation law mentioned above is that an increase in soil resistivity can impede the spreading of the tower grounding grid to the surrounding soil. As a result, the mine current is more likely to spread towards the far end of the extension ray, leading to an increase in the effective spreading area of the tower grounding grid and the soil potential near the grounding grid. This, in turn, exacerbates the impact of the tower grounding grid on the gas pipeline. When the soil resistivity prevents the tower grounding grid from dispersing into the surrounding soil, the induced voltage and withstand voltage of the metal layer and insulating layer of the gas pipeline increase. Conversely, when the mine current decreases, the induced voltage and withstand voltage of the metal layer and insulating layer of the gas pipeline decrease. Therefore, the interaction of these two factors causes the induced voltage and withstand voltage of the metal layer and insulating layer of the gas pipeline to exhibit an upward trend. Figure 10 illustrates that an increase in soil resistivity obstructs the spread of the tower grounding grid box into the surrounding soil.