基于分形理论的雷电冲击土体等离子体通道发展研究

等离子体通道对岩土体破坏过程具有内动力作用，针对雷电冲击岩土体后的等离子体通道发展进行研究，从电击穿的角度构建岩土体击穿通道的随机概率模型，采用拉普拉斯方程计算电场，引入分形理论计算发展概率，得到等离子体通道路径模拟图。采用盒维数法计算分形维数来反映等离子体通道发展情况，分析了土体电阻率、雷电流幅值及内部电压降对分形维数的影响规律。结果表明：随着土体电阻率增大，分形维数逐渐减小；随着雷电流幅值增大，分形维数逐渐增大；随着土体内部电压降增大，分形维数逐渐增大，且在土体电阻率越小时，分形维数变化越显著。研究证明，运用二维图像方式直观表现出岩土体内等离子体通道发展，并利用分形几何定量描述岩土体内等离子体通道的发展规律，有助于预测岩土体破坏过程的发展，便于进一步研究岩土体电击穿的物理本质。

Development of the plasma channels in lightning-impacted soil based on the fractal theory

The plasma channel has an internal dynamic effect on the breaking process of the geotechnical body. For the development of plasma channel of the geotechnical body after the lightning strikes, the stochastic probability model of the geotechnical body breakdown channel was constructed from the viewpoint of the electric breakdown. The electric field was calculated by the Laplace equation, and the development probability was calculated by introducing the fractal theory. Then the simulation diagram of the plasma channel trajectory was obtained. The fractal dimension was calculated by the box dimension method to reflect the development process of the plasma channel. The influence of soil resistivity, lightning current amplitude and internal voltage drop on the fractal dimension was analyzed. The results showed that the fractal dimension decreased as the soil resistivity increased. With the increase of lightning current amplitude, the fractal dimension gradually increased, and the change of fractal dimension was more significant when the resistivity of soil was smaller. As the voltage drop inside the soil increased, the fractal dimension gradually increased. In this paper, the development of plasma channels within the geotechnical body was visualized by means of the two-dimensional images, and the development of plasma channels within the geotechnical body was quantitatively described by using fractal geometric relations, which can help predict the development law of the damage process of the geotechnical body and facilitates the physical nature of the electric breakdown of the geotechnical body.