图 1  高压电脉冲等效放电电路

L为回路电感，用来储存磁能，其电流不能突变，表现为感性阻抗；C为放电电容，用来储存电能，其电压U不能突变，表现为容性阻抗；R_z为放电装置的电阻；R_ch为电弧通道的电阻；S为开关；下同

Figure 1.  Equivalent discharge circuit of high-voltage electrical pulse

图 2  高压电脉冲放电过程步骤

$ {U}_{0} $为$ t=0 $时放电电压；i'为回路电流；P为冲击波压力；下同

Figure 2.  Steps of high-voltage electrical pulse discharge process

图 3  计算模型示意图

Ω为岩体计算域；$ {\sigma }_{x} $为 $ x $方向初始地应力；$ {\sigma }_{y} $为 $ y $方向初始地应力；$ \mathit{\Gamma } $为预制裂缝（裂缝集合）；$ r $为钻孔半径（通道半径）；$ {l}_{0} $为相场长度尺度参数；下同

Figure 3.  Schematic diagram of calculation model

图 4  RLC 电路电流−电压时程曲线

Figure 4.  Current-voltage time-history curves of RLC circuit

图 5  冲击波压力时程曲线

Figure 5.  Time-history curve of shock wave pressure

图 6  相场模型数值迭代计算步骤

${\boldsymbol{u}}_{i}^{j=0} $，${\boldsymbol{H}}_{i}^{j=0} $，$\phi_{i}^{j=0} $分别为第i个计算步、第0次迭代时的位移场、历史场、相场的初始值；${\boldsymbol{u}}_i^j $，${\boldsymbol{H}}_{i}^{j} $，$\phi_i^j $分别为第i个计算步、第j次迭代时的位移场、历史场、相场；${\boldsymbol{u}}_{i}^{j+1} $，${\boldsymbol{H}}_{i}^{j+1} $，$\phi_{i}^{j+1} $分别为第i个计算步、第j+1次迭代更新后的位移场、历史场、相场。N-R为Newton-Raphson

Figure 6.  Numerical iterative calculation steps of phase-field model

图 7  本模型与文献[39]结果对比

Figure 7.  Comparison between this model and results from reference ^[39]

图 8  高压电脉冲作用下岩体裂缝扩展演化规律

云图颜色仅表征裂缝、损伤场及位移场的空间分布形态，不可作为定量数值读取依据，图12同此说明

Figure 8.  Propagation and evolution patterns of rock fractures under high-voltage electrical pulse

图 9  0～600 μs 岩体裂缝扩展、损伤面积与冲击波压力演化曲线

Figure 9.  Evolution curves of rock mass fracture propagation, damage area, and shock wave pressure during 0–600 μs

图 10  高压电脉冲作用下不同时刻岩体位移场云图

Figure 10.  Contour maps of rock mass displacement field at different moments under high-voltage electric pulse

图 11  电脉冲作用点位移与冲击波压力时程曲线

Figure 11.  Time-history curves of displacement at electrical pulse application point and shock wave pressure

图 12  不同放电电压U₀下冲击波压力时程(a)及初始裂缝扩展至模型边界时岩体位移云图(b～d)

Figure 12.  Time-history curves of shock wave pressure (a) and displacement contours of rock mass as the initial crack extends to the model boundary (b-d) under different discharge voltages U₀

图 13  不同放电电压U₀下初始裂缝增长长度与岩石损伤面积

Figure 13.  Initial fracture growth length and rock damage area under different discharge voltages U₀

图 14  不同电容C下冲击波压力时程(a)与峰值时刻t=300 μs时岩体破裂统计结果(b)

Figure 14.  Time-history curves of shock wave pressure (a) and statistical results of rock mass fracture at peak time t=300 μs (b) under different capacitances C

图 15  不同回路电感L下冲击波压力时程(a)与峰值时刻t=300 μs时岩体破裂统计结果(b)

Figure 15.  Time-history curves of shock wave pressure (a) and statistical results of rock mass fracture at peak time t=300 μs (b) under different inductances L

图 16  不同等离子体通道长度l_ch下冲击波压力时程(a)与峰值时刻t=300 μs时岩体破裂统计结果(b)

Figure 16.  Time-history curves of shock wave pressure (a) and statistical results of rock mass fracture at peak time t=300 μs (b) under different plasma channel lengths l_ch