Experimental Investigation and Mechanism Analysis on Rock Damage by High Voltage Spark Discharge in Water: Effect of Electrical Conductivity

High voltage spark discharge (HVSD) could generate strong pressure waves that can be combined with a rotary drill bit to improve the penetration rate in unconventional oil and gas drilling. However, there has been little investigation of the effect of electrical conductivity on rock damage and the fragmentation mechanism caused by HVSD. Therefore, we conducted experiments to destroy cement mortar, a rock-like material, in water with five conductivity levels, from 0.5 mS/cm to 20 mS/cm. We measured the discharge parameters, such as breakdown voltage, breakdown delay time, and electrical energy loss, and investigated the damage mechanism from stress waves propagation using X-ray computed tomography. Our study then analyzed the influence of conductivity on the surface damage of the sample by the pore size distribution and the cumulative pore area, as well as studied the dependence of internal damage on conductivity by through-transmission ultrasonic inspection technique. The results indicated that the increase in electrical conductivity decreased the breakdown voltage and breakdown delay time and increased the energy loss, which led to a reduction in the magnitude of the pressure wave and, ultimately, reduced the sample damage. It is worth mentioning that the relationship between the sample damage and electrical conductivity is non-linear, showing a two-stage pattern. The findings suggest that stress waves induced by the pressure waves play a significant role in sample damage where pores and two types of tensile cracks are the main failure features. Compressive stresses close horizontal cracks inside the sample and propagate vertical cracks, forming the tensile cracks-I. Tensile stresses generated at the sample–water interface due to the reflection of stress waves produce the tensile cracks-II. Our study is the first to investigate the relationship between rock damage and electrical conductivity, providing insights to guide the design of drilling tools based on HVSD.


Introduction
Improving the rate of penetration (ROP) is the focus of research in petroleum industries, because ROP is inversely proportional to drilling cost in unconventional reservoirs, which is typically 30% to 40% of the total well costs. Drilling at great depth is challenging, due to the hostile environment and the enhanced mechanical properties of the rock, making conventional rotary drilling methods inadequate. Over the past few decades, researchers and engineers have proposed some unconventional drilling techniques based on a different rock damage mechanism rather than using the drill bit's mechanical force to cut the rock. Laser drilling applies a continuous high-power laser beam to remove

Sample Preparation
The absolute mass ratio of water, ordinary 42.5R Portland cement, and sand for pouring mortar was 0.5:1:1.8. The mechanical properties of the samples after 28 days of curing in water are shown in Table 1. Cubic samples of 100 mm in length, 100 mm in width, and 50 mm in height were prepared, from which some cylindrical samples of 25 mm in diameter and 30 mm in thickness were cut out ( Figure 2). Mortar, like natural rocks, is a brittle material, and is often used in rock-breaking experiments, so the rock-breaking mechanism obtained from mortar is also applicable to natural rocks [13,23]. Since the mechanical properties of mortar samples from the same batch are almost identical, whereas the properties of natural rocks vary greatly, we used mortar to quantitatively study the effect of conductivity on rock damage.

Experimental Procedure
Experiments were conducted with high voltage discharge equipment, which consisted of a high voltage pulse power supply, a pressure wave generator, and a monitoring system. Figure 3a-c shows the diagram of the experimental equipment, the pulsed power supply components, and the pressure wave generator, respectively.
The power supply mainly comprised a transformer, a rectifier, a high voltage capacitor bank, and an air-gap switch. When the power supply worked, the transformer raised the 220 V alternating current (AC) to a maximum of 70 kV, and then the rectifier converted the AC into the direct current (DC) to fully charge the capacitor bank. When the air-gap switch was closed, the energy stored on the capacitor was released into the pressure wave generator through high-voltage coaxial cables,

Sample Preparation
The absolute mass ratio of water, ordinary 42.5R Portland cement, and sand for pouring mortar was 0.5:1:1.8. The mechanical properties of the samples after 28 days of curing in water are shown in Table 1. Cubic samples of 100 mm in length, 100 mm in width, and 50 mm in height were prepared, from which some cylindrical samples of 25 mm in diameter and 30 mm in thickness were cut out ( Figure 2). Mortar, like natural rocks, is a brittle material, and is often used in rock-breaking experiments, so the rock-breaking mechanism obtained from mortar is also applicable to natural rocks [13,23]. Since the mechanical properties of mortar samples from the same batch are almost identical, whereas the properties of natural rocks vary greatly, we used mortar to quantitatively study the effect of conductivity on rock damage.

Experimental Procedure
Experiments were conducted with high voltage discharge equipment, which consisted of a high voltage pulse power supply, a pressure wave generator, and a monitoring system. Figure 3a-c shows the diagram of the experimental equipment, the pulsed power supply components, and the pressure wave generator, respectively.

Analysis of Damage Characteristics
The X-ray computed tomography (CT, nanoVoxel3502E, and imaging resolution of ≥0.5 μm) was applied to observe the microscopic features of cylindrical sample before and after damage, to understand the mechanism of rock damage caused by pressure waves. Our study used the number of pores, and the distribution of pore sizes on the sample surface, to quantify the effect of conductivity on the surface damage. The pores were approximated as two-dimensional circles. Those with a diameter of less than 1 mm were neglected because they were mostly air bubbles caused during the sample casting process.
Apart from surface damage, it is also necessary to study the internal damage of the sample. Microcracks, the main form of the internal damage, occurring inside the sample due to the impacts The power supply mainly comprised a transformer, a rectifier, a high voltage capacitor bank, and an air-gap switch. When the power supply worked, the transformer raised the 220 V alternating current (AC) to a maximum of 70 kV, and then the rectifier converted the AC into the direct current (DC) to fully charge the capacitor bank. When the air-gap switch was closed, the energy stored on the Energies 2020, 13, 5432 5 of 16 capacitor was released into the pressure wave generator through high-voltage coaxial cables, creating strong pressure waves from the electrohydraulic effect.
The capacitor bank contained four nominally 0.5 µF capacitors in parallel, providing operating pulse energy from 50 J/pulse up to 4.9 kJ/pulse. The pressure wave generator consisted of a cubic tank with 80 cm sides filled with water of varying conductivity, a pair of electrodes, and a sample clamping table. The electrodes were made of stainless steel with a tapered tip, 17 cm long and 1.5 cm in diameter. The sample was placed on the clamping table and confined by a baffle to prevent it from being moved by pressure waves. The gap between electrodes and the distance between the sample surface and the electrodes were then adjusted to 5 mm. Water with different conductivities was filled in the pressure wave generator until the electrodes were completely submerged.
Next, the pulse power was turned on to increase the voltage across the capacitor bank to a preset value. Once the capacitor bank was fully charged, the air-gap switch was closed to provide electrical energy to the electrodes.
A strong electric field was built up between the electrodes to break down the water and form a spark channel, bridging the electrodes under the Joule heating effect (Figure 3a). The temperature and pressure in the plasma-filled channel rise dramatically in a short time (about tens of microseconds), pushing the water around the channel and radiating pressure waves. The magnitude of the pressure waves can reach several hundred MPa, and can destroy rocks with a wide range of mechanical properties.
The voltage and current waveforms were measured by a high-voltage probe (Pintech P6039A) and a Rogowski coil, respectively, and recorded with an oscilloscope (Tektronix TPS2024B, the bandwidth of 200 MHz, and sample rates of 2 GS/s).
A charging voltage of 38 kV, a capacitance of 2 µF, single 158 pulse energy of 1444 J, and a discharge number of five were set. Five solutions with different conductivities of 0.5 mS/cm (tap water), 5 mS/cm, 10 mS/cm, 15,136 mS/cm, and 20 mS/cm were prepared by mixing tap water and NaCl (99.5% purity). Three mortar samples were used for each type of water with different conductivity.

Analysis of Damage Characteristics
The X-ray computed tomography (CT, nanoVoxel3502E, and imaging resolution of ≥0.5 µm) was applied to observe the microscopic features of cylindrical sample before and after damage, to understand the mechanism of rock damage caused by pressure waves. Our study used the number of pores, and the distribution of pore sizes on the sample surface, to quantify the effect of conductivity on the surface damage. The pores were approximated as two-dimensional circles. Those with a diameter of less than 1 mm were neglected because they were mostly air bubbles caused during the sample casting process.
Apart from surface damage, it is also necessary to study the internal damage of the sample. Microcracks, the main form of the internal damage, occurring inside the sample due to the impacts of pressure waves and the interaction of the mortar particles with the stress waves, will hinder the propagation of acoustic waves, thereby attenuating the acoustic wave amplitude.
The acoustic wave amplitude was measured by an ultrasonic flaw detector (OLYMPUS 5077PR) with the through-transmission ultrasonic inspection technique ( Figure 4). A transmitter (transmitting waves) and a receiver (receiving waves) were attached to opposite sides of the sample that were not directly damaged by the pressure waves. The two transducers and the sample were coupled by the ultrasonic coupling agent to ensure the transmission efficiency of acoustic energy. The attenuation of the wave amplitude, A c , can be written in the form where A 0 is the ultrasonic wave amplitude measured before the sample was impacted by the pressure wave and A 1 is the wave amplitude after the impact of pressure wave.

Electrical Characteristics of Underwater Discharge at Different Conductivity
The voltage waveforms on the pair of electrodes were measured in water with different conductivity, and typical voltage waveforms are shown in Figure 5. The discharge voltage refers to the voltage on the positive electrode. The breakdown voltage is the voltage across the electrodes when the plasma channel is formed, and the time to breakdown is called breakdown delay time.
where Et = ½ C V 2 d, Epl = ½ C V 2 b (Vd is the discharge voltage, Vb is the breakdown voltage, and C is the capacitance of the capacitor bank). Figure 6 shows the experimental data on the breakdown voltage under different electrical conductivity. Each value is an average of 15 replicates with a 95% confidence interval. As the electrical

Electrical Characteristics of Underwater Discharge at Different Conductivity
The voltage waveforms on the pair of electrodes were measured in water with different conductivity, and typical voltage waveforms are shown in Figure 5. The discharge voltage refers to the voltage on the positive electrode. The breakdown voltage is the voltage across the electrodes when the plasma channel is formed, and the time to breakdown is called breakdown delay time.

Electrical Characteristics of Underwater Discharge at Different Conductivity
The voltage waveforms on the pair of electrodes were measured in water with different conductivity, and typical voltage waveforms are shown in Figure 5. The discharge voltage refers to the voltage on the positive electrode. The breakdown voltage is the voltage across the electrodes when the plasma channel is formed, and the time to breakdown is called breakdown delay time. (2) where Et = ½ C V 2 d, Epl = ½ C V 2 b (Vd is the discharge voltage, Vb is the breakdown voltage, and C is the capacitance of the capacitor bank). Figure 6 shows the experimental data on the breakdown voltage under different electrical conductivity. Each value is an average of 15 replicates with a 95% confidence interval. As the electrical is the breakdown voltage, and C is the capacitance of the capacitor bank).
Energies 2020, 13, 5432 7 of 16 Figure 6 shows the experimental data on the breakdown voltage under different electrical conductivity. Each value is an average of 15 replicates with a 95% confidence interval. As the electrical conductivity ranged from 0.5 mS/cm to 20 mS/cm, the breakdown voltage dropped from 31.1 kV to 14.8 kV. A similar result was also reported by Wang et al., where the breakdown voltage in 36 mS/cm KCL solution was lower than that in deionized water [24]. The mechanism of high voltage pulsed electrical breakdown in water indicates that the bubbles generated at the tip of the electrode are responsible for the breakdown of the water and the formation of the plasma channel [25][26][27]. In high-conductivity water, the electric field near the electrode tip produces a more intense field emission current, which will cause more water to evaporate and form more bubbles under the Joule heating effect, thus making electrical breakdown more likely to occur, which is manifested as a lower breakdown voltage on the voltage waveform.  [24]. The mechanism of high voltage pulsed electrical breakdown in water indicates that the bubbles generated at the tip of the electrode are responsible for the breakdown of the water and the formation of the plasma channel [25][26][27]. In highconductivity water, the electric field near the electrode tip produces a more intense field emission current, which will cause more water to evaporate and form more bubbles under the Joule heating effect, thus making electrical breakdown more likely to occur, which is manifested as a lower breakdown voltage on the voltage waveform.  Figure 7 shows the relationship between breakdown delay time, tb, and electrical conductivity. The most interesting aspect in this figure is that the tb at 0.5 mS/cm is significantly larger than that of the other conductivities, while the value of tb slightly decreases from 13 μs to 10.2 μs when the conductivity is increased from 5 mS/cm to 20 mS/cm. This result may be related to the Joule energy loss, Eloss (J), before water breakdown occurs, calculated by Equation (3)   Figure 7 shows the relationship between breakdown delay time, t b , and electrical conductivity. The most interesting aspect in this figure is that the t b at 0.5 mS/cm is significantly larger than that of the other conductivities, while the value of t b slightly decreases from 13 µs to 10.2 µs when the conductivity is increased from 5 mS/cm to 20 mS/cm. This result may be related to the Joule energy loss, E loss (J), before water breakdown occurs, calculated by Equation (3) Energies 2020, x FOR PEER REVIEW 7 of 16 conductivity ranged from 0.5 mS/cm to 20 mS/cm, the breakdown voltage dropped from 31.1 kV to 14.8 kV. A similar result was also reported by Wang et al., where the breakdown voltage in 36 mS/cm KCL solution was lower than that in deionized water [24]. The mechanism of high voltage pulsed electrical breakdown in water indicates that the bubbles generated at the tip of the electrode are responsible for the breakdown of the water and the formation of the plasma channel [25][26][27]. In highconductivity water, the electric field near the electrode tip produces a more intense field emission current, which will cause more water to evaporate and form more bubbles under the Joule heating effect, thus making electrical breakdown more likely to occur, which is manifested as a lower breakdown voltage on the voltage waveform.  Figure 7 shows the relationship between breakdown delay time, tb, and electrical conductivity. The most interesting aspect in this figure is that the tb at 0.5 mS/cm is significantly larger than that of the other conductivities, while the value of tb slightly decreases from 13 μs to 10.2 μs when the conductivity is increased from 5 mS/cm to 20 mS/cm. This result may be related to the Joule energy loss, Eloss (J), before water breakdown occurs, calculated by Equation (  Energies 2020, 13, 5432 8 of 16 Figure 8 shows that the electrical energy leaking into the water increases with increasing electrical conductivity. The major role of E loss is to generate Joule heat in the water and form bubbles that contribute to the formation of electrical breakdown. Therefore, increasing the E loss helps to reduce the breakdown delay time. When the conductivity is increased from 0.5 mS/cm to 5 mS/cm, E loss increases by 71%, which explains the significant decrease in the breakdown delay time from 48 µs to 13 µs in this conductivity range (Figure 7).
Energies 2020, x FOR PEER REVIEW 8 of 16 Figure 8 shows that the electrical energy leaking into the water increases with increasing electrical conductivity. The major role of Eloss is to generate Joule heat in the water and form bubbles that contribute to the formation of electrical breakdown. Therefore, increasing the Eloss helps to reduce the breakdown delay time. When the conductivity is increased from 0.5 mS/cm to 5 mS/cm, Eloss increases by 71%, which explains the significant decrease in the breakdown delay time from 48 μs to 13 μs in this conductivity range (Figure 7).

CT Results and Discussion
We applied the X-ray computed tomography (CT) to study the microscopic characteristics of a cylindrical sample with a diameter of 2.5 cm and a height of 3 cm. Figure 9 presents a sample model reconstructed by 3D visualization software before and after it was subjected to the pressure waves generated by underwater discharge. In Figure 9a, the pores (less than 1 mm in diameter) were air bubbles caused during the sample preparation process. As can be seen from Figure 9b, the sample was severely damaged after being hit by the pressure waves five times to a crushing depth of 6 mm, which significantly deteriorated the mechanical properties of the sample and made it easier to be crushed by the drill bit. Besides, some pits and cracks extended to the edge, causing the boundary of the sample to fall off.
(a) Sample morphology before the pressure waves

CT Results and Discussion
We applied the X-ray computed tomography (CT) to study the microscopic characteristics of a cylindrical sample with a diameter of 2.5 cm and a height of 3 cm. Figure 9 presents a sample model reconstructed by 3D visualization software before and after it was subjected to the pressure waves generated by underwater discharge. In Figure 9a, the pores (less than 1 mm in diameter) were air bubbles caused during the sample preparation process. As can be seen from Figure 9b, the sample was severely damaged after being hit by the pressure waves five times to a crushing depth of 6 mm, which significantly deteriorated the mechanical properties of the sample and made it easier to be crushed by the drill bit. Besides, some pits and cracks extended to the edge, causing the boundary of the sample to fall off.
Energies 2020, x FOR PEER REVIEW 8 of 16 Figure 8 shows that the electrical energy leaking into the water increases with increasing electrical conductivity. The major role of Eloss is to generate Joule heat in the water and form bubbles that contribute to the formation of electrical breakdown. Therefore, increasing the Eloss helps to reduce the breakdown delay time. When the conductivity is increased from 0.5 mS/cm to 5 mS/cm, Eloss increases by 71%, which explains the significant decrease in the breakdown delay time from 48 μs to 13 μs in this conductivity range (Figure 7).

CT Results and Discussion
We applied the X-ray computed tomography (CT) to study the microscopic characteristics of a cylindrical sample with a diameter of 2.5 cm and a height of 3 cm. Figure 9 presents a sample model reconstructed by 3D visualization software before and after it was subjected to the pressure waves generated by underwater discharge. In Figure 9a, the pores (less than 1 mm in diameter) were air bubbles caused during the sample preparation process. As can be seen from Figure 9b, the sample was severely damaged after being hit by the pressure waves five times to a crushing depth of 6 mm, which significantly deteriorated the mechanical properties of the sample and made it easier to be crushed by the drill bit. Besides, some pits and cracks extended to the edge, causing the boundary of the sample to fall off.
(a) Sample morphology before the pressure waves   Figure 10 illustrates the sample surface's tomographic images and the images of 6 mm depth from the surface, respectively. It reveals that cracking and erosion are the main forms of damage caused by pressure waves. These results can be explained by the interaction between pressure waves and the mortar specimen (Figure 11a). A stress wave can be decomposed into a compressive stress wave and a shear stress wave. Rock samples often have pre-existing flaws, such as vertical cracks and horizontal cracks. When the sample is subjected to compressive stresses perpendicular to the sample surface, the horizontal cracks in the sample will close, and the vertical cracks will open and extend. According to the Inglis theory [28], stresses are concentrated and amplified at the tip of a vertical crack, and when the compressive stresses are higher than the strength at the crack tip, the crack grows parallel to the direction of compressive stresses. This type of crack refers to cracks-I in Figure 11a, common in uniaxial compression testing of brittle materials, and is also referred to as longitudinal splitting [29][30][31].  Tensile cracks-II, located at the edge of the sample, has a different formation mechanism than cracks-I. A stress wave propagates from the interior of the sample to the sample-water interface, where it is reflected and converted into a tensile wave, since the acoustic impedance of the sample is much higher than that of the water. This tensile stress causes tensile cracks if it exceeds the material's  Figure 10 illustrates the sample surface's tomographic images and the images of 6 mm depth from the surface, respectively. It reveals that cracking and erosion are the main forms of damage caused by pressure waves. These results can be explained by the interaction between pressure waves and the mortar specimen (Figure 11a). A stress wave can be decomposed into a compressive stress wave and a shear stress wave. Rock samples often have pre-existing flaws, such as vertical cracks and horizontal cracks. When the sample is subjected to compressive stresses perpendicular to the sample surface, the horizontal cracks in the sample will close, and the vertical cracks will open and extend. According to the Inglis theory [28], stresses are concentrated and amplified at the tip of a vertical crack, and when the compressive stresses are higher than the strength at the crack tip, the crack grows parallel to the direction of compressive stresses. This type of crack refers to cracks-I in Figure 11a, common in uniaxial compression testing of brittle materials, and is also referred to as longitudinal splitting [29][30][31].   Figure 10 illustrates the sample surface's tomographic images and the images of 6 mm depth from the surface, respectively. It reveals that cracking and erosion are the main forms of damage caused by pressure waves. These results can be explained by the interaction between pressure waves and the mortar specimen (Figure 11a). A stress wave can be decomposed into a compressive stress wave and a shear stress wave. Rock samples often have pre-existing flaws, such as vertical cracks and horizontal cracks. When the sample is subjected to compressive stresses perpendicular to the sample surface, the horizontal cracks in the sample will close, and the vertical cracks will open and extend. According to the Inglis theory [28], stresses are concentrated and amplified at the tip of a vertical crack, and when the compressive stresses are higher than the strength at the crack tip, the crack grows parallel to the direction of compressive stresses. This type of crack refers to cracks-I in Figure 11a, common in uniaxial compression testing of brittle materials, and is also referred to as longitudinal splitting [29][30][31].  Tensile cracks-II, located at the edge of the sample, has a different formation mechanism than cracks-I. A stress wave propagates from the interior of the sample to the sample-water interface, where it is reflected and converted into a tensile wave, since the acoustic impedance of the sample is much higher than that of the water. This tensile stress causes tensile cracks if it exceeds the material's lithotripsy [32][33][34]. The cracks propagate further and interconnect with other cracks to form a continuous fault plane. When the stress exceeds the frictional resistance on the plane, frictional sliding and erosion will occur.
There were tensile cracks-I, tensile cracks-II, and extensive erosion of the sample surface ( Figure  10a). As the depth increased, the damage degree decreased, and the damage was dominated by tensile cracks-II and erosion (Figure 10b).  Figure 12a shows the surface features of a raw sample, and Figure 12b-f show the typical surface macroscopic damage characteristics produced by pressure waves at different conductivities. The raw sample surface is smooth, while there are many cracks and pores on the surface of the samples crushed by the pressure waves. As the conductivity increased from 0.5 mS/cm to 20 mS/cm, the number of pores and the density of cracks gradually decreased. Figure 11. Schematic for the formation mechanism of tensile cracks-I and -II.

Surface Damage Results and Discussion
Tensile cracks-II, located at the edge of the sample, has a different formation mechanism than cracks-I. A stress wave propagates from the interior of the sample to the sample-water interface, where it is reflected and converted into a tensile wave, since the acoustic impedance of the sample is much higher than that of the water. This tensile stress causes tensile cracks if it exceeds the material's tensile strength, known as spalling damage, and is typical of blast-induced damage and shock wave lithotripsy [32][33][34]. The cracks propagate further and interconnect with other cracks to form a continuous fault plane. When the stress exceeds the frictional resistance on the plane, frictional sliding and erosion will occur.
There were tensile cracks-I, tensile cracks-II, and extensive erosion of the sample surface ( Figure 10a). As the depth increased, the damage degree decreased, and the damage was dominated by tensile cracks-II and erosion (Figure 10b). We used the cumulative area of the pores, S, to quantitatively assess the effect of electrical conductivity on sample damage, with a higher S value indicating more significant damage. As shown in Figure 13, the value of S decreases significantly in water with high conductivity. For example, S at 20 mS/cm conductivity is only one-fifth of the value at 5 mS/cm. This result is related to the peak pressure of the pressure waves. The increase in conductivity leads to more energy leaking in the water, and less energy to form pressure waves, decreasing the peak pressure, P, and the S value ( Figure 14). The P (MPa) is given in Equation (4)

Surface Damage Results and Discussion
where Epl (J) is the electrical energy deposited into plasma channel, d (mm) is the distance between the channel and sample surface, and α denotes a coefficient, which is 0.35 in the experiment. We used the cumulative area of the pores, S, to quantitatively assess the effect of electrical conductivity on sample damage, with a higher S value indicating more significant damage. As shown in Figure 13, the value of S decreases significantly in water with high conductivity. For example, S at 20 mS/cm conductivity is only one-fifth of the value at 5 mS/cm. This result is related to the peak pressure of the pressure waves. The increase in conductivity leads to more energy leaking in the water, and less energy to form pressure waves, decreasing the peak pressure, P, and the S value ( Figure 14). The P (MPa) is given in Equation (4) [35]: where E pl (J) is the electrical energy deposited into plasma channel, d (mm) is the distance between the channel and sample surface, and α denotes a coefficient, which is 0.35 in the experiment. Energies 2020, x FOR PEER REVIEW 12 of 16   Figure 15 illustrates the relationship between the average size distribution of pores on the sample surface and electrical conductivity. The pore size was dominated by 1 to 3 mm, and no pores larger than 6 mm in diameter were formed when the conductivity exceeded 10 mS/cm. Intuitively, the number of pores should be inversely proportional to the conductivity, but the number of pores with a 1 mm diameter increased first, and then decreased. One possible explanation is that in water with conductivities of 0.5 mS/cm and 5 mS/cm, many 1 mm pores are initiated early, but soon develop into larger dimensions because of the higher amplitude of the pressure waves ( Figure 14). Therefore, in low conductivity, the number of 1 mm pores is fewer than that of relatively higher conductivity. However, when the conductivity is 20 mS/cm, the peak of pressure waves is considerably reduced by about 40%, resulting in a significant reduction in the number of pores of various sizes.   Figure 15 illustrates the relationship between the average size distribution of pores on the sample surface and electrical conductivity. The pore size was dominated by 1 to 3 mm, and no pores larger than 6 mm in diameter were formed when the conductivity exceeded 10 mS/cm. Intuitively, the number of pores should be inversely proportional to the conductivity, but the number of pores with a 1 mm diameter increased first, and then decreased. One possible explanation is that in water with conductivities of 0.5 mS/cm and 5 mS/cm, many 1 mm pores are initiated early, but soon develop into larger dimensions because of the higher amplitude of the pressure waves ( Figure 14). Therefore, in low conductivity, the number of 1 mm pores is fewer than that of relatively higher conductivity. However, when the conductivity is 20 mS/cm, the peak of pressure waves is considerably reduced by about 40%, resulting in a significant reduction in the number of pores of various sizes.  Figure 15 illustrates the relationship between the average size distribution of pores on the sample surface and electrical conductivity. The pore size was dominated by 1 to 3 mm, and no pores larger than 6 mm in diameter were formed when the conductivity exceeded 10 mS/cm. Intuitively, the number of pores should be inversely proportional to the conductivity, but the number of pores with a 1 mm diameter increased first, and then decreased. One possible explanation is that in water with conductivities of 0.5 mS/cm and 5 mS/cm, many 1 mm pores are initiated early, but soon develop into larger dimensions because of the higher amplitude of the pressure waves ( Figure 14). Therefore, in low conductivity, the number of 1 mm pores is fewer than that of relatively higher conductivity. However, when the conductivity is 20 mS/cm, the peak of pressure waves is considerably reduced by about 40%, resulting in a significant reduction in the number of pores of various sizes.

Internal Damage Results and Discussion
The through-transmission ultrasonic inspection technique allows the measurement of damage inside the sample, which is revealed in the reduced amplitude of received ultrasound waves, due to internal cracks and flaws that block the propagation of ultrasound waves. Figure 16 shows the amplitude attenuation rate of samples, Ac, at different electrical conductivity. Each value is an average of three samples with 95% confidence interval precision. Interestingly, we found a two-stage pattern of internal damage. The Ac experienced a significant reduction from 61.1% at 0.5 mS/cm to 37.1% at 10 mS/cm, suggesting a rapid decrease in internal damage to the samples in this conductivity range. In contrast, there is little variation in Ac between 10 mS/cm and 20 mS/cm, indicating the number of flaws and microcracks within the samples are reducing, but at a slower rate. This two-stage pattern is also reflected in the sample surface damage (Figure 13), where the difference in surface damage between 0.5 mS/cm and 10 mS/cm is much more significant than the difference between 10 mS/cm and 20 mS/cm. The positive correlation between the internal and surface damages may suggest that pores and cracks on the surface grow downward under stress, creating new microcracks inside the sample, and deteriorating the mechanical properties of the sample. It seems that only when the stresses generated by the pressure wave are sufficiently higher than the compressive and tensile strengths, severe damage occurs.

Internal Damage Results and Discussion
The through-transmission ultrasonic inspection technique allows the measurement of damage inside the sample, which is revealed in the reduced amplitude of received ultrasound waves, due to internal cracks and flaws that block the propagation of ultrasound waves. Figure 16 shows the amplitude attenuation rate of samples, A c, at different electrical conductivity. Each value is an average of three samples with 95% confidence interval precision. Interestingly, we found a two-stage pattern of internal damage. The A c experienced a significant reduction from 61.1% at 0.5 mS/cm to 37.1% at 10 mS/cm, suggesting a rapid decrease in internal damage to the samples in this conductivity range. In contrast, there is little variation in A c between 10 mS/cm and 20 mS/cm, indicating the number of flaws and microcracks within the samples are reducing, but at a slower rate. This two-stage pattern is also reflected in the sample surface damage (Figure 13), where the difference in surface damage between 0.5 mS/cm and 10 mS/cm is much more significant than the difference between 10 mS/cm and 20 mS/cm. The positive correlation between the internal and surface damages may suggest that pores and cracks on the surface grow downward under stress, creating new microcracks inside the sample, and deteriorating the mechanical properties of the sample. It seems that only when the stresses generated by the pressure wave are sufficiently higher than the compressive and tensile strengths, severe damage occurs.

Internal Damage Results and Discussion
The through-transmission ultrasonic inspection technique allows the measurement of damage inside the sample, which is revealed in the reduced amplitude of received ultrasound waves, due to internal cracks and flaws that block the propagation of ultrasound waves. Figure 16 shows the amplitude attenuation rate of samples, Ac, at different electrical conductivity. Each value is an average of three samples with 95% confidence interval precision. Interestingly, we found a two-stage pattern of internal damage. The Ac experienced a significant reduction from 61.1% at 0.5 mS/cm to 37.1% at 10 mS/cm, suggesting a rapid decrease in internal damage to the samples in this conductivity range. In contrast, there is little variation in Ac between 10 mS/cm and 20 mS/cm, indicating the number of flaws and microcracks within the samples are reducing, but at a slower rate. This two-stage pattern is also reflected in the sample surface damage (Figure 13), where the difference in surface damage between 0.5 mS/cm and 10 mS/cm is much more significant than the difference between 10 mS/cm and 20 mS/cm. The positive correlation between the internal and surface damages may suggest that pores and cracks on the surface grow downward under stress, creating new microcracks inside the sample, and deteriorating the mechanical properties of the sample. It seems that only when the stresses generated by the pressure wave are sufficiently higher than the compressive and tensile strengths, severe damage occurs.

Conclusions
This paper aims to investigate the characteristics of pulse discharge and the rock damage at different electrical conductivity, as well as the damage mechanism of pressure waves generated by HVSD.
Our study reveals that an increase in conductivity decreased the breakdown voltage and increased energy loss, thus decreasing the energy efficiency and the pressure wave's magnitude. However, the increase in conductivity reduces the difficulty and shortens the time required to form electrical breakdown, and accelerates the generation of pressure waves. As the conductivity increased from 0.5 mS/cm to 5 mS/cm, the breakdown delay time decreased rapidly, and remained almost constant as the conductivity increased. The sample damage exhibited a two-stage pattern in the range of 0.5 mS/cm to 20 mS/cm. Therefore, in practice, to balance energy efficiency, electrical breakdown time, and sample damage, the conductivity of water is preferably 5 mS/cm. The damage is mainly caused by pores and two types of tensile cracks, which are created by induced compressive stresses and tensile stresses induced by stress wave reflection at the mortar-water interface, respectively.
A limitation of this study is that we used the empirical formula from the literature [32] to calculate the peak pressure of the pressure wave, rather than measuring it experimentally. However, considering that our experimental system is the same as in the literature, the error in the peak pressure should be quite small. Besides, we neglected the effect of confining pressure and temperature on the damage process. In the future, we will establish an experimental system that can simulate the real stress state in the underground environment, and conduct HVSD rock-breaking tests at different temperatures and confining pressures to lay the foundation for the practical application of HVSD drilling technology in the oilfield.