**4. Conclusions**

This paper aims to investigate the characteristics of pulse discharge and the rock damage at di fferent 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 e fficiency and the pressure wave's magnitude. However, the increase in conductivity reduces the di fficulty 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 e fficiency, 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 e ffect 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 di fferent temperatures and confining pressures to lay the foundation for the practical application of HVSD drilling technology in the oilfield.

**Author Contributions:** All the authors conceived and designed the study. Experiments: Z.C. and K.L.; data process: Z.C. and H.Z.; writing—original draft: Z.C. and H.Z.; writing—review and editing: Y.C., Q.Y., and K.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (Grant No. 51774304, Grant No.51734010, Grant No. U1762211, Grant No. 51574262, Grant No. 51774063, Grant No. U19B6003), National Oil and Gas Major Project (Grant No. 2017ZX05009), the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51821092), Strategic Cooperation Technology Projects of CNPC and CUPB (Grant No. ZLZX2020-01), Sinopec Joint Fund—Topic 5 (Grant No. U19B6003-5).

**Acknowledgments:** Thanks to Igor Timoshkin of the University of Strathclyde for his advice and help on the mechanism of underwater electrical discharge breakdown.

**Conflicts of Interest:** The authors declare that there is no conflict of interest regarding the publication of this paper.
