## 5 Conclusions  
This study aimed to investigate the rock erosion and crushing characteristics of an SPWJ, and the experimental results were evaluated based on factors such as erosion depth, erosion area, spalling volume, and unit input pressure erosion volume. The goal was to improve the performance of water jet erosion and crushing of granite and apply it to the erosion and crushing of hard rock. The main results of this study are as follows:  
1. During the process of SPWJ erosion of hard rock, the water hammer stress waveforms tensile cracks inside the rock, and the jet enters the cracks to further water wedge and crack the granite, forming preliminary erosion pits. As the jet erosion target distance increases, the jet energy decays to the point where cracks cannot be formed, and the rock fragmentation reaches the limit position.
2. With an increase in pressure, the rock-breaking capacity of SPWJ initially increases and then decreases, reaching its maximum at 60 MPa. Under the experimental conditions, the erosion ability of CWJ is better than that of SPWJ when the pressure is lower than 60 MPa, and the erosion ability of SPWJ is better than that of CWJ when the pressure is above 60 MPa.
3. The optimal dimensionless standoff distance for the SPWJ is approximately twice that of the CWJ. Under the experimental conditions, the optimal dimensionless target distance for the CWJ is 100, while for the SPWJ, it is 200. Moreover, the SPWJ is more sensitive to the target distance than the CWJ. When the SPWJ is offset from the experimental optimal standoff distance of S = 200 by either 50 to 150 or 250, the jet erosion volume is reduced by 87.5% and 78.7%, respectively. In comparison, for CWJ, this reduction in jet erosion volume is only 25.8%.
4. SPWJ's feedback on the erosion time is relatively rapid, and the peak value of crushing can be reached at the beginning of the erosion. With the extension of the erosion time, the effective crushing amount of the squeeze pulse water jet hardly increases. When the erosion time is less than the 90 s, the crushing ability of SPWJ is better than CWJ.
5. Under the condition of unit input pressure, the overall erosion ability of SPWJ on granite is better than that of CWJ. The mechanism of SPWJ erosion and decomposition of granite needs to be analyzed theoretically and experimentally.  
Conceptualization, Y.Z., J.T. and H.L.; methodology, H.L., Y.L., Y.Z. and J.T.; validation, Y.Z. and Y.L.; formal analysis, Y.Z.; investigation, Y.Z., Y.L. and Y.L.; resources, H.L. and Y.Z.; data curation, Y.Z. and H.L.; writing--original draft preparation, Y.Z.; writing--review and editing, Y.Z., J.T., H.L. and Y.L.; visualization, Y.Z.; supervision, Y.Z.; project administration, Y.Z.; funding acquisition, J.T. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation Outstanding Youth Fund Project (No. 51625401), the Chongqing Natural Science Foundation Project (No. cstc2018 jcyjAX0542), the Major Research Plan of the National Science and Technology in the 13 th Five-Year Plan (No.  
2017 ZX05049-003-011), and the Program for Changjiang Scholars and Innovative Research Team in Chongqing University (Grant No. IRT17R112).  
Not applicable.  
**Data Availability Statement:** The data presented in this study are available in the article.  
We thank Elsevier Language Editing Services (www.sciencedirect.com, accessed on 16 August 2021) for its linguistic assistance during the preparation of this manuscript. All authors have confirmed their support for the publication of this article.  
The authors declare no conflict of interest.