## 6 Conclusions  
Compression tests were conducted on sandstone specimens, both intact and with prefabricated cracks of varying thicknesses, to investigate the changes in dynamic mechanical properties. The average particle size was used to quantitatively analyze the degree of fragmentation, and the crack propagation mechanism was analyzed. The main conclusions are as follows:  
1. The dynamic stress-strain curve of prefabricated fractured sandstone samples is similar to that of intact sandstone samples. There are three stages that can be roughly divided according to the stress-strain curves of the specimens: elasticity, plasticity and failure.
2. With the increase in the thickness of prefabricated cracks, there is a quadratic decrease in the dynamic compressive strength of sandstone specimens, the dynamic strain decreases in a power exponential function, and the dynamic elastic modulus decreases linearly.
3. By increasing the thickness of the prefabricated cracks, the average particle size of the sandstone specimens decreases in a quadratic function, and the degree of fragmentation becomes increasingly obvious. As the dynamic compressive strength increases, the fractal dimension of the sandstone specimens after crushing reduces linearly.
4. When the sandstone specimens with a prefabricated crack thickness of 1.5-2.5 mm are impacted, airfoil and secondary cracks are generated. When the prefabricated crack thickness is 3-3.5 mm, airfoil, coplanar secondary, and secondary oblique cracks are generated. The intact sandstone specimens develop axial cracks caused by axial tensile failure.
5. The specimen with a 45\({}^{\circ}\) angle between the prefabricated crack and the loading direction possess the most ideal crack propagation condition; therefore, the stress intensity on the crack surface is the largest, and the initiation of an airfoil crack at the tip of the prefabricated crack is the most suitable. The shear stress in the crack'sprogressive stress drives airfoil cracking. Crack propagation can be explained by the sliding crack model theory.  
A large number of cracks will be produced by natural factors in the formation of rocks, and if we ignore the influence of other factors, including the development of internal joints, fissures, and other structural elements and their relationships, we will not be able to truly understand the nature of rock body disasters. This study can provide a certain theoretical basis for the mechanical properties of fractured rocks in the process of coal mine excavation and roadway support, and the influence of fracture geometry on the mechanical properties of rocks should be studied in the future.  
Conceptualization, Q.P.; software, Q.P.; validation, X.L.; formal analysis, X.L.; data curation, X.L.; writing--original draft, X.L.; writing--review and editing, Q.P. and X.L. All authors have read and agreed to the published version of the manuscript.  
This study received funding from the National Natural Science Foundation of China (no. 52074005, and no. 52074006), the Anhui Natural Science Foundation (no. 1808085 ME134), and the Anhui Postdoctoral Science Foundation (no. 2015B058).  
Not applicable.  
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.  
The data used to support the findings of this study are available from the corresponding author upon request. The data are not publicly available due to privacy.  
We would like to thank the State Key Laboratory of Mine Response and Disaster, Anhui University of Science and Technology for facilitating the experimental conditions. We would also like to thank [PERSON], [PERSON], [PERSON], [PERSON], and the other reviewers.  
The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.