## 7 Conclusions  
In this paper, the crack extension and damage characteristics of prefabricated conjugate crack specimens under uniaxial compression conditions are investigated using the DIC and DEM methods, and the effects of the conjugate crack's angle on crack extension, damage characteristics, and the stress-strain relationship of rock-like specimens are analyzed. Comparing the numerical simulation results of crack initiation, extension, and aggregation of the prefabricated fractured rock specimens, which are in good agreement with the indoor test results, the results are finally verified by using the energy dissipation, and the following conclusions are preliminarily drawn:The peak strength of specimens containing a combination of both single and conjugate cracks is related to the \(\beta\)-angle within the prefabricated conjugate cracks. Under the same conditions, as the \(\beta\) angle increases from 30\({}^{\circ}\) to 90\({}^{\circ}\), the peak strength decreases and then increases, reaching a minimum at \(\beta\) = 45\({}^{\circ}\) (Type IV).
2. The geometry of the conjugate crack affects the location of the crack clusters in the rock specimens. Except for the conjugate cracks with \(\beta\) = 45\({}^{\circ}\), the positions of crack clusters in specimens with conjugate crack clusters are biased towards the lower part of the specimen. The numerical simulation results show that the damage caused by secondary cracks generated by tensile cracks dominates the crack extension process and is the main controlling crack leading to the decrease in rock-bearing capacity;
3. The positive correlation between specimen integrity and energy dissipation rate was verified using the energy dissipation rate method. The crack development law of multiple conjugate crack combination specimens under uniaxial compression conditions was obtained, which helps to infer the process of crack initiation, expansion, and merging in fractured pressure-bearing rock bodies in actual engineering.  
In this study, the mechanical properties and failure characteristics of rock samples with conjugate cracks under uniaxial loading are compared and analyzed by combining laboratory tests and numerical simulations, which provides a new reference type for the identification of internal cracks in natural rock mass in practical engineering. This study only analyzes the characteristics of conjugate crack failure under uniaxial loading conditions, and the subsequent plan is to change the stress path to study the development of secondary cracks under different loading conditions.  
Conceptualization, K.W.; data curation, W.Z., Y.Y. and T.X.; funding acquisition, K.W.; investigation, J.Z.; methodology, K.W. and J.Z.; resources, W.Z. and Y.Y.; software, W.Z. and T.X.; writing--original draft, J.Z.; writing--review and editing, J.Z. and Y.Y. All authors have read and agreed to the published version of the manuscript.  
National Natural Science Foundation of China: 51679215; Science Technology Department of Zhejiang Province: LGF21E090005.  
Not applicable.  
The data supporting our findings and analyses are contained in the article itself. Readers can access this data by referring to the article.  
The research described in this paper is financially supported by Zhejiang University of Technology. The authors are grateful for the financial support from the Science Technology Department of Zhejiang Province (LGF21E090005).  
The authors declare no conflicts of interest.