# Mechanical and Acoustic Emission (AE) Characteristics of Rocks under Biaxial Confinements
## 5 Conclusions  
In this study, the mechanical and AE characteristics of cubic granite, marble, and sandstone specimens were investigated in the biaxial compression tests. The following conclusions can be drawn:  
(1) In the biaxial compression tests, the elastic moduli of granite, marble, and sandstone show a decreasing trend with the increase of \(\sigma_{2}\). The intermediate principal stress \(\sigma_{2}\) has a significant effect on lateral strain of rock under biaxial confinement. For the three types of rocks in this study, the \(\sigma_{2}\) over 10 MPa can restrain the development of micro-cracks along the direction of \(\sigma_{2}\).  
(2) The biaxial compressive strengths (\(\sigma_{\rm{bcs}}\)) of granite, marble, and sandstone increased initially and then subsequently decreased with the increase of \(\sigma_{2}\). The turning-points \(\sigma_{\rm{2-t}}\) of \(\sigma_{2}\) corresponding to peak biaxial compressive strengths \(\sigma_{\rm{bcs,peak}}\) for different rocks are different, and the harder rock has a greater \(\sigma_{\rm{2-t}}\).  
(3) The AE hit rate and AE count rate can reflect the damage degree of rock under biaxial compression. The sharp increases of the AE hit rate and AE count rate indicate the rapid accumulation of internal damage, which is always accompanied by a decrease in \(b\)-value. In the loading process, the dynamic \(b\)-value fluctuates, and it presents a downward trend on the whole.  
(4) From the distribution characteristics of AF-RA, it can be found that few shear cracks in the rock are formed before the failure stage, but the number of shear cracks increases obviously during the failure stage. Tensile cracks in the rock are generated during the entire loading process, but the generation rate of cracks is increasing with the increase of \(\sigma_{1}\).  
(5) More tensile cracks are produced in rock during the loading process with the increase of \(\sigma_{2}\). The failures of granite and marble are mainly caused by tension cracks, while the failure of sandstone is mainly caused by shear cracks.  
Conceptualization, K.D., M.L. and C.Y.; methodology, K.D. and C.Y.; software, M.L. and C.Y.; validation, K.D., M.L. and S.W.; formal analysis, K.D. and M.L.; investigation, K.D., M.L., C.Y. and S.W.; resources, K.D., F.F. and M.T.; data curation, M.L. and C.Y.; writing--original draft preparation, M.L.; writing--review and editing, K.D., M.T. and S.W.; visualization, M.L.; supervision, K.D.; project administration, K.D. and C.Y.; funding acquisition, K.D. All authors have read and agreed to the published version of the manuscript.  
Figure 16: Failure criterion data and theoretical solutions of Drucker–Prager criterion in \(I_{2}^{1/2}\)-\(I_{1}\) space: (**a**) granite, (**b**) marble, and (**c**) sandstone.  
**Funding:** This research was funded by the National Natural Science Foundation of China (Nos: 51904333 and 51774326), the open fund of Mining Disaster Prevention and Control Ministry Key Laboratory at Shandong University of Science and Technology (No: MDPC201917).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data sharing not applicable.  
**Conflicts of Interest:** There are no conflict of interest regarding the publication of this paper.