# Failure in Confined Brazilian Tests on Sandstone
## 4 Conclusions  
Confined Brazilian tests conducted on sandstone indicate that the strength measured with confined Brazilian tests was a strong function of the intermediate principal stress. Increasing the intermediate principal stress significantly increased the strength of the sandstone.  
In \(\sigma_{1}\)-\(\sigma_{3}\) stress space, the strength data from the confined Brazilian tests follow a straight line. This result suggests that the strength of the sandstone under the stress conditions of the confined Brazilian tests involve frictional processes. The strength data from the unconfined Brazilian tests do not fit the trend of the confined Brazilian test data in \(\sigma_{1}\)-\(\sigma_{3}\) stress space, nor are they consistent with a simple tension cut-off. The uniaxial compressive strength is on the order of 30% lower than the biaxial compressive strength of the confined Brazilian tests.  
All of the strength data were evaluated with respect to the Mogi-Coulomb strength criterion which, in contrast to most strength criteria for rocks, explicitly accounts for the role of the intermediate principal stress. The Mogi-Coulomb criterion represents strength derived from largely frictional processes. In this stress space, the confined Brazilian data and the uniaxial compressive strength were well represented by a straight line, suggesting that accounting for the intermediate principal stress reconciles strengths determined under different stress paths and stress conditions. The unconfined Brazilian strength data falls below the straight line, suggesting that tensile processes are increasingly controlling the strength in this test. Observation of post-failure fracture surfaces reveal that samples tend to show more indication of shear processes with increasing confining stress, namely, fracture surfaces tend to be ground down. For the sandstone tested here, additional confined Brazilian tests under confining pressures between 0 (unconfined) and 2.76 MPa would be helpful to better describe the transition from tension to shear dominated strength. For other rock types, the confined Brazilian test can be used to determine the failure behavior in the confined tension region and provide insight into the transition between tensile and shear failure processes.  
The numerical models consistently replicated the strength and failure behavior of the confined Brazilian tests, demonstrating the ability of HOSS to reasonably capture trends and behaviors in the confined tension stress space. The Mogi-Coulomb criterion also is well fit to the unconfined Brazilian and UCS simulations, suggesting that numerical calculations reflect the transition from tensile to frictional processes driving failure in the confined tension region.  
For applications where rock may be subjected to confined tension conditions, the results herein suggest that the failure criterion used should account for the intermediate principal stress. Numerical methods should be evaluated to ensure the predicted strength in the confined tension region reflects the role of the intermediate principal stress.  
Conceptualization, J.C.S. and M.R.T.; methodology, J.C.S.; software, T.H., E.R., E.E.K.; validation, T.H., E.R., E.E.K.; formal analysis, T.H.; investigation, T.H.; resources, M.R.T., J.C.S.; data curation, T.H.; writing--original draft preparation, T.H.; writing--review and editing, T.H., M.R.T., E.R., E.E.K., J.C.S.; visualization, T.H.; supervision, J.C.S.; project administration, J.C.S.; funding acquisition, J.C.S., M.R.T., E.R., E.E.K. All authors have read and agreed to the published version of the manuscript.  
This research was funded by New Mexico Consortium and Los Alamos National Laboratory, LA-UR-20-3083.  
Not applicable.  
Data Availability Statement: Data are available upon request from the corresponding author.  
The authors declare no conflict 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.