# Failure in Confined Brazilian Tests on Sandstone
## 3 Results  
### Experimental Results  
The maximum and minimum principal stresses at the peak load at the sample center for the confined Brazilian tests are calculated from Equations (1) and (3) and are shown in Figure 5. In addition, results from unconfined Brazilian tests and unconfined compression tests are shown in this figure. A curve has been fit through the mean values at each confining pressure. Most of the tests failed in the confined tension region, that is, where \(\sigma_{1}\) is compressive and \(\sigma_{3}\) is tensile. At the greatest confining pressure, failure occurred under all compressive stresses. The variability in the confined Brazilian strength data at the same confining pressure may be due to a number of different factors. Samples were produced from a number of different slabs, and thus may account for some variability. In addition, the samples were tested without regard to its bedding orientation which can affect Brazilian test results on sedimentary rocks [7]. The complex sample jacketing configuration may also contribute to some variability, although it is not likely to be responsible for all of the variability as the unjacketed unconfined Brazilian test data has some variability as well. There were not enough tests performed at each confining pressure to determine a meaningful standard deviation in the strength data. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Young’s Modulus** & **E (GPa)** & **2.74** \\ \hline Poisson’s Ratio & \(\
u\) & 0.20 \\ Density & \(\rho\) (kg/m\({}^{3}\)) & 2483 \\ Tensile Strength & \(\sigma\) (MPa) & 4.69 \\ Shear Strength & \(\tau\) (MPa) & 30.0 \\ Friction Coefficient: Sandstone/Sandstone & \(\mu_{\text{I}}\) & 0.57 \\ Friction Coefficient: Sandstone/Steel & \(\mu_{\text{II}}\) & 0.60 \\ Maximum Normal and Shear Displacements & \(\xi_{\text{I}}\), \(\xi_{\text{II}}\) (mm) & 0.036, 0.028 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sandstone Material Properties used in HOSS Simulations. Figure 4: Geometric representation of **(a)** a confined Brazilian test and **(b)** a uniaxial compression test to be used in numerical computations. The results from the confined Brazilian tests follow an approximately positive linear relationship between \(\sigma_{1}\) and \(\sigma_{3}\). However, the unconfined Brazilian test results deviate from this line, and in fact, indicate that \(\sigma_{3}\) increases (becomes less negative) at the lower \(\sigma_{1}\) in this test. The result that \(\sigma_{3}\) increases (becomes less negative) as \(\sigma_{1}\) decreases has been observed over portions of other tests in the confined tension region using confined tension tests of dogbone samples [1; 3; 10] and confined Brazilian tests [15]. The shape of the strength curve in this region is not consistent with a tension cut-off or a strength criterion in the tensile region developed from Griffith fracture criteria [2; 6]. A possible explanation for the apparently lower than expected strength during the unconfined Brazilian test reported here is that without confinement, cracks initiate from \"open\" micro-flaws or microcracks. Confinement would tend to close the open microcracks, and thereby increase their strength. The uniaxial compressive strength is on the order of 30% lower than the biaxial compressive strength of the confined Brazilian tests (where the curve crosses the \(\sigma_{3}=0\) axis). [PERSON] and [PERSON] [13] saw a similar behavior in some of their confined Brazilian tests. Results from [PERSON] [10] and [PERSON] and [PERSON] [1] on dog bone samples also indicate that the biaxial compressive strength is greater than the unconfined compressive strength (refer to Figure 2). [PERSON] and [PERSON] [4] conclude that tests with an intermediate principal stress increases the peak strength in the confined tension region. The strength data from the confined and unconfined Brazilian tests are presented as a function of the intermediate stress, that is, \(\sigma_{1}\) vs. \(\sigma_{2}\) and \(\sigma_{3}\) vs. \(\sigma_{2}\). in Figures 6 and 7, respectively.