## 4 Direct Compression Tests  
The compressive apparatus used for the direct compression tests is a Schenck press of maximum capacity: 1 MN. The test is displacement-driven to compute the postpeak behaviour of the material. A LVDT is placed to provide an external measurement of the displacement (see Figure 6). A knee join is used to compensate any parallelism defect between contact surfaces. The velocity assigned to the press was 0.05 to 0.07 mm/s. The specimens used in direct compression tests are cylinders, 45.4 mm in diameter and 140 mm in length, cored out from large blocks by drilling and with ground ends. The selected height-diameter ratio, about 3:1 (3.08), exceeds the value usually considered (2:1) to better observe the influence of potential structural defects. However, according to several authors, the effect of length-to-diameter ratio of a rock core specimen on uniaxial compressive strength (UCS) is concluded to be small in the range (2:1-3:1) [24]. In addition, since uniaxial compression tests are not used directly in the identification of the KST-DFH model, the length-to-diameter ratio is not studied further.  
Figure 5: Graphical fitting of the Weibull distribution, where \(P_{\mathit{f}}\) denotes the failure probability and \(\sigma_{\mathit{f}}\) denotes each failure stress calculated according to Equation (5).  
The experimental results are gathered in Table 2. The stress-strain curves of specimens #1, #2, #3, and #5 are plotted in Figure 7. All of them exhibit a nonlinear response up to about 30 MPa. Afterwards, the response becomes linear until the peak providing a quasistatic Young's modulus in compression of about 32.06 GPa in average value. The very low compression strength of test #5 is assumed to be the result of a structural defect that initiates the macroscopic failure in compression, and accordingly may not be considered as a valid material property. In conclusion, despite the care taken to perform these experiments, uniaxial compression tests show significant variations in the measured Young's modulus and important scatter regarding the ultimate strengths and stress-strain curve foots that are supposed to result from structural defects within the tested samples. Both the nature of structural defects (thickness, length, and cohesion strength) and their orientation might have contributed to the scatter observed regarding the peak and prepeak response. The strain corresponding to the curve foot (ranging from \(7\times 10^{-4}\) to \(1.4\times 10^{-3}\)) could correspond to one or two horizontal structural defects with an opening of 0.1 mm. This gap will be considered as input in a numerical simulation in a parallel study [1].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & **Max Force (kN)** & \begin{tabular}{c} **Compression** \\ **Strength (MPa)** \\ \end{tabular} & \
\begin{tabular}{c} **Young’s** \\ **Modulus (GPa)** \\ \end{tabular} &
\begin{tabular}{c} **Stress Rate (MPa/s)** \\ \end{tabular} \\ \hline \#1 & 105.3 & 65.06 & 30.33 & 3.12 \\ \hline \#2 & 169.5 & 104.98 & 38.87 & 1.50 \\ \hline \#3 & 125.4 & 77.49 & 27.04 & 1.22 \\ \hline \#5 & 58.25 & 35.86 & 32.00 & 1.22 \\ \hline \multicolumn{4}{c}{Average} & 70.85 & 32.06 & 1.765 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Results of simple compression tests.  
Figure 6: Compression test setup used with the Schenck press in 3 SR lab.