## Materials and Methods  
### Specimen Geometry and Preparation  
The material used in this study was gypsum. The material is a mixture of Hydrocal B-11 (gypsum manufactured by Gypsum Company, Charlotte, NC, USA), Dicalite (diatomaceous earth manufactured by Grefco Inc., Torrance, CA, USA), and water. The proportions used are as follows: gypsum, 560 gwater, 224 ml; and diatomaceous earth, 6.4 g. The material properties of the gypsum specimen are summarized in Table 1. Its mechanical properties are similar to those of typical sedimentary rocks, and the ratio of tensile strength to compressive strength is close to 1:10. Therefore, the gypsum mixture is a relatively ideal rock-like material with high brittleness.  
The specimen's dimensions are 152.4 mm high, 76.2 mm wide, and around 30 mm thick. Two pre-existing flaws of length \(2a=12.7\) mm were arranged in the center of the specimen. A thickness of 0.1 mm steel shims were arranged in the mold to produce the desired flaw thickness of 0.1 mm (Figure 2). Open flaws were used in this study. These flaws remained open during a compression test, so no stresses are transmitted across them.  
The flaw inclination angle, \(\beta\), is the angle of the flaw with the horizontal direction. Continuity, \(c\), is the distance between flaws measured along their respective plane. Spacing, \(s\), is the distance between two flaws measured along a direction perpendicular to their plane. The rock bridge length, \(l\), is the shortest distance between the inner tips, and the rock bridge angle, \(\alpha\), is the angle of the ligament with the horizontal direction. The flaw geometry is defined in the form of \"flaw inclination angle (\(\beta\))-spacing (\(s\))-continuity (\(c\))\". Spacing, continuity and rock bridge length are represented by multiples of '\(a\)' (\(a=\) half flaw length). A total of 34 different flaw geometries were prepared. The geometry parameters of the specimen are presented as follows:  
Flaw inclination angle (\(\beta\)): 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), spacing (\(s\)): 0, \(a\), 2\(a\), continuity (\(c\)): 0, \(a\), 2\(a\), 3\(a\), 4\(a\)  
The same flaw geometries were used in the previous studies [6; 7; 8] to facilitate the comparison of previous and new findings.  
Table 2 shows a list of all the geometries and the number of specimens for this study. A total of 292 specimens were prepared and tested.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Uniaxial Compressive Strength [MPa]** & **Tensile Strength [MPa]** & **Poisson’s Ratio** & **Young’s Modulus [GPa]** \\ \hline
34.5 & 3.2 & 0.15 & 5.96 \\ \hline \end{tabular}
\end{table}
Table 1: Material properties of the gypsum specimen.  
The procedure for the specimen preparation is detailed below:  
1. Assemble the two PMMA plates and the four metallic plates. Insert steel shims for open cracks.
2. The water and diatomaceous earth are poured in a mixer and mixed for 20 s.
3. Add the gypsum to the water-diatomaceous earth mixture and mix for 4 min.
4. Pour mixture into the mould, then vibrate the mould for 2 min to remove entrapped air in the mixture.
5. After an hour following vibration, the steel shims are pulled out.
6. The gypsum specimens solidify within an hour. Then, the specimens are taken out of the mould.
7. Dry for 24 h at room temperature.
8. All faces of the specimens are polished in a rotating grinding machine to achieve a smooth surface and an even thickness.
9. For curing, the specimens are placed in an oven at 40 \({}^{\circ}\)C for four days. Then, the specimens are removed from the oven and tested.  
After four days of curing, there was little change in the strength of the specimen.