## 2 Identification of Mechanical Parameters of Rock Samples in Static Tests
### Results of Static Tests  
The Barwald sandstone is characterized by a volumetric density of 2448 kg/m\({}^{3}\), compressive strength of 78.8 MPa, tensile strength of 5.7 MPa, Young's modulus (Et) of 9.2 GPa, modulus of elasticity (E\({}_{\text{A}}\)) of 8.5 GPa, and porosity of 0.65%. In contrast, the Apricot Pink sandstone exhibits a lower volumetric density (2314 kg/m\({}^{3}\)) but significantly higher compressive strength (126.7 MPa) and tensile strength (8.6 MPa), along with greater values of Young's modulus (Et = 11.5 GPa, E\({}_{\text{A}}\) = 10.4 GPa) and porosity at 8.32%. The most distinctive is the Kandla Grey sandstone with a density of 2539 kg/m\({}^{3}\), the highest compressive strength (206.2 MPa) and tensile strength (11.1 MPa), and significantly higher values of Young's modulus (Et = 24.1 GPa, E\({}_{\text{A}}\) = 17.2 GPa) with a minimal porosity of 0.03%. These significant differences in physical and mechanical parameters indicate potential diversification in the applications of these materials in engineering and construction, emphasizing their unique properties and adaptability to specific construction requirements. Table 1 compiles the average results for all conducted tests. Figure 5 depicts the obtained results in box-and-whisker plots (frame range 25-75%). In the study of three materials, Apricot, Barwald, and Kandla, the variability of physico-mechanical parameters such as volumetric density, compressive strength, tensile strength, Young's modulus, porosity, and energy was also analyzed. Variability was measured using the coefficient of variation, expressed as a percentage (Table 2). The Apricot sandstone exhibited the least variability in porosity (1.03%), indicating that the samples of this material were very homogeneous in terms of internal structure. The greatest variability for this material was observed in tensile strength (21.68%), demonstrating that the tensile mechanical strength varied significantly among the samples. Barwald showed the least variability in volumetric density (0.37%), indicating a high homogeneity of this parameter in the samples, which is further confirmed by the relatively low variability in porosity. The greatest variability for this material was found in compressive strength (26.46%), implying that samples of this material had significant differences in their structure or composition. Kandla Grey exhibited the least variability in volumetric density (0.29%), indicating a very homogeneous structure in terms of density. However, the greatest variability was observed \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**No**} & \multirow{2}{*}{**Name**} & **Volumetric** & **Compressive** & **Tensile** & **Young** & **Young** & **Energy** \\  & & **Density** & **Strength** & **Strength** & **Modulus** & **Modulus** & **Modulus** \\  & & **(y), kg/m\({}^{3}\)** & **(R\({}_{\text{c}}\)), MPa** & **(R\({}_{\text{t}}\)), MPa** & **(E\({}_{\text{t}}\)), GPa** & **(E\({}_{\text{A}}\)), GPa** & & \\ \hline
1. & Apricot & 2314 & 126.7 & 8.6 & 11.5 & 10.4 & 8.32 & 0.42 \\ \hline
2. & Barwald & 2448 & 78.8 & 5.7 & 9.2 & 8.5 & 0.65 & 0.28 \\ \hline
3. & Kandla & 2539 & 206.2 & 11.1 & 24.1 & 17.2 & 0.03 & 1.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Compilation of average physico-mechanical parameters determined for the examined samples. Figure 4: Placement of the sample inside the tomograph chamber. in porosity (25.53%), suggesting that the internal structure of the Kandla samples was diverse, simultaneously affecting the variety of mechanical properties. The analysis of the obtained results of basic physical and mechanical parameter testing allows us to conclude that the bulk density of the tested sandstones is significantly dependent on their porosity. This is especially visible in the case of Apricot Pink sandstone, which is characterized by the lowest density and the highest porosity.