## 2 Identification of Mechanical Parameters of Rock Samples in Static Tests
### Methodology  
For the samples subjected to static testing, the following properties were determined: volumetric density, compressive strength, tensile strength, Young's modulus, and strain energy. Volumetric density determination was carried out in accordance with ISRM guide  
Figure 1: Rock sample used in the tests: sandstone Apricot Pink (**left**), sandstone Barwald (**middle**), Kandla Grey sandstone (**right**).  
lines (ISRM 1977) [30], using the direct measurement method on uniform samples specially prepared for strength testing. The determination of uniaxial compressive strength was carried out according to ISRM guidelines (ISRM 1979) [31]. A hydraulic press with automatic piston feed, force, and piston displacement recording was used for uniaxial compressive strength testing. The loading rate was set at 0.1 MPa/s. The uniaxial compressive strength (R\({}_{\text{c}}\)) was determined based on the ratio of the maximum destructive force (F\({}_{\text{max}}\)) obtained during the uniaxial compression of the sample in the press to the cross-sectional area (A). Cylindrical samples with a diameter close to 50 mm and a height-to-diameter ratio close to 2.5 were used for the study. The sample diameter was greater than 10 times the largest grain size in the rock. The samples were tested in an air-dry state. Ten uniaxial compression tests were conducted for each material, with simultaneous measurement of deformation parameters. Strain measurements were conducted following ISRM guidelines (ISRM 1979). Linear elastic modulus (E) was determined in two variants: tangent Young's modulus at 50% of the ultimate stress level and average Young's modulus for a straight-line stress-strain curve. Tensile strength determination for the tested material was performed in accordance with ISRM guidelines (ISRM 1978) [32]. Due to difficulties in obtaining core material and preparing laboratory samples of sufficient length for direct tension tests, the tensile strength was determined using the indirect Brazilian test method. The side of the sample was subjected to compressive force along opposing faces. Tensile testing using the Brazilian method was conducted using a testing machine, and ten tests were performed for each material (Figure 2).  
In their considerations, the authors analyzed the energy accumulated by the material in samples to reach maximum stresses. Data exported from the hydraulic servo-controlled press Walter + bei ag (2010, Lohningen, Switzerland) were used to determine the destruction energy in the static compression test. A similar methodology for determining accumulated energy is presented in [33; 34]. Samples with dimensions \(\diameter 23\times 58\) mm were subjected to static loading at a speed of 0.1 MPa/s. The data included information about the displacement of the press piston and the force acting on the sample. Graphically, the data were arranged in charts as shown in Figure 3 below.  
Based on the function presented by Equation (1), the energy accumulated by the material can be described as:  
\[W_{\text{s}}=\sum_{j=0}^{i_{max}-1}\left(\varepsilon_{i+1}-\varepsilon_{i} \right)\times\left(\frac{\sigma_{i}+\sigma_{i+1}}{2}\right) \tag{1}\]  
Figure 2: A sample prepared for tensile strength testing by splitting (**left**) and a sample prepared for compressive strength testing (**right**).