## 2 Materials and Methods
### Numerical Studies
#### 2.3.1 Model Description  
The samples were modeled with a diameter of 50 mm and a height of 100 mm as shown in Figure 5a. The steel platen dimensions were taken into account as being 60 mm in diameter and 20 mm in height. Interface elements were placed between the sample and loading platens. Surfaces were located at 3 different positions along the sample volume at heights of 25 mm (H25), 50 mm (H50) and 75 mm (H75). This was performed in order to force mesh node positions at the intended cross sections, and thus to be able to evaluate the deformations at these locations. Figure 5b provides a graphical representation of the considered horizontal cross sections.  
In addition, two surfaces were defined within the sample volume parallel to the \(yz\)- and the \(xz\)-plane and passing through the sample axis. These surfaces helped in achieving a higher mesh symmetry. In total, the mesh comprised 64,468 10-node tetrahedral elements and a number of 100,649 element nodes.  
The steel material was modeled as elastic with an isotropic stiffness. For the rock material, the jointed rock (JR) model [40] was adopted. It considers elastic anisotropy by the implementation of a transversely isotropic stiffness matrix and plastic anisotropy by checking stresses against local Mohr-Coulomb failure criteria in implicit joint directions. In this study, any required input of strength parameters was chosen as sufficiently high to prevent yielding of the rock material. The interface on top and bottom of the sample was modeled using a Mohr-Coulomb constitutive model with zero cohesion. Two values for the friction angle of the interface were analyzed. The highest considered anisotropy ratio from the analytical study of \(E/E^{\prime}=2\) was adopted for the rock samples within the numerical simulations. This was performed in accordance with the highest expected influence of sample-platen friction on the elastic strain distributions. Tables 2-4 provide an overview of the selected material parameters for the numerical simulations.  
With regard to the kinematic boundary conditions, all displacement components at the bottom boundary of the model were fixed. Movement at the vertical model boundary along the steel platens was only permitted in vertical direction and was locked in horizontal direction. The applied boundary conditions are presented in Figure 5c.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value(s)** & **Unit** \\ \hline Young’s modulus & \(E\) & 20,000 & MPa \\ Poisson’s ratio & \(\
u\) & 0.3 & (-) \\ Friction angle & \(\varphi\) & 0, 15 & (°) \\ Cohesion & \(c\) & 0 & MPa \\ \hline \hline \end{tabular}
\end{table}
Table 4: Material parameters for the interface between rock specimen and steel platens.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value(s)** & **Unit** \\ \hline Young’s modulus & \(E\) & 4000 & MPa \\ Poisson’s ratio & \(\
u\) & 0.075, 0.1 \({}^{\star}\), 0.15, 0.225, 0.3 & (-) \\ Young’s modulus & \(E^{\prime}\) & 2000 & MPa \\ Poisson’s ratio & \(\
u^{\prime}\) & 0.15 & (-) \\ Shear modulus & \(G^{\prime}\) & 888 (0.8\(G^{\prime}_{\text{S}\text{U}}\)), 1111 \({}^{\star}\) (\(G^{\prime}_{\text{S}\text{U}}\)), 1333 (1.2\(G^{\prime}_{\text{S}\text{U}}\)) & MPa \\ Plane inclination & \(\beta\) & 0, 45, 90 & (°) \\ \hline \hline \end{tabular}  
* Herein regarded as the “basis” parameter set.  
\end{table}
Table 2: Material parameters for the rock sample.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value(s)** & **Unit** \\ \hline [PERSON]’s modulus & \(E\) & 200,000 & MPa \\ [PERSON]’s ratio & \(\
u\) & 0.3 & (-) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Material parameters for the steel platens.