## 5 Comparison between the RVE Model and Published Laboratory Experiments  
Prior to compiling this paper, numerous simulations were conducted with alternative set-ups, such as other spatial distributions of contact elements, other property values of the contacts and of the blocks, different initial stress states, different stress paths, and others. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**(a)** & & & & \\ \hline \multicolumn{5}{c}{Stress State at Failure} & \multicolumn{5}{c}{Percentage of All Activated Contacts} \\ \hline Minor Principal & Major Principal & & & \\ Stress (S3), MPa & & & & \\ Stress (S1), MPa & & & & \\ \hline
30.1 & 79.4 & 42\% & 40\% & 18\% \\
46.6 & 104.2 & 36\% & 36\% & 28\% \\
63.6 & 137.6 & 32\% & 46\% & 22\% \\ \hline
**(b)** & & & & \\ \hline \multicolumn{5}{c}{Stress state at failure} & \multicolumn{5}{c}{Percentage of all activated contacts} \\ \hline Minor principal & Major principal & & & \\ stress (S3), MPa & & & & \\ \hline
23.4 & 79.4 & 30\% & 46\% & 24\% \\
34.7 & 104.2 & 28\% & 39\% & 33\% \\
47.4 & 137.6 & 25\% & 40\% & 35\% \\ \hline
**(c)** & & & & \\ \hline \multicolumn{5}{c}{Stress state at failure} & \multicolumn{5}{c}{Percentage of all activated contacts} \\ \hline Minor principal & Major principal & & & \\ stress (S3), MPa & stress (S1), MPa & & & \\ \hline
13.5 & 79.4 & 30\% & 42\% & 28\% \\
14.8 & 104.2 & 31\% & 38\% & 31\% \\
31.2 & 137.6 & 26\% & 34\% & 40\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Percentage of activation modes (i.e., tensile only, mixed mode, or shear only) for all activated contact elements at moment of failure when applying the uniaxial unloading (S1(=),S3(unl)) stress path. (a) Initial stress anisotropy of 100%; (b) initial stress anisotropy of 75%; (c) initial stress anisotropy of 50%. Figure 9: Variation of the contact failure modes (i.e., tensile only, shear only, and mixed mode) for two anisotropy ratios of the initial stress state, as a function of the stress path, i.e., from the initial stress state until the load level of failure, corresponding to 50% failed contacts. The top cases of Figure 8 are presented (uniaxial unloading, S1(=),S3(unl)). (a) Anisotropy of 75%; (**b**) anisotropy of 50%. All of them provided a picture that was similar to the one presented and discussed in detail above for the so-called medium-to-strong black box rock. Incorporating in the paper all the other simulations would not provide any additional value. However, it was thought useful, mainly to validate the approach of using a RVE model, to apply a complex stress path, published recently [28]. The stress paths presented by [PERSON] et al. [28] corresponded to a complex in situ path occurring in the roof of a coal seam during mining. Laboratory specimens of bedded sandstone were loaded by these complex in situ stress paths, and the results were compared to classic loading tests [28]. Their research project aimed to investigate the stability of roadways and the prevention and control of rockburst in deep coal mines. First, cylindrical specimens were tested by applying the conventional triaxial loading path, whereby three different confining stresses were applied (i.e., 5, 10, and 20 MPa). Since the rock can be classed as transversally isotropic, five different inclination angles of the bedding planes were tested per confining stress, i.e., 0\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), and 90\({}^{\circ}\). In other words, 15 specimens were tested in this way. Second, the same number of cylindrical specimens were loaded following a three-step stress path. The zero-stress specimens were loaded in a way that was approximately isotropic until a stress state of about 25 MPa (circumference) to 27 MPa (axial) was reached. In the next step, the circumferential stress was decreased until a value of 5, 10, or 20 MPa was reached. In the final step, the axial load was increased until failure occurred. The circumferential stress was then kept constant.