## 5 Comparison between the RVE Model and Published Laboratory Experiments
The provided data [28] allow for a comparison between the strength for both stress paths. The average of the five reduction values, i.e., for the five different inclination angles, showed that the specimens with a confinement stress of 5 MPa were about 24% weaker when the three-step stress path of loading-unloading-loading was applied in comparison to the conventional triaxial tests. For larger confinement stresses, these reductions were 11% and 6% on average for 10 MPa and 20 MPa of confinement stress, respectively. The aim of the simulations presented below was not to simulate the tests conducted by [PERSON] et al. [28]. There are various reasons why that is not opportune for this study, e.g., the shapes and volumes of the specimens were different, calibration was needed, and the transversally isotropic property must be integrated in the model. However, by applying the more complex stress paths on the RVE model, one could learn something about the merits of the RVE model and the approach presented in this paper, i.e., when similar percentages in the strength reductions are observed between the laboratory experiments [28] and the RVE model. The same input parameters for the medium-to-strong black box rock were considered, as applied in the presented simulations above. The initial stress state corresponded to an isotropic stress of 25 MPa, and, in a first step, one principal stress component was reduced to 10 MPa, 12.5 MPa, and 15 MPa (Figure 10a). Afterwards, the major principal stress was increased until failure occurred. For the black box model, a reduction to 5 MPa in the first step would already result in a full failure. A reduction to 20 MPa would not induce the activation of a contact element. The reason for both findings is that the black box rock is different from the bedded sandstone [28]. For a confining stress of 10 MPa in the loading part, the strength reduction along the final stress path was 47% in comparison to the failure criterium of uniaxial loading (73 MPa (Figure 10b, Table 5 (b)) vs. 138 MPa (Table 2 (a))). This reduction decreased to 21% (116 MPa vs. 147 MPa) and 3% (153 MPa vs. 157 MPa) for confining stresses of 12.5 MPa and 15 MPa, respectively. The trend in reduction is similar to that in [28]. Less unloading, i.e., a larger confining stress, resulted in less reduction of the strength. By taking the differences into account between the laboratory experiments and specimens, as well as the model, it can be concluded that similar reduction percentages were obtained. Above, the averages over five inclination angles were given for the laboratory experiments on bedded sandstone (i.e., 6%, 11%, and 24%). The strength reduction for the same inclination angle and confining stress varied more [28]. Sometimes, no reduction was observed, and sometimes the reduction values were larger. For example, a reduction of 41% was observedfor the two specimens with an inclination of 45\({}^{\circ}\) and a low confining stress (5 MPa) [28]. Or, in other words, the 47% reduction that was calculated for the simulations with the smallest confining stress certainly seemed to be realistic. \begin{table}
\begin{tabular}{l l l l l} \hline \hline \multicolumn{4}{l}{**(a)**} \\ \hline \multicolumn{4}{l}{Stress State at Change from} \\ \multicolumn{4}{l}{Unloading to Loading} \\ \hline Minor Principal & Major Principal & \multicolumn{1}{l}{} \\ Stress (S3), MPa & Stress (S1), MPa & \multicolumn{1}{l}{} \\ \hline
10.0 & 25.0 & 86\% & 11\% & 3\% \\
12.5 & 25.0 & 100\% & 0\% & 0\% \\
15.0 & 25.0 & 100\% & 0\% & 0\% \\ \hline \multicolumn{4}{l}{**(b)**} \\ \hline \multicolumn{4}{l}{Stress state at failure} \\ \hline Minor principal & Major principal & \multicolumn{1}{l}{} \\ stress (S3), MPa & stress (S1), MPa & \multicolumn{1}{l}{} \\ \hline
10.0 & 72.8 & 55\% & 19\% & 26\% \\
12.5 & 116.1 & 38\% & 22\% & 40\% \\
15.0 & 153.0 & 26\% & 18\% & 56\% \\ \hline \hline \end{tabular}
\end{table}