## 3 Distinct Element Model for Simulating Loading and Unloading Paths
Different property values were given to the inclusions and the surrounding material or matrix material. The blocks only deformed elastically. Three different contact characteristics were considered, i.e., contacts within the soft inclusions, contacts within the cemented matrix material, and contacts matrix-inclusions. Mohr-Coulomb criteria were applied. The simulated fracture patterns were comparable to those observed in real soil-mix specimens that were loaded uniaxially. For the study presented here, a much smaller model was created, allowing for a larger number of simulations and facilitating the interpretation of failure types. The entire model contained 273 elements. The number of elements was small but sufficient for studying a RVE, as is shown by the results presented further. Figure 3 is a view of part of the model. The thick green lines are the contact lines and possible future fracture paths. These lines form the boundaries of the elastically deformable blocks, which are subdivided further in triangular elements (Figure 3, thin grey lines). The chosen values for the properties are based on earlier studies. The most relevant property is the failure criterium of the contacts. [PERSON] et al. [55] calibrated the model with laboratory experiments, resulting in a ratio of 2 between the cohesion and the tensile strength of the contacts within the matrix material. For very weak rock, i.e., slate, the tensile strength was 75% of the cohesion for the various types of contacts [54]. For the black box rock in this study, the contacts were characterised by a Mohr-Coulomb criterium with a cohesion of 20 MPa, a friction angle of 30\({}^{\circ}\), and a tensile strength of 10 MPa. These values are for the contacts and should not be confused with the macro-behaviour of an entire rock specimen. The orientations of the contact lines were chosen in such a way that the orientations were distributed equally over individual classes at 30\({}^{\circ}\) intervals. Hence, the black box rock that was chosen behaves on a macro-scale as an isotropic rock. As explained above, no specific test set-up was being modelled. The RVE of the black box rock model had a square shape. Its size can be assumed to be dimensionless. No platens were integrated into the model, and normal stresses were applied directly (and changed) on the specimen boundaries. So, the specimen can deform freely. The consequence is that no stress-strain curve was recorded and that the testing was stress driven rather than strain driven. Various percentages of failed contact elements were evaluated, but the most stable percentage to indicate full failure was the activation of 50% of all contact elements. For some simulations, a larger percentage would result in a loss of coherence between the individual blocks. A smaller percentage does not clearly represent the full failure process. Figure 3: Zoomed-in view of the distinct element UDEC model, representing a RVE of the black box rock. The thick lines represent the weak elements, i.e., possible fracture paths. The thin lines are the subdivision in triangles of the deformable blocks. During the simulations, the type of failure or activation of a contact element was recorded, i.e., tensile, shear, or mixed mode. The focus was on three basic types of stress paths (Figure 4). All three stress paths started from an isotropic stress state, including a zero-stress state. The first type was characterised by an increase in successive steps of the major principal stress until failure, for a constant minor principal stress. This stress path is similar to the conventional compressive testing, but it is not exactly the same (i.e., square specimen, stress driven, etc.). This type of stress path is abbreviated as S1(loa),S3(=). The second type was just the other way, S1(=),S3(unl), i.e., the minor principal stress was decreased and the major principal stress remained constant. The third type was a combination of the previous two types. It corresponded to the example presented above (Figure 1).