## 3 Distinct Element Model for Simulating Loading and Unloading Paths  
The aim of the study that is presented was to try to quantify the effect of different loading and unloading paths both on the evolution of the induced (micro-)damage and on the final strength of rock. The choice was made to study the topic by numerical simulations and to consider a small RVE only. So, at this stage of the research, the aim was not to simulate entire specimens under laboratory conditions, or the rock mass surrounding an excavation, but to focus entirely on the single effect of different stress paths. The RVE model should be considered to represent a black box rock. Before applying a stress path, one does not know the strength of the RVE model under a specific stress path. However, the choice of the values for the various input parameters is based on past experience, whereby both observed fracture patterns and measured stress-strain curves were used to calibrate distinct element models [54; 55]. The readers are referred to these publications to learn more about the set-up of a distinct element model and about the calibration of the input parameters. One of the main benefits of the approach by numerical simulations is that one can repeat loading or unloading the exact same model, which is impossible in laboratory experiments because a new core or block must be used for each test. To study the initiation and growth of fractures, my research team at the KU Leuven has used with success in the past the two-dimensional Universal Distinct Element Code (UDEC), which was developed for the simulation of rock blocks and their deformation and relative movements [56; 57]. The latter is still the main application of this code. However, an intact rock can be approximated by an assembly of individual blocks, whereby initially these blocks are glued together along all contact lines. These contact lines are possible future fracture paths. A contact between two adjacent blocks does not represent a physical crack as long as it is not activated or has passed the pre-defined failure criterion. In my opinion, the fact that future fractures are composed of relatively straight lines is an advantage in comparison to some other discrete element codes. Thus, the contact lines or elements are given strength properties and hence can fail in shear and/or tension, simulating the occurrence of (micro-)fractures. After activation, the contact elements can deform, slide, and open. The blocks also are able to deform, e.g., in a linear elastic way. Both the individual blocks, as the contact elements within a single model, can have different property values. [PERSON] and [PERSON] [54] used UDEC to study transversely isotropic rock slate, which has a very large strength anisotropy. The distinction was made between contacts that represent the schistosity and the contacts in other directions. The blocks were allowed to undergo plastic behaviour. Although a block cannot break internally, the plastic deformation of a block could physically be interpreted as the occurrence of very small fractures on a sub-grid scale. Both uniaxial compressive and Brazilian tests were simulated and compared to observed fracture patterns in laboratory experiments. The simulations of the diametric load tests provided further insight concerning the fracture mechanisms. The simulations confirmed that millimetre-scale strength anisotropy resulted in a strength anisotropy on the specimen scale. Moreover, analysis of the stress distribution and of the contact strength properties explained the failure modes of the different fractures. [PERSON] et al. [55] studied the heterogeneous nature of soil-mix specimens and more specifically the effect of soft inclusion on the induced fracture patterns. The starting point was the distribution of such soft inclusions in real specimens, but the simulations allowed them to conduct a sensitivity analysis of the number of inclusions, their sizes, and their relative positions on the strength and fracture pattern.