Natural and synthetic cohesive, porous materials subjected to laboratory loading conditions exhibit complex pressure dependent stress-strain responses and failure modes. In this paper the elasto-plastic behaviour of porous rock loaded under axisymmetric laboratory conditions and the resultant modes of localised deformation are investigated using Distinct Element Method (DEM) numerical models in which rock is idealised as an assemblage of spherical, unbreakable, cemented particles. The emergent elasto-plastic bulk behaviour observed in the numerical simulations is qualitatively similar to that observed for natural rock and includes (i) pressure and stress-state sensitive elasticity, (ii) a positive correlation between friction coefficient and dilatancy factor, and (iii) yield/failure envelopes that depend on the third stress invariant. The shear band orientations and kinematics in the DEM models are quantitatively compared with localisation theory (see figure below).

*Plot of shear band angle measurements (circles) from DEM numerical models deformed at various confining pressure. The average of the DEM model data is just a few degrees greater than predicted by localisation theory. Fracture angles of < 45 degrees observed in the highest confining pressure compression test models suggest that localisation theory is more appropriate for predicting shear band inclinations than the more commonly used Mohr-Coulomb fracture hypothesis.*

These relatively simple models also illustrate that the transition from dilational shear bands at low confining pressure to compactional shear bands at high confining pressure is successfully predicted by localisation theory. Moreover, compactional shear bands can develop, at least during localisation, in the absence of particle size reduction (i.e. crushing) provided that the material can accommodate pore reduction by particle rearrangement.

__Schöpfer, M.P.J.__ & Childs, C. (2013). The orientation and dilatancy of shear bands in a bonded particle model for rock. International Journal of Rock Mechanics & Mining Sciences **57**, 75-88.

Link to article: www.sciencedirect.com/science/article/pii/S1365160912001566