The dynamic fragmentation of jointed rock blocks during rockslide avalanches has been investigated by discrete element method simulations for a multiple arrangement of a rock block sliding over a simple slope geometry. The rock blocks are released along an inclined sliding plane and subsequently collide onto a flat horizontal plane at a sharp kink point. The contact force chains generated by the impact appear initially at the bottom frontal corner of the rock block and then propagate radially upward to the top rear part of the block. The jointed rock blocks exhibit evident contact force concentration and discontinuity of force wave propagation near the joint, associating with high energy dissipation of granular dynamics. The corresponding force wave propagation velocity can be less than 200 m/s, which is much smaller than that of an intact rock (1,316 m/s). The concentration of contact forces at the bottom leads to high rock fragmentation intensity and momentum boosts, facilitating the spreading of many fine fragments to the distal ends. However, the upper rock block exhibits very low rock fragmentation intensity but high energy dissipation due to intensive friction and damping, resulting in the deposition of large fragments near the slope toe. The size and shape of large fragments are closely related to the orientation and distribution of the block joints. The cumulative fragment size distribution can be well fitted by the Weibull's distribution function, with very gentle and steep curvatures at the fine and coarse size ranges, respectively. The numerical results of fragment size distribution can match well some experimental and field observations.

a b s t r a c tIn this paper the onset of instabilities in elastoplastic materials is theoretically studied and a conceptual basis for understanding the physical implications of a loss of uniqueness and/or existence of the incremental response is provided. For this purpose, the concept of test controllability is reinterpreted and mixed stress-strain loading programmes are accounted for. A set of scalar indices, the moduli of instability, related with the inception of an unstable response is introduced and their dependency on the loading programme is explicitly illustrated. The paper shows that the use of these newly defined scalar measures provides support for an alternative definition for mechanical stability, which is closely related with the mathematical notions of existence and uniqueness of the predicted incremental response. In the final section, some mathematical properties of the moduli of instability are discussed, suggesting a novel reinterpretation of other well established theories and providing additional tools for the future application of the proposed framework.

Extremely energetic rockfalls (EERs) are defined here as rockfalls for which a combination of both large volume and free fall height of hundreds of meters results in energy larger than about 80 GJ released in a short time. Examples include several events worldwide. In contrast to low energy rockfalls where block disintegration is limited, in EERs the impact after free fall causes immediate release of energy much like an explosion. The resulting air blast can snap trees hundreds of meters ahead of the fall area. Pulverized rock at high speed can abrade vegetation in a process of sandblasting, and particles suspended by the blast and the subsequent debris cloud may travel farther than the impact zone, blanketing vast areas. Using published accounts and new data, we introduce physically based models formulated on analogies with explosions and explosive fragmentation to describe EERs. Results indicate that a portion of the initial potential energy of the block is spent in rock disintegration at impact (typically 0.2%–18%), while other sources of energy loss (air drag, seismic, sound, and ground deformation) are negligible; consequently, more than 80% of the potential energy is converted to kinetic energy of the fragmented block (ballistic projection, shock wave, sand blast, and dust cloud). We also propose simple estimates for the flow of the dust cloud associated with an EER and its long settling time. The areal extent of the affected zone is estimated from the energy balance and an empirical power law relationship.

Interaction diagrams in the generalized 3D loading space of vertical (V), horizontal (H) and moment (M) actions constitute the basis of the design of foundation structures in case of complex loads combinations. The mechanical response of such systems is frequently interpreted in terms of the 'macroelement' theory, where a generalized incremental constitutive relationship is introduced, linking the displacements and rotations of the foundation (playing the role of generalized strains) to the histories of applied loading components (i.e. the generalized stresses). In this paper an attempt to extend a classical macroelement framework, to the case of root-soil interaction presented. The model is calibrated on small scale experimental data on 3D printed plastic root systems, subject to combined V-H-M loads, and a parametric analysis on the main governing parameters is discussed. The comparison between numerical and experimental data suggests that the macroelement approach could be an efficient and simple analytical tool for describing the whole moment-rotation curve, overcoming the main simplifying hypotheses currently employed in arboriculture practice.

In this paper, the results of an oedometric numerical test campaign, performed by means of a 3D Discrete Ele- ment Code on idealised cemented granular cylindrical specimens, are illustrated. The idealised microstructure taken into account is characterised by the following: (i) rigid grains bonded to one another; (ii) a high void ratio; and (iii) two different families of voids: the micro and the macro-voids. The compaction process developing within the specimens, as well as the localization along tabular zones of pure compressive deformation (compaction banding) that in some cases takes place, are discussed. The influ- ence on the evolution of this peculiar strain localization process of many microstructural/numerical parameters like material porosity, macro-void size, the constitutive relationship adopted for the bonds and the bond damage rate is analysed. Tests for different values of porosity were run. Below a certain porosity threshold value, the onset of mixed modes of localisation was detected whereas the increase in the macro-void size is observed to favour the onset of instabilit