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Wooden structures made of felled trees are used in forested slopes as protection structures against rockfall. A model based on the Discrete Element Method is developed to analyse their response to normal impacts of blocks. The interaction between the blocks and the stems and the stem response are explicitly integrated. After the model calibration using impact tests, a wide range of impact scenarii representative of real configurations is explored. The influence of three parameters (stem diameter, impact velocity and block diameter) is analysed. Three impact types were identified for different ratios R D between the block and stem diameters. For small R D , the impact is limited to a brief contact. For intermediate R D , successive contacts of similar duration are observed. After the last contact, the block is sent back with a large velocity. For large R D , two contacts are observed. The second contact can be assimilated to a quasi-static loading of the stem. In addition, structure damage increases for increasing R D ranging from almost no damage for the first impact type to rupture of the stem for the third type. The largest R D associated with the first impact type is the target configuration that favours block energy decrease and limits structure damage. [ABSTRACT FROM AUTHOR]

In order to model rockfall on forested slopes, we developed a trajectory rockfall model based on the discrete element method (DEM). This model is able to take the complex mechanical processes at work during an impact into account (large deformations, complex contact conditions) and can explicitly simulate block/soil, block/tree contacts as well as contacts between neighbouring trees. In this paper, we describe the DEM model developed and we use it to assess the protective effect of different types of forest. In addition, we compared it with a more classical rockfall simulation model. The results highlight that forests can significantly reduce rockfall hazard and that the spatial structure of coppice forests has to be taken into account in rockfall simulations in order to avoid overestimating the protective role of these forest structures against rockfall hazard. In addition, the protective role of the forests is mainly influenced by the basal area. Finally, the advantages and limitations of the DEM model were compared with classical rockfall modelling approaches. [ABSTRACT FROM AUTHOR]

The objective of this research was to use numerical models based on mechanical approaches to improve the integration of the protective role of forests against rockfall into block propagation models. A model based on the discrete element method (DEM) was developed to take into account the complex mechanical processes involved during the impact of a block on a tree. This modelling approach requires the definition of many input parameters and cannot be directly integrated into block propagation models. A global sensitivity analysis identified the leading parameters of the block kinematics after impact (i.e. block energy reduction, trajectory changes, and rotational velocity): the impact velocity, the tree diameter, and the impact point horizontal location (i.e. eccentricity). Comparisons with the previous experimental and numerical studies of block impacts on trees demonstrated the applicability of the DEM model and showed some of the limitations of earlier approaches. Our sensitivity analysis highlights the significant influence of the impact velocity on the reduction of the block's kinetic energy. Previous approaches usually also focus on parameters such as impact height, impact vertical incidence, and tree species, whose importance is only minor according to the present results. This suggests that the integration of forest effects into block propagation models could be both improved and simplified. The DEM model can also be used as an alternative to classical approaches for the integration of forest effects by directly coupling it with block propagation models. This direct coupling only requires the additional definition of the location and the diameter of each tree. Indeed, the input parameters related to the mechanical properties of the stem and the block/stem interaction in the DEM model can be set to average values because they are not leading parameters. The other input parameters are already defined or calculated in the block propagation model. [ABSTRACT FROM AUTHOR]

Abstract: The analysis of the influence of the roots on the shear resistance of the soil requires identifying the effect of the different root–soil interaction processes depending on soil and roots properties. For that purpose, a numerical model of direct shear tests of non-rooted and rooted granular soils based on the Discrete Element Method was developed. The soil is modeled as an assembly of locally interacting spheres and the roots are modeled as deformable cylinders in the soil matrix. The model allows accounting for the root tensile loading until breakage, the root bending loading, the root–soil adhesive links until adhesion breakage, the root slippage associated with a frictional resistance at the root–soil interface. The study focuses on identifying the different root–soil interaction mechanisms depending on the soil type. Both frictional and cohesive granular soil types were used in the simulations. The effects of the roots mechanical properties – tensile, bending modulus and root–soil interfacial friction angle – and of the root number were also analyzed for the different soil types. The results first show that the effect of the roots strongly depends on the shear strain for any soil type. For frictional soils, an increasing shear strain induces progressively a pure tensile loading of the roots until slippage of the root–soil interface. For cohesive granular soils, the pure tensile loading of the roots is followed by a progressive breakage of the adhesive root–soil links and by a complete slippage of the roots. The results show that the influence of the root number is significant if the prevailing processes are root tensile loading combined with slippage whereas it is less important if root loading is combined with progressive breakage of the adhesive links for the root configurations explored. Finally, the results show that the shear strain range associated with the different processes strongly depends on the relative rigidities of the roots and soil matrix. The model developed was shown of great interest to analyze the shear resistance of the rooted soil assemblies depending on the shear strain. Such an approach could therefore be used to test the different assumptions done in the analytical models. Developing analytical models of slope stability based on the calculation of the shear resistance of rooted soil depending not only on soil and root properties but also on shear strain intensity also constitutes a perspective for the use of the model developed. [Copyright &y& Elsevier]

Abstract: The impact of a projectile on a granular material induces important changes in the micromechanical properties of the impacted material. These changes are studied using a Discrete Element Method model of the impact. The numerical results show that the impact first entails an energy propagation from the impact point to the limit of the sample through the existing force chains. A significant kinetic energy and a total breakage of the existing contact force chains are the main consequences of the energy propagation. During the long recovery balance phase observed after the energy propagation phase, frictional processes cause the kinetic energy dissipation. The motions of the particles and the numerous contact openings first prevent the formation of stable force chains. However, for long durations after the beginning of the impact, contact openings stop. The balance recovery phase therefore finally results in the creation of new stable contact force networks. [Copyright &y& Elsevier]

• Two different DEM models used to predict the barrier response under various loadings • Analysis of the experimental barrier response under single and successive impacts • The discrete element method is assessed for flexible rockfall barrier modeling This paper addresses the use of discrete element modeling approaches for predicting the impact response of flexible rockfall protection barriers. In this purpose, two different models are considered and their results are compared to detailed results from full-scale impact experiments. The studied barrier is a prototype made from a 4-contacts ring net and having a 270 kJ nominal capacity. The two discrete elements method models, developed by separate entities with different codes (Yade-DEM and GENEROCK), use different models for the ring net, the cables and cable-net connections, while other structural elements are modelled the same way : posts, anchors, energy dissipating devices, and boulder. The models for the structural elements (ring net, energy dissipating devices) are calibrated individually from quasi-static tensile tests results. The barrier model is then created assembling the structural elements, before being impacted. The tests consist in a impacting in its center a 3-module barrier, first, to one high kinetic energy impact and, second, to three consecutive impacts with a lower kinetic energy. The models results are confronted to measurements made during the experiments, considering a large set of parameters. Both models reveal satisfactory in predicting the structure response, on quantitative and qualitative points of view, and considering the boulder displacement, forces in the main cables and forces acting within the various energy dissipating devices. The quality of the prediction by each model compared to the other depends on the considered parameter. Little deviations from the experimental results are attributed to the model calibration procedure and to slight differences between the real structure and the modeled ones. In the end, the DEM approach appears suitable for modelling flexible barriers in complex loading conditions (high velocity and successive impacts). [ABSTRACT FROM AUTHOR]