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This article presents the development and calibration of a numerical model simulating the response of a novel rockfall protection structure subjected to localized dynamic loading. This structure is made of piled-up concrete blocks interconnected via metallic components whose dynamics response under projectile impact is examined via real-scale experiments. The corresponding numerical model is developed in a python based open source software Siconos which implements the Non-Smooth Contact Dynamics (NSCD) method. The geometrical features and mechanical properties are incorporated in the model via specific developments pertinent to the modelling requirements in Siconos. Some parameters peculiar to the numerical model are calibrated against the spatial–temporal measurements from two full-scale impact experiments. The Bayesian interface statistical learning method aided by the polynomial chaos expansion based meta-model of the NSCD model is deployed for the calibration. The additional understanding of the model dynamics through the byproducts of the meta-model is highlighted. In the end, the NSCD model is successfully calibrated against the spatial–temporal response of the experimental structure with more than 90% accuracy for impact energies up to 1 MJ. • Non-smooth contact dynamics (NSCD) based numerical model of a novel rockfall protection structure. • Model development incorporating the design intricacies in the counterpart full-scale experimental structure. • Identification of model parameters for spatio-temporal calibration against experimental database. • Model calibration via Bayesian interface statistical learning method aided by the surrogate models. [ABSTRACT FROM AUTHOR]

The paper addresses the response of a semi-rigid rockfall protection barrier using numerical models. The study show a large dependence of the barrier response to the impact conditions. The block size and impact position, rather than the velocity direction and magnitude induce different modes of failure of the fence, which in turn result in different values of failure energy. As a result, the barrier capacity cannot be established in a deterministic way. The effectiveness of structures as such can be more successfully evaluated through a reliability probabilistic approach. Results can be used to create a meta-model of the barrier response which can be incorporated into rockfall simulation models, enabling a reliable and comprehensive design of rockfall mitigation interventions performed with this type of structure. [ABSTRACT FROM AUTHOR]

Highlights: [•] Using a finite element method, we developed a 3D slope stability model. [•] We modelled the impact of 5 mountain forest management scenarios on slope stability. [•] Slope geomorphology plays an essential role in slope stability. [•] The distribution of roots with soil depth significantly affects slope stability. [Copyright &y& Elsevier]

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 accuracy of rockfall trajectory simulations depends to a large extent on the calculation of the rebound of falling boulders on different parts of a slope where rockfalls could occur. The models commonly used for rebound calculation are based on restitution coefficients, which can only be calibrated subjectively in the field. To come up with a robust and objective procedure for rebound calculation, a stochastic impact model associated with an objective field data collection method was developed and tested in this study. The aims of this work were to assess the adequacy of this approach and to evaluate the minimum amount of field data required to obtain simulation results with a satisfactory level of predictability. To achieve these objectives, the rebound calculation procedure developed was integrated into a three-dimensional rockfall simulation model, and the simulated results were compared with those obtained from field rockfall experiments. For rocky slopes, the simulations satisfactorily predict the experimental results. This approach is advantageous because it combines precise modelling of the mechanisms involved in the rebound and of their related variability with an objective field data collection procedure which basically only requires collecting the mean size of soil rocks. The approach proposed in this study therefore constitutes an excellent basis for the objective probabilistic assessment of rockfall hazard. [Copyright &y& Elsevier]

• Hydrological and mechanical reinforcement from vegetation was assessed. • Roots in high elevation forests are slow to recover after soil disturbance. • Roots in gaps in low elevation forests recover quickly after soil disturbance. • Hydrological reinforcement fluctuates more strongly with season than mechanical reinforcement. • Mechanical reinforcement is more reliable than hydrological reinforcement. Natural hazards such as shallow landslides are common phenomena that disturb soil and damage forests. Quantifying the recovery of forest vegetation after a hazard is important for determining the window of susceptibility to new disturbance events, especially at high elevations, where extreme weather events are frequent and the growing season is short. Plant roots can reduce the size of this window on unstable hillslopes, by adding mechanical reinforcement (c r) to soil and increasing its matric suction, termed here as hydrological reinforcement (c h). These data are used in landslide models to calculate the Factor of Safety (FoS) of a hillslope. We calculated temporal variations in c r and c h in naturally regenerated mixed, montane forests in the French Alps. In these closed-canopy forests, open-canopy gaps were present, with understory vegetation comprising herbs, forbs and shrubs. At three altitudes (1400, 1700 and 2000 m), we dug small trenches as proxies for shallow landslide events and calculated c r before soil disturbance in both open gaps and closed forests. Then, using monthly tree root initiation and mortality data measured in rhizotrons, we calculated monthly c r for four years after the disturbance. To compare results with c r , c h was estimated using matric suction data that were measured in trenches at 1400 m for >1 year. Temporal FoS was then calculated using an infinite slope stability model. Results showed that finer, short-lived roots contributed little to soil reinforcement compared to thicker, long-lived roots. After disturbance, mean c r (over the entire soil profile) never fully recovered to the initial value at any site, although >90% recovery was observed in open gaps at 1400 m. Mean c r was slow to recover in closed forests, especially at 2000 m, where only 19% recovery occurred after 41 months. The c h in closed forests was considerable during the summer months, but marked increases in soil water moisture resulted in lower FoS, especially during December to April, when soil was near saturation. As c r changed little throughout the year, it was a more reliable contributor to slope stability. Our results show therefore, that particular attention should be paid to high elevation forests after a disturbance. Also, during the process of recovery, the highly variable soil water dynamics in closed forest can result in seasonal hotspots of vulnerability. Therefore, when tree transpiration is low, our results highlight a need for careful monitoring on steep or unstable slopes, especially in disturbed closed-canopy forests. [ABSTRACT FROM AUTHOR]

In mountain environments, precise rockfall risk evaluation is crucial to reduce death tolls and costs. However, to date, existing rockfall risk assessment procedures remain scarce, as they focus only on existing elements at risk and with the damage expectation as sole risk measure. Here, we propose an approach to evaluate the distribution of damages on an individual basis as a continuous function of space. Furthermore, rockfall risk is evaluated through (i) the damage expectation and based on (ii) the value-at-risk (VAR) and (iii) the expected shortfall (ES). VaR and ES risk measures allow better assessing the risk due to extreme events and accounting for various short-term/long-term constraints faced by stakeholders. This procedure is applied to Le Brocey slope (municipality of Crolles, French Alps), frequently affected by rockfall events, illustrating its potential for land-use planning. Notably, obtained individual risk values can be confronted with acceptability thresholds to perform legal zoning on sound basis. Also, they allow comparison of risk management strategies as function of different behaviors towards risk, budgetary constraints and/or temporal horizons. Hence, the approach provides valuable tools for future land-use planning and decision-making. It could easily be transferred to other hazards as a wider contribution to the determination of the best balance between safety and sustainability. [ABSTRACT FROM AUTHOR]

Coulomb friction model with unilateral contact is a basic, but reliable, model to represent the resistance to sliding between solid bodies. It is nowadays well-known that this model can be formulated as a second–order cone complementarity problem, or equivalently, as a variational inequality. In this article, the Coulomb friction model is enriched to take into account the resistance to rolling, also known as rolling friction. Introducing the rolling friction cone, an extended Coulomb's cone, and its dual, a formulation of the Coulomb friction with rolling resistance as a cone complementarity problem is shown to be equivalent to the standard formulation of the Coulomb friction with rolling resistance. Based on this complementarity formulation, the maximum dissipation principle and the bi-potential function are derived. Several iterative numerical methods based on projected fixed point iterations for variational inequalities and block-splitting techniques are given. The efficiency of these methods strongly relies on the computation of the projection onto the rolling friction cone. In this article, an original closed-form formula for the projection on the rolling friction cone is derived. The abilities of the model and the numerical methods are illustrated on the examples of a single sphere sliding and rolling on a plane, and of the evolution of spheres piles under gravity. • Formulation of the Coulomb friction with rolling resistance as a cone complementarity problem. • Derivation of the maximum dissipation principle and the bi-potential function. • Iterative numerical methods based on projected _xed point iterations for variational inequalities and block-splitting techniques are given. • An original closed-form formulae for the projection on the rolling friction cone is derived. • Examples of a single sphere sliding and rolling on a plane, and of the evolution of spheres piles under gravity. [ABSTRACT FROM AUTHOR]

The paper illustrates the development of metamodels of the response of steel piles driven in sand and subjected to pull-out. The metamodels are created for the prediction of the pile tensile capacity and secant stiffness. They were developed using the results of finite element analyses, which made use of finite element models of robustness assessed employing a selection of available data from large-scale model pile tests. Four hundred finite element analyses allowed for the calibration of very accurate metamodels, which were also demonstrated to closely track the outputs of the experimental results. Once calibrated, the metamodels can be used independently from the finite element models they stemmed from. The outcomes of the study show that metamodels of piles response can yield very accurate results within a wide and realistic range of soil-pile configuration, avoiding the laborious implementation and computational cost which underpins the use of finite element models. As the use of metamodels in this context is new, the paper relies on particularly simplified problem, but the procedure could be extended to accommodate modelling features of higher complexity. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with a theoretical question as to the definition of instabilities in a granular assembly and its proper formulation at the microscopic level. Recently, this question has taken up much prominence with the emergence of intriguing failure modes such as diffuse failure associated to unstable plasticity of granular materials and microstructural instabilities. An analysis of the second-order work as a general and necessary criterion to detect instabilities is conducted both at the macroscopic and microscopic levels including large deformations. On the basis of a micromechanical analysis of a body consisting of arbitrary interacting particles in a representative element volume (REV), a general formula is derived to quantify the microscopic second-order work involving local variables on the grain scale. The latter emerges as a sum of a configurational term that involves contact forces between neighboring grains, plus a kinetic part consisting of the mechanical unbalance of intergranular forces under dynamics at incipient failure. The present analysis is thought to serve as a clarification of the question of failure in geomaterials typified by a transition from static to a dynamic regime with release of kinetic energy originating from microstructural interactions. [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]

Several studies have debated the incidence of global warming on the probability of rock instability, whereas the impacts of land use and land cover (LULC) changes on rockfall propagation and associated hazards have received comparably little interest. In this study we evaluate the impacts of LULC changes on rockfall hazards on the slopes above the village of Crolles (Chartreuse massif, Grenoble conurbation, French Alps) through a three-level approach: (i) diachronic landscape analysis for four different periods of the past (i.e. 1850, 1956, 1975, and 2013), (ii) computation of 3D rockfall simulations taking explicitly account of reconstructed LULC changes, and (iii) resulting changes in rockfall hazards over time. We reveal that the disappearance of viticultural landscapes (relating to the decline of cropping areas during the interwar period) and intense afforestation of the steepest upper portion of the slope resulted in a significant increase of rockfall return period associated to a gradual decrease of mean kinetic energy at the level of the urban front of Crolles. According to the Eurobloc methodology, the degree of hazard decreased significantly despite the continuous and rapid urban sprawl on the slopes. These results underline that forests can indeed have significant protection function but also call for a more systematic inclusion of LULC changes in hazard assessments in the future. [ABSTRACT FROM AUTHOR]