Ratcheting of granular materials

We investigate the quasi-static mechanical response of soils under cyclic loading using a discrete model of randomly generated convex polygons. This response exhibits a sequence of regimes, each one characterized by a linear accumulation of plastic deformation with the number of cycles. At the grain level, a quasi-periodic ratchet-like behavior is observed at the contacts, which excludes the existence of an elastic regime. The study of this slow dynamics allows to explore the role of friction in the permanent deformation of unbound granular materials supporting railroads and streets.Comment: Changed content Submitted to Physical Review Letter

A Model for Granular Texture with Steric Exclusion

We propose a new method to characterize the geometrical texture of a granular packing at the particle scale including the steric hindrance effect. This method is based on the assumption of a maximum disorder (entropy) compatible both with strain-induced anisotropy of the contact network and steric exclusions. We show that the predicted statistics for the local configurations is in a fairly agreement with our numerical data.Comment: 9 pages, 5 figure

Scenario modelling of basin-scale, shallow landslide sediment yield, Valsassina, Italian Southern Alps

International audienceThe SHETRAN model for determining the sediment yield arising from shallow landsliding at the scale of a river catchment was applied to the 180-km2 Valsassina basin in the Italian Southern Alps, with the aim of demonstrating that the model can simulate long term patterns of landsliding and the associated sediment yields and that it can be used to explore the sensitivity of the landslide sediment supply system to changes in catchment characteristics. The model was found to reproduce the observed spatial distribution of landslides from a 50-year record very well but probably with an overestimate of the annual rate of landsliding. Simulated sediment yields were within the range observed in a wider region of northern Italy. However, the results suggest that the supply of shallow landslide material to the channel network contributes relatively little to the overall long term sediment yield compared with other sources. The model was applied for scenarios of possible future climate (drier and warmer) and land use (fully forested hillslopes). For both scenarios, there is a modest reduction in shallow landslide occurrence and the overall sediment yield. This suggests that any current schemes for mitigating sediment yield impact in Valsassina remain valid. The application highlights the need for further research in eliminating the large number of unconditionally unsafe landslide sites typically predicted by the model and in avoiding large overestimates of landslide occurrence

Modelling the impact of forest loss on shallow landslide sediment yield, Ijuez river catchment, Spanish Pyrenees

International audienceThe SHETRAN model for simulating the sediment yield arising from shallow landslides at the scale of a river catchment was applied to the 45-km2 Ijuez catchment in the central Spanish Pyrenees, to investigate the effect of loss of forest cover on landslide and debris flow incidence and on catchment sediment yield. The application demonstrated how such a model, with a large number of parameters to be evaluated, can be used even when directly measured data are not available: rainfall and discharge time series were generated by reference to other local records and data providing the basis for a soil map were obtained by a short field campaign. Uncertainty bounds for the outputs were determined as a function of the uncertainty in the values of key model parameters. For a four-year period and for the existing forested state of the catchment, a good ability to simulate the observed long term spatial distribution of debris flows (represented by a 45-year inventory) and to determine catchment sediment yield within the range of regional observations was demonstrated. The lower uncertainty bound on simulated landslide occurrence approximated the observed annual rate of landsliding and suggests that landslides provide a relatively minor proportion of the total sediment yield, at least in drier years. A scenario simulation in which the forest cover was replaced by grassland indicated an increase in landsliding but a decrease in the number of landslides which evolve into debris flows and, at least for drier years, a reduction in sediment delivery to the channel network

Optimal Wind Bidding Strategies in Day-Ahead Markets

This paper presents a computer application for wind energy bidding in a day-ahead electricity market to better accommodate the variability of the energy source. The computer application is based in a stochastic linear mathematical programming problem. The goal is to obtain the optimal bidding strategy in order to maximize the revenue. Electricity prices and financial penalties for shortfall or surplus energy deliver are modeled. Finally, conclusions are drawn from an illustrative case study, using data from the day-ahead electricity market of the Iberian Peninsula

Unilateral interactions in granular packings: A model for the anisotropy modulus

Unilateral interparticle interactions have an effect on the elastic response of granular materials due to the opening and closing of contacts during quasi-static shear deformations. A simplified model is presented, for which constitutive relations can be derived. For biaxial deformations the elastic behavior in this model involves three independent elastic moduli: bulk, shear, and anisotropy modulus. The bulk and the shear modulus, when scaled by the contact density, are independent of the deformation. However, the magnitude of the anisotropy modulus is proportional to the ratio between shear and volumetric strain. Sufficiently far from the jamming transition, when corrections due to non-affine motion become weak, the theoretical predictions are qualitatively in agreement with simulation results.Comment: 6 pages, 5 figure

Solid behavior of anisotropic rigid frictionless bead assemblies

We investigate the structure and mechanical behavior of assemblies of frictionless, nearly rigid equal-sized beads, in the quasistatic limit, by numerical simulation. Three different loading paths are explored: triaxial compression, triaxial extension and simple shear. Generalizing recent results [1], we show that the material, despite rather strong finite sample size effects, is able to sustain a finite deviator stress in the macroscopic limit, along all three paths, without dilatancy. The shape of the yield surface is adequately described by a Lade-Duncan (rather than Mohr-Coulomb) criterion. While scalar state variables keep the same values as in isotropic systems, fabric and force anisotropies are each characterized by one parameter and are in one-to-one correspondence with principal stress ratio along all three loading paths.The anisotropy of the pair correlation function extends to a distance between bead surfaces on the order of 10% of the diameter. The tensor of elastic moduli is shown to possess a nearly singular, uniaxial structure related to stress anisotropy. Possible stress-strain relations in monotonic loading paths are also discussed

Geometric origin of mechanical properties of granular materials

Some remarkable generic properties, related to isostaticity and potential energy minimization, of equilibrium configurations of assemblies of rigid, frictionless grains are studied. Isostaticity -the uniqueness of the forces, once the list of contacts is known- is established in a quite general context, and the important distinction between isostatic problems under given external loads and isostatic (rigid) structures is presented. Complete rigidity is only guaranteed, on stability grounds, in the case of spherical cohesionless grains. Otherwise, the network of contacts might deform elastically in response to load increments, even though grains are rigid. This sets an uuper bound on the contact coordination number. The approximation of small displacements (ASD) allows to draw analogies with other model systems studied in statistical mechanics, such as minimum paths on a lattice. It also entails the uniqueness of the equilibrium state (the list of contacts itself is geometrically determined) for cohesionless grains, and thus the absence of plastic dissipation. Plasticity and hysteresis are due to the lack of such uniqueness and may stem, apart from intergranular friction, from small, but finite, rearrangements, in which the system jumps between two distinct potential energy minima, or from bounded tensile contact forces. The response to load increments is discussed. On the basis of past numerical studies, we argue that, if the ASD is valid, the macroscopic displacement field is the solution to an elliptic boundary value problem (akin to the Stokes problem).Comment: RevTex, 40 pages, 26 figures. Close to published paper. Misprints and minor errors correcte

Modeling sediment mobilization using a distributed hydrological model coupled with a bank stability model

In addition to surface erosion, stream bank erosion and failure contributes significant sediment and sediment-bound nutrients to receiving waters during high flow events. However, distributed and mechanistic simulation of stream bank sediment contribution to sediment loads in a watershed has not been achieved. Here we present a full coupling of existing distributed watershed and bank stability models and apply the resulting model to the Mad River in central Vermont. We fully coupled the Bank Stability and Toe Erosion Model (BSTEM) with the Distributed Hydrology Soil Vegetation Model (DHSVM) to allow the simulation of stream bank erosion and potential failure in a spatially explicit environment. We demonstrate the model\u27s ability to simulate the impacts of unstable streams on sediment mobilization and transport within a watershed and discuss the model\u27s capability to simulate watershed sediment loading under climate change. The calibrated model simulates total suspended sediment loads and reproduces variability in suspended sediment concentrations at watershed and subbasin outlets. In addition, characteristics such as land use and road-to-stream ratio of subbasins are shown to impact the relative proportions of sediment mobilized by overland erosion, erosion of roads, and stream bank erosion and failure in the subbasins and watershed. This coupled model will advance mechanistic simulation of suspended sediment mobilization and transport from watersheds, which will be particularly valuable for investigating the potential impacts of climate and land use changes, as well as extreme events