Discrete modelling of capillary mechanisms in multi-phase granular media

A numerical study of multi-phase granular materials based upon micro-mechanical modelling is proposed. Discrete element simulations are used to investigate capillary induced effects on the friction properties of a granular assembly in the pendular regime. Capillary forces are described at the local scale through the Young-Laplace equation and are superimposed to the standard dry particle interaction usually well simulated through an elastic-plastic relationship. Both effects of the pressure difference between liquid and gas phases and of the surface tension at the interface are integrated into the interaction model. Hydraulic hysteresis is accounted for based on the possible mechanism of formation and breakage of capillary menisci at contacts. In order to upscale the interparticular model, triaxial loading paths are simulated on a granular assembly and the results interpreted through the Mohr-Coulomb criterion. The micro-mechanical approach is validated with a capillary cohesion induced at the macroscopic scale. It is shown that interparticular menisci contribute to the soil resistance by increasing normal forces at contacts. In addition, more than the capillary pressure level or the degree of saturation, our findings highlight the importance of the density number of liquid bonds on the overall behaviour of the material

Une description générale de la rupture dans les sols et son implication dans la stabilité des ouvrages hydrauliques

National audienceLa rupture des sols est classiquement décrite par le critère de Mohr-Coulomb correspondant à la condition limite de plasticité. Toutefois, les matériaux tels que les sols (présentant une règle d'écoulement non associée) peuvent être sujets à des modes de rupture pour des états de contrainte situés strictement à l'intérieur du critère de Mohr-Coulomb. Cela signifie que la vérification de la stabilité d'un ouvrage en sol s'appuyant uniquement sur un critère de rupture de type Mohr-Coulomb (soit sur la plastification du sol) ne permet pas, en général, de se prévenir de l'ensemble des modes de rupture pouvant se développer au sein du matériau constitutif. Dans cette communication, nous présentons un cadre unique permettant à la fois la description de la rupture plastique (survenant sur le critère de Mohr-Coulomb), et des ruptures se développant à l'intérieur du critère de Mohr-Coulomb. Nous indiquons comment détecter à l'aide du travail du second ordre les états de contrainte à partir desquels les ruptures sont susceptibles de se développer ; et nous donnons les conditions nécessaires et suffisantes (portant à la fois sur la direction de chargement et sur le mode de contrôle du volume de sol considéré) au développement effectif de ces ruptures. Enfin, l'implication de cette description généralisée de la rupture sur l'analyse de la stabilité des ouvrages hydrauliques en terre est abordée. L'ensemble de la discussion est appuyée sur des résultats d'essais de laboratoire et de simulations numériques

A pore-scale approach of two-phase flow in granular porous media

A pore-scale model is presented for simulating two-phase flow in granular materials. The solid phase is idealized as dense random packings of polydisperse spheres, generated with the discrete element method (DEM). The pore space is conceptualized as a network of pores connected by throats, which is obtained by using regular triangulation. Theoretical formulas for calculating geometrical properties and entry capillary pressure for given pores are developed by extending the Mayer and Stowe-Princen (MS-P) theory of drainage. Such relationships are employed in the network for defining as local invasion criteria, so that the drainage can be represented by the replacement of W-phase when the threshold value is reached. The events of W-phase entrapment are considered during the coupling procedures. This pore-scale model is verified by comparing simulation results with experimental data of quasi-static drainage experiments in a synthetic porous medium. The simulated Pc −Sw curve in primary drainage is in agreement with the experimental one

What is wrong in love-weber stress for unsaturated granular materials?

This paper presents the micromechanical model for unsaturated soil in pendular regime, taking into account the roughness of the grains and the interfaces that separate the different phases present in the medium. It supplements the oral presentation with more technical content. Laplace equation is solved for two grains configuration to calculate the capillary force and all the geometric properties of the meniscus connecting the grains. Many configurations are solved and the look up table method is then used during the simulations. Results for grains moving at constant suction and constant vol- ume are presented. It is also shown that the roughness has an important impact on the value of capillary force and it is evolution with the change of suction

Friction vs Texture at the Approach of a Granular Avalanche

We perform a novel analysis of the granular texture of a granular bed close to stability limit. Our analysis is based on a unique criterion of friction mobilisation in a simulated two-dimensional packing. In this way, we recover the bimodal character of granular texture, and the coexistence of weak and strong phases in the sense of distinct contacts populations. Moreover, we show the existence of a well-defined subset of contacts within the weak contact network. These contacts are characterized by their important friction, and form a highly coherent population in terms of fabric. They play an antagonistic role with respect to force chains. We are thus able to discriminate between incoherent contacts and coherent contacts in the weak phase, and to specify the role that the latter plays in the destabilisation process.Comment: 4 pages, 6 figure

Investigating the Role of Non-Covalent Interactions in Conformation and Assembly of Triazine-Based Sequence-Defined Polymers

Grate and co-workers at Pacific Northwest National Laboratory recently developed high information content triazine-based sequence-defined polymers that are robust by not having hydrolyzable bonds and can encode structure and functionality by having various side chains. Through molecular dynamics (MD) simulations, the triazine polymers have been shown to form particular sequential stacks, have stable backbone-backbone interactions through hydrogen bonding and $\pi$-$\pi$ interactions, and conserve their \emph{cis/trans} conformations throughout the simulation. However, we do not know the effects of having different side chains and backbone structures on the entire conformation and whether the \emph{cis} or \emph{trans} conformation is more stable for the triazine polymers. For this reason, we investigate the role of non-covalent interactions for different side chains and backbone structures on the conformation and assembly of triazine polymers in MD simulations. Since there is a high energy barrier associated to the \emph{cis}-\emph{trans} isomerization, we use replica exchange molecular dynamics (REMD) to sample various conformations of triazine hexamers. To obtain rates and intermediate conformations, we use the recently developed concurrent adaptive sampling (CAS) algorithm for dimer of triazine trimers. We found that the hydrogen bonding ability of the backbone structure is critical for the triazine polymers to self-assemble into nanorod-like structures, rather than that of the side chains, which can help researchers design more robust materials

Smoothing-based Compressed State Kalman Filter for Joint State-parameter Estimation: Applications in Reservoir Characterization and CO2 Storage Monitoring

The operation of most engineered hydrogeological systems relies on simulating physical processes using numerical models with uncertain parameters and initial conditions. Predictions by such uncertain models can be greatly improved by Kalman-filter techniques that sequentially assimilate monitoring data. Each assimilation constitutes a nonlinear optimization, which is solved by linearizing an objective function about the model prediction and applying a linear correction to this prediction. However, if model parameters and initial conditions are uncertain, the optimization problem becomes strongly nonlinear and a linear correction may yield unphysical results. In this paper, we investigate the utility of one-step ahead smoothing, a variant of the traditional filtering process, to eliminate nonphysical results and reduce estimation artifacts caused by nonlinearities. We present the smoothing-based compressed state Kalman filter (sCSKF), an algorithm that combines one step ahead smoothing, in which current observations are used to correct the state and parameters one step back in time, with a nonensemble covariance compression scheme, that reduces the computational cost by efficiently exploring the high-dimensional state and parameter space. Numerical experiments show that when model parameters are uncertain and the states exhibit hyperbolic behavior with sharp fronts, as in CO2 storage applications, one-step ahead smoothing reduces overshooting errors and, by design, gives physically consistent state and parameter estimates. We compared sCSKF with commonly used data assimilation methods and showed that for the same computational cost, combining one step ahead smoothing and nonensemble compression is advantageous for real-time characterization and monitoring of large-scale hydrogeological systems with sharp moving fronts

P-positive definite matrices and stability of non conservative systems

International audienceThe bifurcation problem of constrained non-conservative systems with non symmetric stiffness matrices is investigated. It leads to study the subset $D_{p,n}$ of $ℳn(ℝ)$ of the so called $p$-positive definite matrices ($1 ≤ p ≤ n$). The main result ($D_{1,n} ⊂ D_{p,n}$) is proved, the reciprocal result is investigated and the consequences on the stability of elastic nonconservative systems are highlighted