Crossover from quasi-static to dense flow regime in compressed frictional granular media

We investigate the evolution of multi-scale mechanical properties towards the macroscopic mechanical instability in frictional granular media under multiaxial compressive loading. Spatial correlations of shear stress redistribution following nucleating contact sliding events and shear strain localization are investigated. We report growing correlation lengths associated to both shear stress and shear strain fields that diverge simultaneously as approaching the transition to a dense flow regime. This shows that the transition from quasi static to dense flow regime can be interpreted as a critical phase transition. Our results suggest that no shear band with a characteristic thickness has formed at the onset of instability

Eléments de dimensionnement d'un échangeur air/sol, dit « puits canadien »

L'utilisation d'un échangeur air/sol, système appelé communément « puits canadien » en France et parfois « puits provençal » lorsqu'il sert à rafraîchir l'habitation, connaît un développement important depuis quelques années. Il consiste à utiliser comme entrée pour la ventilation de la maison, de l'air qui a préalablement circulé dans un tube enterré à une certaine profondeur. La température du sous-sol étant moins variable que celle de l'air extérieur cela permet d'avoir une entrée d'air plus tempérée. En hiver, l'air est réchauffé avant de pénétrer dans la maison ; en été il est rafraîchit. Il s'agit ainsi du système de géothermie le plus simple qui soit, avec une consommation électrique réduite à la celle du ventilateur utilisée pour la circulation de l'air. Ce système est utilisé traditionnellement en Amérique du nord pour maintenir les habitations hors gel sans chauffage pendant l'hiver pourtant très rigoureux (à noter que le terme de « puits canadien » n'est pas employé au Canada). Ce système permet de compenser de manière notable la perte de chaleur induite par les débits de ventilation imposés par la réglementation française actuelle. En été, il permet d'abaisser la température maximale de quelques degrés. Le système doit être désactivé pendant les intersaisons afin de ne pas refroidir la maison alors que l'on recherche la chaleur. L'entrée d'air est alors directement prise sur l'extérieur sans passer par le puits canadien. Le dimensionnement d'un puits canadien est assez délicat du fait du nombre de paramètres à optimiser : longueur, diamètre et nombre de tubes, profondeur d'enfouissement, distance entre les tubes, débit de ventilation. La notice de dimensionnement présentée ici a pour but de proposer des critères objectifs pour le choix de ces différentes caractéristiques. Ce travail est basé sur des simulations numériques d'échange thermique par convection forcée dans un tube enterré. Ceci permet de mettre en évidence l'effet du diamètre, de la longueur, du débit volumétrique de la différence de température entre le sol et l'air entrant sur le flux thermique fourni par le puits canadien. Dans un second temps, nous présentons des simulations de flux annuel en fonction de la profondeur d'enfouissement de la gaine. Ceci permet de mettre en évidence les périodes d'apport de chaleur et/ou de fraîcheur au cours de l'année et la nécessité de coupure aux intersaisons. Enfin nous donnons quelques éléments pour le calcul des pertes charge aérauliques

Variability in the power-law distributions of rupture events, How and why does b-value change

International audienceRupture events, as the propagation of cracks or the sliding along faults, associated with the deformation of brittle materials are observed to obey power-law distributions. This is verified at scales ranging from laboratory samples to the Earth's crust, for various materials and under various loading modes. Besides the claim that this is a universal characteristic of the deformation of heterogeneous media, spatial and temporal variations are observed in the exponent and tail-shape. These have considerable implications for the ability and the reliability of forecasting large events from smaller ones. There is a growing interest in identifying the factors responsible for these variations. In this work, we first present observations at various scales (laboratory tests, field experiments, landslides, mining induced seismicity, crustal Earthquakes) showing that substantial variations exist in both the slope and the tail-shape of the rupture event size distribution. This review allows us to identify potential explanations for these variations (incorrect statistical methods, heterogeneity, stress, brittle/ductile transition, finite size effects, proximity to the failure). A possible link with the critical point theory is also drawn showing that it is able to explain a part of the observed variations considering the distance to the critical point. Using numerical simulations of progressive failure we investigate the role of mechanical properties on the power-law distributions. The results of simulations agree with the critical point theory for various macroscopic behaviors ranging from ductility to brittleness providing a unified framework for the understanding of power-law variability observed in rupture phenomena

Brittle creep, damage and time to failure in rocks

International audienceWe propose a numerical model based on static fatigue laws in order to model the time-dependent damage and deformation of rocks under creep. An empirical relation between time to failure and applied stress is used to simulate the behavior of each element of our finite element model. We review available data on creep experiments in order to study how the material properties and the loading conditions control the failure time. The main parameter that controls the failure time is the applied stress. Two commonly used models, an exponential tfexp (bs/s0) and a power law function tfsb0 fit the data as well. These time-to-failure laws are used at the scale of each element to simulate its damage as a function of its stress history. An element is damaged by decreasing its Young's modulus to simulate the effect of increasing crack density at smaller scales. Elastic interactions between elements and heterogeneity of the mechanical properties lead to the emergence of a complex macroscopic behavior, which is richer than the elementary one. In particular, we observe primary and tertiary creep regimes associated respectively with a power law decay and increase of the rate of strain, damage event and energy release. Our model produces a power law distribution of damage event sizes, with an average size that increases with time as a power law until macroscopic failure. Damage localization emerges at the transition between primary and tertiary creep, when damage rate starts accelerating. The final state of the simulation shows highly damaged bands, similar to shear bands observed in laboratory experiments. The thickness and the orientation of these bands depend on the applied stress. This model thus reproduces many properties of rock creep, which were previously not modeled simultaneously

Damage-cluster distributions and size effect on strength in compressive failure

We investigate compressive failure of heterogeneous materials on the basis of a continuous progressive damage model. The model explicitely accounts for tensile and shear local damage and reproduces the main features of compressive failure of brittle materials like rocks or ice. We show that the size distribution of damage-clusters, as well as the evolution of an order parameter, the size of the largest damage-cluster, argue for a critical interpretation of fracture. The compressive failure strength follows a normal distribution with a very small size effect on the mean strength, in good agreement with experiments

Scaling analysis of deformation field within granular materials: application to strain localization

Discrete element method (DEM) simulations using periodic boundary conditions and molecular dynamics are conducted on a frictional granular media. Two dimensional strain controlled biaxial tests are carried out on an assembly of circular particles interacting via elastic contacts and Coulomb friction. The spatial correlations that take place within the deformation field along the loading path are tracked by a scaling analysis of the continuous strain rate field. This method allows us to discuss the degree of strain localization occurring throughout the test. The analysis of the correlation length in the early stages of macroscopic deformation leads to the identification of two distinct behaviors. First, a divergence of the correlation length on the first deformation invariant, i.e. the divergence, is reported at the onset of macroscopic dilation. This suggests an interpretation of the contraction peak as a critical point. Secondly, an increase of the correlation length on the second deformation invariant, i.e. the shear, is also observed before the peak load. However, saturation remains on the scaling law. We argue that this second behavior is associated to macroscopic shear banding: our analysis accurately gives its outbreak on the stress versus strain curve. Finally, a dependence of the correlation length as a function of the deformation window considered is reported. This shows that scaling properties within the deformation field emerge from long range interactions within an assembly of rigid frictional particles

Auscultation et surveillance des pertubations hydromécaniques d'ouvrages souterrains par la mesure et l'analyse de la propagation d'ondes dans les roches

International audienceThe excavation of a drift creates a disturbed zone, which is called EDZ (Excavation Disturbed or Damaged Zone). The study of the mechanical characteristics of this zone is essential to estimate the stability of such a drift at short, mean or long term. The propagation of ultrasonic waves is used as a mean of analysis in rock mechanics since the 1960s. Initially, it was used to determine the dynamic elastic properties. Then, it was gradually adapted to the study of the other properties of the material such as cracking, porosity, saturation, etc. With the computer tools continuously more powerful, a more elaborated treatment of the signals became possible, which allows characterization of the "EDZ". The Tests carried out in laboratory, allowed us to correlate P-wave and mechanical parameters of the studied media in elastic and plastic phases. Besides, the mechanical modeling of the EDZ around a drift allows understanding the mechanical phenomena on the scale of the work. Finally, the results of an in-site experiment allowed us to locate the EDZ around an underground mine pillar. It contributed to have a better understanding of the mechanical models available and to estimate the pillar stability.Lorsqu'une galerie est excavée, quelle que soit la méthode d'excavation, la roche encaissante subit des perturbations dans une zone dite EDZ (Excavation Disturbed or Damaged Zone). Ces perturbations peuvent se traduire par différents effets allant d'une faible variation de la pression interstitielle à un endommagement important, voire la rupture de l'ouvrage et peuvent mettre en danger la stabilité d'une partie ou de l'ensemble de l'ouvrage souterrain concerné. L'étude des caractéristiques mécaniques de cette zone " EDZ " est essentielle pour estimer la stabilité de l'ouvrage à court, moyen ou long terme. La propagation des ondes ultrasoniques est utilisée comme moyen d'analyse en mécanique des roches depuis les années 1960. Initialement, elle a été mise au point pour déterminer les modules élastiques dynamiques des roches. Ensuite, elle a progressivement été adaptée à l'étude d'autres propriétés du matériau telles que : fissuration, porosité, saturation, etc. Avec les outils informatiques sans cesse plus puissants, un traitement des signaux plus élaboré est devenu possible, ce qui permet d'envisager la caractérisation de l' " EDZ " par cette méthode. Des essais en laboratoire à la fois acoustiques et mécaniques, nous ont permis de relier qualitativement les paramètres de propagation des ondes et les caractéristiques mécaniques du milieu étudié pendant les phases élastique et plastique. Par ailleurs, la modélisation mécanique de l'EDZ autour d'une galerie permet de comprendre les phénomènes mis en jeux à l'échelle de l'ouvrage. Enfin, les résultats d'une expérimentation in situ ont permis de caractériser la distribution de la zone endommagée autour d'un pilier de mine, ce qui a contribué à la vérification des modèles mécaniques existants et à l'estimation de la stabilité de l'ouvrage

(Finite) statistical size effects on compressive strength

The larger structures are, the lower their mechanical strength. Already discussed by Leonardo da Vinci and Edmé Mariotte several centuries ago, size effects on strength remain of crucial importance in modern engineering for the elaboration of safety regulations in structural design or the extrapolation of laboratory results to geophysical field scales. Under tensile loading, statistical size effects are traditionally modeled with a weakest-link approach. One of its prominent results is a prediction of vanishing strength at large scales that can be quantified in the framework of extreme value statistics. Despite a frequent use outside its range of validity, this approach remains the dominant tool in the field of statistical size effects. Here we focus on compressive failure, which concerns a wide range of geophysical and geotechnical situations. We show on historical and recent experimental data that weakest-link predictions are not obeyed. In particular, the mechanical strength saturates at a nonzero value toward large scales. Accounting explicitly for the elastic interactions between defects during the damage process, we build a formal analogy of compressive failure with the depinning transition of an elastic manifold. This critical transition interpretation naturally entails finite-size scaling laws for the mean strength and its associated variability. Theoretical predictions are in remarkable agreement with measurements reported for various materials such as rocks, ice, coal, or concrete. This formalism, which can also be extended to the flowing instability of granular media under multiaxial compression, has important practical consequences for future design rules

High resolution 3D laser scanner measurements of a strike-slip fault quantify its morphological anisotropy at all scales

The surface roughness of a recently exhumed strikeslip fault plane has been measured by three independent 3D portable laser scanners. Digital elevation models of several fault surface areas, from 1 m2 to 600 m2, have been measured at a resolution ranging from 5 mm to 80 mm. Out of plane height fluctuations are described by non-Gaussian distribution with exponential long range tails. Statistical scaling analyses show that the striated fault surface exhibits self-affine scaling invariance with a small but significant directional morphological anisotropy that can be described by two scaling roughness exponents, H1 = 0.7 in the direction of slip and H2 = 0.8 perpendicular to the direction of slip

Techniques, advances, problems and issues in numerical modelling of landslide hazard

Slope movements (e.g. landslides) are dynamic systems that are complex in time and space and closely linked to both inherited and current preparatory and triggering controls. It is not yet possible to assess in all cases conditions for failure, reactivation and rapid surges and successfully simulate their transient and multi-dimensional behaviour and development, although considerable progress has been made in isolating many of the key variables and elementary mechanisms and to include them in physically-based models for landslide hazard assessments. Therefore, the objective of this paper is to review the state-of-the-art in the understanding of landslide processes and to identify some pressing challenges for the development of our modelling capabilities in the forthcoming years for hazard assessment. This paper focuses on the special nature of slope movements and the difficulties related to simulating their complex time-dependent behaviour in mathematical, physically-based models. It analyses successively the research frontiers in the recognition of first-time failures (pre-failure and failure stages), reactivation and the catastrophic transition to rapid gravitational processes (post-failure stage). Subsequently, the paper discusses avenues to transfer local knowledge on landslide activity to landslide hazard forecasts on regional scales and ends with an outline how geomorphological investigations and supporting monitoring techniques could be applied to improve the theoretical concepts and the modelling performance of physically-based landslide models at different spatial and temporal scales