Depth Averaged Models for Fast Landslide Propagation: Mathematical, Rheological and Numerical Aspects

This paper presents an overview of depth averaged modelling of fast catastrophic landslides where coupling of solid skeleton and pore fluid (air and water) is important. The first goal is to show how Biot-Zienkiewicz models can be applied to develop depth integrated, coupled models. The second objective of the paper is to consider a link which can be established between rheological and constitutive models. Perzyna´s viscoplasticity can be considered a general framework within which rheological models such as Bingham and cohesive frictional fluids can be derived. Among the several alternative numerical models, we will focus here on SPH which has not been widely applied by engineers to model landslide propagation. We propose an improvement, based on combining Finite Difference meshes associated to SPH nodes to describe pore pressure evolution inside the landslide mass. We devote a Section to analyze the performance of the models, considering three sets of tests and examples which allows to assess the model performance and limitations: (i) Problems having an analytical solution, (ii) Small scale laboratory tests, and (iii) Real cases for which we have had access to reliable information

Application of identification techniques to determine effect of carbon content in steels on rheological parameters during hot deformation

The objective of the present work is searching for the correlation between the carbon content in steels and the parameters of the rheological models, which are used to describe the materials behavior during hot plastic deformation. This correlation can be expected in the internal variable models, which are based on physical phenomena occurring in the material. Such a model, based on the dislocation density as the internal variable, is investigated in this work. The experiments including hot torsion tests are used for the analysis.
The procedure is composed of three parts. Plastometric tests were performed for steels with various carbon content. Optimization techniques were applied next to determine the coefficients in the internal variable rheological model for these steels. Two versions of the model are considered. One is based on the average dislocation density and the second accounts for the distribution of dislocation densities. Evaluation of correlation between carbon content and such coefficients in the models as activation energy for self diffusion, activation energy for recrystallization, grain boundary mobility, recovery coefficient etc. was the main objective of the work. In consequence, the model which may be used for simulation of hot forming processes for steels with various chemical compositions, is proposed.

Influence of drying conditions on the rheological properties of prunes

Rheological properties of rehydrated prunes were obtained applying compression-relaxation tests by using a Texture Analyzer TAXT2i. A mathematical development was adopted to determine the stress and area, along the deformation. Experimental data of stress versus time was fitted by using three different rheological models: generalized Maxwell, Normand & Peleg and Maxwell. Results showed that generalized Maxwell model can be used to describe the viscoelastic behavior of the samples. The rheological parameters obtained indicated that prunes exhibited elastic behavior more pronounced at low moisture content and drying air temperature. At high moisture content and temperature the sample became a more viscous and less rigid.

The influence of the mixing time in the rheological behavior of cement pastes

Rheology has the purpose to study the flux and deformation of materials when submitted to some tension or outer mechanical solicitation. In practice, the effective scientific field broached by rheology is restricted only to the study of homogeneous fluids behavior, in which are included eminent liquids, particles suspensions, and emulsions. The viscosity (η) and the yield stress (τ 0) are the two basic values that define the fluids' behavior. The first one is the proportionality constant that relates the shear rate (γ) with the shear stress (τ) applied, while the second indicates the minimal tension for the flowage beginning. The fluids that obey the Newton's relation - Newtonians fluids - display the constant viscosity and the null yield stress. It's the case of diluted suspensions and grate amount of the pure liquids (water, acetone, alcohol, etc.) in which the viscosity is an intrinsic characteristic that depends on temperature and, in a less significant way, pressure. The suspension, titled Cement Paste, is defined as being a mixture of water and cement with, or without, a superplasticizer additive. The cement paste has a non-Newtonian fluid behavior (pseudoplastic), showing a viscosity that varies in accord to the applied shear stress and significant deformations are obtained from a delimited yield stress. In some cases, systems can also manifest the influence of chemical additives used to modify the interactions fluid/particles, besides the introduced modifications by the presence of incorporated air. To the cement paste the rheometric rehearsals were made using the rheometer R/S Brookfield that controls shear stress and shear rate in accord to the rheological model of Herschel-Bulkley that seems to better adapt to this kind of suspension's behavior. This paper shows the results of rheometrical rehearsals on the cement paste that were produced with cements HOLCIM MC-20 RS and CPV-ARI RS with the addition of superplasticizer additives based of napthaline and polycarboxilate, with and without a constant agitation of the mixture. The obtainment of dosages of superplasticizer additives, as well as the water/cement ratio, at the cement at the fluidify rate determination, was done in a total of 12 different mixtures. It's observed that the rheological parameters seem to vary according to the cement type, the superplasticizer type, and the methodology applied at the fluidity rate determination.

Rheological behavior of binary aqueous solutions of poly(ethylene glycol) of 1500 g·mol-1 as affected by temperature and polymer concentration

The rheological behavior of poly(ethylene glycol) of 1500 g·mol -1(PEG1500) aqueous solutions with various polymer concentrations (w = 0.05, 0.10, 0.15, 0.20 and 0.25) was studied at different temperatures (T = 283.15, 288.15, 293.15, 298.15 and 303.15) K. The analyses were carried out considering shear rates ranging from (20 to 350) s-1, using a cone-and-plate rheometer under controlled stress and temperature. Classical rheological models (Newton, Bingham, Power Law, Casson, and Herschel-Bulkley) were tested. The Power Law model was shown suitable to mathematically represent the rheological behavior of these solutions. Well-adjusted empirical models were derived for consistency index variations in function of temperature (Arrhenius-type model; R2 > 0.96), polymer concentration (exponential model; R2 > 0.99) or the combination of both (R 2 > 0.99). Additionally, linear models were used to represent the variations of behavior index in the functions of temperature (R2 > 0.83) and concentration (R2 > 0.87). © 2013 American Chemical Society.

Generalized Viscoplastic Modeling of Debris Flow

Various concepts have been proposed or used in the development of rheological models for debris flow. The earliest model developed by Bagnold was based on the concept of the “dispersive” pressure generated by grain collisions. Bagnold’s concept appears to be theoretically sound, but his empirical model has been found to be inconsistent with most theoretical models developed from non-Newtonian fluid mechanics. Although the generality of Bagnold’s model is still at issue, debris-flow modelers in Japan have generally accepted Takahashi’s formulas derived from Bagnold’s model. Some efforts have recently been made by theoreticians in non-Newtonian fluid mechanics to modify or improve Bagnold’s concept or model. A viable rheological model should consist both of a rate-independent part and a rate-dependent part. A generalized viscoplastic fluid (GVF) model that has both parts as well as two major rheological properties (i.e., the normal stress effect and soil yield criterion) is shown to be sufficiently accurate, yet practical, for general use in debris-flow modeling. In fact, Bagnold’s model is found to be only a particular case of the GVF model. Analytical solutions for (steady) uniform debris flows in wide channels are obtained from the GVF model based on Bagnold’s simplified assumption of constant grain concentration.

Fundamentals of steady state, non-Newtonian rimming flow

Rimming flow on the inner surface of a horizontal rotating cylinder is investigated. Using a scale analysis, a theoretical description is obtained for steady-state non-Newtonian flow. Simple lubrication theory is applied since the Reynolds number is small and the liquid film is thin. Since the Deborah number is very small the flow is viscometric. The shear-thinning number, which characterizes the shear-thinning effect, may be small or large. A general constitutive law for this kind of flow requires only a single function relating shear stress and shear rate that corresponds to a generalized Newtonian liquid. For this case the run-off condition for rimming flow is derived. Provided the run-off condition is satisfied, the existence of a continuous steady-state solution is proved. The rheological models, which show Newtonian behavior at low shear rates with transition to power-law shear thinning at moderate shear rates, are considered. Numerical results are carried out for the Carreau and Ellis models, which exhibit Newtonian behavior near the free surface and power-law behavior near the wall of the rotating cylinder.

Influence des caractéristiques rhéologiques des bétons autoplaçants sur leur durabilité

Résumé : De même degré d’importance que les paramètres de formulation, les conditions de consolidation sont des facteurs déterminants pour la durabilité des bétons conventionnels vibrés. Dans le cas des bétons autoplaçants (BAP), grâce à leur grande fluidité, la mise en place dans les coffrages a lieu par écoulement libre sous l’effet de leur poids propre. Leur consolidation se fait sans vibration grâce à leurs caractéristiques rhéologiques. Il est donc légitime de penser que les caractéristiques rhéologiques des BAP peuvent avoir une influence importante sur les propriétés qui déterminent la durabilité. Cette thèse étudie les liens possibles entre les caractéristiques rhéologiques des BAP et leur durabilité vis-à-vis du transport des agents agressifs. Dix-sept formulations de BAP couvrant une large gamme de caractéristiques rhéologiques et se différenciant uniquement par leur dosage en adjuvants ont été étudiées à cet effet. Trois modèles rhéologiques classiques ont été mis en œuvre pour la détermination des paramètres rhéologiques des bétons étudiés. L’essai de sorptivité et dans une moindre mesure l’essai de carbonatation accélérée ont été utilisés comme indicateur de durabilité vis-à-vis du transport des agressifs. La durabilité de la couche superficielle au contact respectivement avec le coffrage en bois et en PVC a été étudiée et les résultats ont été comparés à la durabilité du béton à cœur. Cette étude a été faite en tenant compte des échanges hydriques et de l’arrangement granulaire au droit du coffrage. D’autre part, l’étude de la durabilité de la couche superficielle dans des conditions de mise en place proches du chantier a été faite sur 6 poutres partiellement armées longues de 2 m ainsi que sur 3 bétons semi-autoplaçants légèrement vibrés. Les résultats montrent qu’il existe une corrélation forte entre la viscosité plastique du modèle Bingham modifié ou le coefficient de consistance du modèle Herschel-Bulkley et la sorptivité. Très probablement, la viscosité agit sur le volume relatif des pores capillaires de gros diamètres. L’étude spécifique de la couche superficielle a montré que sa sorptivité dépend du type de coffrage utilisé à cause des éventuels échanges hydriques opérés entre le béton et la surface du coffrage. De plus, l’arrangement granulaire au droit du coffrage est également influencé. Ainsi, la sorptivité de la couche superficielle au contact du PVC est proche mais inférieure à celle du béton à cœur. La sorptivité de la couche superficielle au contact du bois est significativement inférieure à celle de la couche superficielle au contact du PVC tout en restant corrélé avec la viscosité plastique du modèle Bingham modifié ou le coefficient de consistance du modèle Herschel-Bulkley.

Ice internal friction: Standard theoretical perspectives on friction codified, adapted for the unusual rheology of ice, and unified

Sea ice contains flaws including frictional contacts. We aim to describe quantitatively the mechanics of those contacts, providing local physics for geophysical models. With a focus on the internal friction of ice, we review standard micro-mechanical models of friction. The solid's deformation under normal load may be ductile or elastic. The shear failure of the contact may be by ductile flow, brittle fracture, or melting and hydrodynamic lubrication. Combinations of these give a total of six rheological models. When the material under study is ice, several of the rheological parameters in the standard models are not constant, but depend on the temperature of the bulk, on the normal stress under which samples are pressed together, or on the sliding velocity and acceleration. This has the effect of making the shear stress required for sliding dependent on sliding velocity, acceleration, and temperature. In some cases, it also perturbs the exponent in the normal-stress dependence of that shear stress away from the value that applies to most materials. We unify the models by a principle of maximum displacement for normal deformation, and of minimum stress for shear failure, reducing the controversy over the mechanism of internal friction in ice to the choice of values of four parameters in a single model. The four parameters represent, for a typical asperity contact, the sliding distance required to expel melt-water, the sliding distance required to break contact, the normal strain in the asperity, and the thickness of any ductile shear zone.

Possibilities to include in numerical simulation stochastic and discontinuous phenomena occurring in material

Simulation of materials processing has to face new difficulties regarding proper description of various discontinuous and stochastic phenomena occurring in materials. Commonly used rheological models based on differential equations treat material as continuum and are unable to describe properly several important phenomena. That is the reason for ongoing search for alternative models, which can account for non-continuous structure of the materials and for the fact, that various phenomena in the materials occur in different scales from nano to mezo. Accounting for the stochastic character of some phenomena is an additional challenge. One of the solutions may be the coupled Cellular Automata (CA) – Finite Element (FE) multi scale model. A detailed discussion about the advantages given by the developed multi scale CAFE model for strain localization phenomena in contrast to capabilities provided by the conventional FE approaches is a subject of this work. Results obtained from the CAFE model are supported by the experimental observations showing influence of many discontinuities existing in the real material on macroscopic response. An immense capabilities of the CAFE approach in comparison to limitations of the FE method for modeling of real material behavior is are shown this work as well.

Avaliação do comportamento reológico de pastas de cimento para poços de petróleo com adição de plastificantes

The isolation of adjacent zones encountered during oilwell drilling is carried out by Portland-based cement slurries. The slurries are pumped into the annular positions between the well and the casing. Their rheological behavior is a very important component for the cementing process. Nowadays, several alternative materials are used in oilwell cementing, with goal the modification and the improvement of their properties, mainly the increase of the fluidity. And this can be reached by using plasticizers additives able to account for different oilwell conditions, yielding compatible cement slurries and allowing enough time for the complete cementing operation. If the rheological properties of the slurry are properly characterized, the load loss and flow regime can be correctly predicted. However, this experimental characterization is difficult. Rheological models capable of describing the cement slurry behavior must be capable of predicting the slurry cement deformation within reasonable accuracy. The aim of this study was to characterize rheologically the slurries prepared with a especial class of Portland cement, water and plasticizers based on lignosulfonate, melamine and polycarboxylate at temperatures varying from 27°C to 72°C. The tests were carried out according to the practical recommendations of the API RP 10B guidelines. The results revealed a great efficiency and the dispersive power of the polycarboxylate, for all temperatures tested. This additive promoted high fluidity of the slurries, with no sedimentation. High lignosulfonate and melamine concentrations did not reduce the rheological parameters (plastic viscosity and yield stress) of the slurries. It was verified that these additives were not compatible with the type of cement used. The evaluated rheological models were capable of describing the behavior of the slurries only within concentration and temperature ranges specific for each type of additive

Solids rheology for dehydrated food and biological materials

Mechanical properties of food products and biological materials are greatly affected by the drying process and are considered one of the most important quality attributes of dehydrated products. The aim of this work was to review theoretical principles and mathematical modeling, analyzing the measurement techniques and major experimental results that exist in the literature about rheological properties of dehydrated foods and biological materials. Different methods of measuring rheological parameters (fundamental and empiric or imitative) are discussed and major experimental results, as well as the rheological models used in their analysis, published in recent years are presented.

Viscoelastic behavior of persimmons dried at constant air temperature

The viscoelastic behavior of dried persimmons at different air-drying temperatures and velocities was evaluated. Air temperatures and velocities were varied according to a second-order central composite design, with temperature ranging from 40degreesC to 70degreesC and air velocity from 0.8 to 2.0 m/s. After drying, persimmons were equilibrated at four different water activities: 0.432, 0.576, 0.625 and 0.751. The rheological behavior of dried and conditioned persimmons was studied under uniaxial compression-relaxation tests. Three different rheological models were fitted to the experimental relaxation curves: Maxwell, Generalized Maxwell and Peleg and Normand. Based on the root mean square of residuals, the Generalized Maxwell model showed the best fit and a regression analysis was applied to obtain response surfaces for the model parameters. The dependence of the rheological properties on water activity was also analysed. Results showed that only the linear effect of air temperature was significant at a 5% level on the equilibrium stress and relaxation times. In a general way, these parameters increased with increasing air temperature and decreasing water activity. (C) 2004 Swiss Society of Food Science and Technology. Published by Elsevier Ltd. All rights reserved.

Influência da faixa de taxas de deformação na precisão de caracterizações reológicas de fluidos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Reologia de vinhos tintos secos produzidos no Sul do Brasil

Pós-graduação em Engenharia e Ciência de Alimentos - IBILCE