The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

The tendency of granular materials in rapid shear ow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear flow of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

Dense shallow granular flows

Simplified equations are derived for a granular flow in the `dense' limit where the volume fraction is close to that for dynamical arrest, and the `shallow' limit where the stream-wise length for flow development (L) is large compared with the cross-stream height (h). The mass and diameter of the particles are set equal to 1 in the analysis without loss of generality. In the dense limit, the equations are simplified by taking advantage of the power-law divergence of the pair distribution function chi proportional to (phi(ad) - phi)(-alpha), and a faster divergence of the derivativ rho(d chi/d rho) similar to (d chi/d phi), where rho and phi are the density and volume fraction, and phi(ad) is the volume fraction for arrested dynamics. When the height h is much larger than the conduction length, the energy equation reduces to an algebraic balance between the rates of production and dissipation of energy, and the stress is proportional to the square of the strain rate (Bagnold law). In the shallow limit, the stress reduces to a simplified Bagnold stress, where all components of the stress are proportional to (partial derivative u(x)/partial derivative y)(2), which is the cross-stream (y) derivative of the stream-wise (x) velocity. In the simplified equations for dense shallow flows, the inertial terms are neglected in the y momentum equation in the shallow limit because the are O(h/L) smaller than the divergence of the stress. The resulting model contains two equations, a mass conservation equations which reduces to a solenoidal condition on the velocity in the incompressible limit, and a stream-wise momentum equation which contains just one parameter B which is a combination of the Bagnold coefficients and their derivatives with respect to volume fraction. The leading-order dense shallow flow equations, as well as the first correction due to density variations, are analysed for two representative flows. The first is the development from a plug flow to a fully developed Bagnold profile for the flow down an inclined plane. The analysis shows that the flow development length is ((rho) over barh(3)/B) , where (rho) over bar is the mean density, and this length is numerically estimated from previous simulation results. The second example is the development of the boundary layer at the base of the flow when a plug flow (with a slip condition at the base) encounters a rough base, in the limit where the momentum boundary layer thickness is small compared with the flow height. Analytical solutions can be found only when the stream-wise velocity far from the surface varies as x(F), where x is the stream-wise distance from the start of the rough base and F is an exponent. The boundary layer thickness increases as (l(2)x)(1/3) for all values of F, where the length scale l = root 2B/(rho) over bar. The analysis reveals important differences between granular flows and the flows of Newtonian fluids. The Reynolds number (ratio of inertial and viscous terms) turns out to depend only on the layer height and Bagnold coefficients, and is independent of the flow velocity, because both the inertial terms in the conservation equations and the divergence of the stress depend on the square of the velocity/velocity gradients. The compressibility number (ratio of the variation in volume fraction and mean volume fraction) is independent of the flow velocity and layer height, and depends only on the volume fraction and Bagnold coefficients.

System reliability analysis of granular filter for protection against piping in dams

Granular filters are provided for the safety of water retaining structure for protection against piping failure. The phenomenon of piping triggers when the base soil to be protected starts migrating in the direction of seepage flow under the influence of seepage force. To protect base soil from migration, the voids in the filter media should be small enough but it should not also be too small to block smooth passage of seeping water. Fulfilling these two contradictory design requirements at the same time is a major concern for the successful performance of granular filter media. Since Terzaghi era, conventionally, particle size distribution (PSD) of granular filters is designed based on particle size distribution characteristics of the base soil to be protected. The design approach provides a range of D15f value in which the PSD of granular filter media should fall and there exist infinite possibilities. Further, safety against the two critical design requirements cannot be ensured. Although used successfully for many decades, the existing filter design guidelines are purely empirical in nature accompanied with experience and good engineering judgment. In the present study, analytical solutions for obtaining the factor of safety with respect to base soil particle migration and soil permeability consideration as proposed by the authors are first discussed. The solution takes into consideration the basic geotechnical properties of base soil and filter media as well as existing hydraulic conditions and provides a comprehensive solution to the granular filter design with ability to assess the stability in terms of factor of safety. Considering the fact that geotechnical properties are variable in nature, probabilistic analysis is further suggested to evaluate the system reliability of the filter media that may help in risk assessment and risk management for decision making.

Granular anchors under vertical loading - axial pull

Granular anchors are a relatively new concept in ground engineering with relatively little known regarding their load–displacement behaviour, failure modes, ultimate pullout capacity and also potential applications. A granular anchor consists of three main components: a base plate; tendon and compacted granular backfill. The tendon is used to transmit the applied load to the base plate which compresses the granular material to form the anchor. A study of the load–displacement response and ultimate pullout capacity of granular anchors constructed in intact lodgement till and made ground deposits is reported in this paper. Parallel tests were also performed on cast insitu concrete anchors which are traditionally used for anchoring purposes. A new method of analysis for the determination of the ultimate pullout capacity of granular anchors is presented and verified experimentally, with the dominant mode of failure controlled by the column length to diameter ratio. Granular anchors with L/D > 7 principally failed on bulging whereas short granular anchors failed on shaft resistance, with the latter mobilising similar pullout capacities as conventional concrete anchors.

Desenvolvimento de um sistema misto de pasta à base de geopolímero e cimento portland para correção de perda de circulação

The materials engineering includes processes and products involving several areas of engineering, allowing them to prepare materials that fulfill the needs of various new products. In this case, this work aims to study a system composed of cement paste and geopolymers, which can contribute to solving an engineering problem that directly involves the exploitation of oil wells subject to loss of circulation. To correct it, has been already proposed the use of granular materials, fibers, reducing the drilling fluid or cement paste density and even surface and downhole mixed systems. In this work, we proposed the development of a slurry mixed system, the first was a cement-based slurry and the second a geopolymer-based slurry. The cement-based slurry was formulated with low density and extenders, 12.0 ppg (1.438 g/cm ³), showing great thixotropic characteristics. It was added nano silica at concentrations of 0.5, 1.0 and 1.5 gps (66.88, 133.76 and 200.64 L/m3) and CaCl2 at concentrations of 0.5, 1, 0 and 1.5%. The second system is a geopolymer-based paste formulated from molar ratios of 3.5 (nSiO2/nAl2O3), 0.27 (nK2O/nSiO2), 1.07 (nK2O/nAl2O3) and 13.99 (nH2O/nK2O). Finally, we performed a mixture of these two systems, for their application for correction of circulation lost. To characterize the raw materials, XRD, XRF, FTIR analysis and titration were performed. The both systems were characterized in tests based on API RP10B. Compressive strength tests were conducted after curing for 24 hours, 7 and 28 days at 58 °C on the cement-based system and the geopolymer-based system. From the mixtures have been performed mixability tests and micro structural characterizations (XRD, SEM and TG). The results showed that the nano silica, when combined with CaCl2 modified the rheological properties of the cement slurry and from the concentration of 1.5 gpc (200.64 L / m³) it was possible to obtain stable systems. The system mixture caused a change in the microstructure of the material by favoring the rate of geopolymer formation to hinder the C3S phase hydration, thus, the production of CSH phases and Portlandite were harmed. Through the mixability tests it can be concluded that the system, due to reduced setting time of the mixture, can be applied to plug lost circulation zones when mixed downhole

Alterações histológicas de glândulas submandibulares e testículos induzidas por dietas à base de soja e dieta zinco deficiente em ratos.

The purpose of this study was to examine in rats the histologic alterations of the submandibular glands and testicles induced by soy diets and zinc deficient diet. The zinc deficiency produced testicles alterations including seminiferous tubulus atrophy, germinative epithelium degeneration, spermatogenesis alterations and a significant atrophy of the submandibular glands which presented no much delimitated acines. The soy diet without complementations also compromised the spermatogenesis by showing seminiferous tubulus atrophied and a reduction of the germinative epithelium. The soy diet complemented by saline and vitaminic mixtures didn't produced testicles alterations but its induced in the submandibular glands a hypertrophy of the ductal component mainly in relation to the granular component.

Avaliação da remoção de compostos farmacológicos em filtro ecológico seguido por filtro de carvão granular biologicamente ativado

Pós-graduação em Engenharia Civil - FEIS

Optimización granulométrica de morteros de base cemento

En la práctica habitual, para la elaboración de morteros se recomienda la utilización de granulometrías continuas. El requisito de continuidad y que los tamaños de partícula se encuentren dentro de los límites establecidos por “husos granulométricos” surge de las teorías clásicas de Fuller – Thompson y se apoya en la necesidad de obtener mezclas con adecuada docilidad en el estado fresco. Sin embargo, las distribuciones continuas de árido no representan las únicas alternativas para obtener mezclas que tengan una adecuada docilidad en estado fresco y mediante nuevos criterios de interferencia de partículas es posible demostrar que las distribuciones discontinuas aun siendo más compactas y con menor requerimientos de volumen de pasta pueden ser igual de dóciles en estado fresco. Aunque el volumen mínimo de pasta está condicionado por su fluidez y viscosidad estos parámetros pueden modificarse mediante la incorporación de filler de distinta naturaleza y aditivos químicos de reciente desarrollo. En consecuencia, se propone analizar la posibilidad de minimizar el contenido de pasta de morteros de base cemento, manteniendo las prestaciones en el estado fresco, con el objetivo de obtener una mejor estabilidad volumétrica, posibilitando mejor control de la retracción y de la fisuración. Para ello se emplearán criterios de interferencia de partículas, combinados con el uso de filler de distinta naturaleza La reducción del contenido de pasta conducirá también a mejorar el perfil sostenible de los morteros. El proceso de optimización tiene una base racional y, por lo tanto, será aplicable a distintos tipos de mortero, y las proporciones óptimas podrán adecuarse según las prestaciones requeridas para el material. SUMMARY In common practice, continuous sand gradings are recommended to produce ordinary mortars. This requirement, along with grading limits are based on classical theories, such as Fuller, aimed at achieving a reasonable packing density without compromising workability at the fresh state. Nevertheless, there are other alternatives, such as discontinuous curves based on particle interference criteria, which are capable of having even higher packing density. The less the content of voids in the granular skeleton, the less the amount of cement paste required to fill in these voids and coating the particles. Yet, the minimum volume of paste in a mortar is determined by requirements associated to the fresh state and thus, fluidity and viscosity of the paste play a significant role on the matter. These two properties can be modified by the use of suitable fillers and by the use of last-generation chemical admixtures. As a result, it is proposed to analyse the possibility of combining current particle interference criteria with the use of different types of filler and chemical admixtures to optimise cement-based mortar formulations. This optimisation is aimed at reducing the paste content while maintaining a suitable performance at the fresh state. The reduction in paste content would lead to a better dimensional stability, with better control of shrinkage and cracking behaviour. The foreseen optimisation process will have a strong rational basis and thus, it should be potentially useful to optimise mortar proportions according to a performance-based approach.

Representing microstates of static granular matter in a stress phase space

A stress phase space is proposed to compare the static packings of a granular system (microstates) that are compatible to a macrostate described by external stresses. The equivalent stress of each particle of a static packing can be obtained from the mechanical interaction forces, and the associated volume is given by the respective Voronoi cell. Therefore, particles can be located at different stress levels and grouped into categories or configurations, which are defined in base of the geometrical features of the local arrangement (in particular, of the number of forces that keep them force-balanced). They can be represented as points in a stress phase space. The nature of this space is analyzed in detail. The integration limits of the stress variables that avoid or limit tensile states and the capability of each configuration to represent specific stress states establish its main features. Furthermore, if some stress variables are used, instead of the usual components of the Cauchy stress tensor, then some symmetries can be found. Results obtained from molecular dynamics simulations are used to check this nature. Finally, some statistical ensembles are written in terms of the coordinates of this phase space. These require some assumptions that are made in base on continuum mechanics principles.

Desenvolvimento de um sistema misto de pasta à base de geopolímero e cimento portland para correção de perda de circulação

The materials engineering includes processes and products involving several areas of engineering, allowing them to prepare materials that fulfill the needs of various new products. In this case, this work aims to study a system composed of cement paste and geopolymers, which can contribute to solving an engineering problem that directly involves the exploitation of oil wells subject to loss of circulation. To correct it, has been already proposed the use of granular materials, fibers, reducing the drilling fluid or cement paste density and even surface and downhole mixed systems. In this work, we proposed the development of a slurry mixed system, the first was a cement-based slurry and the second a geopolymer-based slurry. The cement-based slurry was formulated with low density and extenders, 12.0 ppg (1.438 g/cm ³), showing great thixotropic characteristics. It was added nano silica at concentrations of 0.5, 1.0 and 1.5 gps (66.88, 133.76 and 200.64 L/m3) and CaCl2 at concentrations of 0.5, 1, 0 and 1.5%. The second system is a geopolymer-based paste formulated from molar ratios of 3.5 (nSiO2/nAl2O3), 0.27 (nK2O/nSiO2), 1.07 (nK2O/nAl2O3) and 13.99 (nH2O/nK2O). Finally, we performed a mixture of these two systems, for their application for correction of circulation lost. To characterize the raw materials, XRD, XRF, FTIR analysis and titration were performed. The both systems were characterized in tests based on API RP10B. Compressive strength tests were conducted after curing for 24 hours, 7 and 28 days at 58 °C on the cement-based system and the geopolymer-based system. From the mixtures have been performed mixability tests and micro structural characterizations (XRD, SEM and TG). The results showed that the nano silica, when combined with CaCl2 modified the rheological properties of the cement slurry and from the concentration of 1.5 gpc (200.64 L / m³) it was possible to obtain stable systems. The system mixture caused a change in the microstructure of the material by favoring the rate of geopolymer formation to hinder the C3S phase hydration, thus, the production of CSH phases and Portlandite were harmed. Through the mixability tests it can be concluded that the system, due to reduced setting time of the mixture, can be applied to plug lost circulation zones when mixed downhole

Primary students’ spatial visualization and spatial orientation : an evidence base for instruction

This paper reports on the performance of 58 11 to 12-year-olds on a spatial visualization task and a spatial orientation task. The students completed these tasks and explained their thinking during individual interviews. The qualitative data were analysed to inform pedagogical content knowledge for spatial activities. The study revealed that “matching” or “matching and eliminating” were the typical strategies that students employed on these spatial tasks. However, errors in making associations between parts of the same or different shapes were noted. Students also experienced general difficulties with visual memory and language use to explain their thinking. The students’ specific difficulties in spatial visualization related to obscured items, the perspective used, and the placement and orientation of shapes.