Gradation Parameters Research Articles

Study of Microscopic Structure of Ceramic Materials Prepared from Nonmetallic Mineral Group Associated with Skarn-Type Gold Deposits.

The microscopic structure of ceramic bodies has an essential influence on their performance. In this study, a ceramic material was prepared by modifying a nonmetallic mineral group (J) associated with a skarn-type gold mine in Hubei. The nano and microsized structures of the fired ceramic bodies under different contents of nonmetallic mineral group (J) and varying temperature conditions were systematically observed and tested by scanning electron microscopy (SEM), Malvern laser particle size analysis, differential scanning calorimetry (DSC) and X-ray diffraction (XRD). The J content affects the sintering and melt degree of the ceramic body, the contact mode of the particles inside the ceramic body and the pore structure. When the content of J is less than 70%, the performance parameters of the sintered body can meet the requirements of Group AII in the International Standard of Ceramic Tiles. It is concluded that the microscopic structure of the ceramic body is affected by the complex phase transition process including the dehydration, oxidation, melting and recrystallization of nonmetallic minerals during the firing process and is closely related to the properties of the ceramic body. It is feasible to improving the properties of ceramic bodies by adJusting the gradation parameters of J and increasing the proportion of fine grains under the same dosage. Considering the features of the ceramic body and J' utilization ratio, the optimum content of nonmetallic minerals associated with the skarn-type gold deposit in Hubei Province is 68-43%, and the optimum sintering temperature is approximately 1150 °C.

Research on the influence of manufactured sand gradation on concrete performance

Based on experiments of C30 concrete with manufactured sand, this paper studied on the workability and compressive strength of the manufactured sand concrete with 7 different fineness modulus and different weight fractions (0%, 2%, 4%, 6%, 8%, 10%) of stone powder. The results show that the fineness modulus and the stone powder content in the gradation parameters of manufactured sand have great effects on the concrete performance. When the fineness modulus of manufactured sand is about 2.8, the workability and compressive strength of concrete can be improved. As the content of stone powder increases, the workability and compressive strength of concrete firstly increase and then decrease, and the optimal weight fraction of stone powder is about 6%. The research results can provide reference for the production and application of gneiss manufactured sand.

Static stability of higher order functionally graded beam under variable axial load

This article investigates effects of axial load distribution on buckling loads and their modes of functionally graded (FG) beams including a shear effect for the first time, since all previous studies focused on constant axial load. The parabolic higher order shear theory of Reddy is proposed to consider the shear effect of both thick and thin beams. The gradation of the material is distributed continuously through thickness direction with generalized power-law function. The in-plane axial compressive load is simulated by continuous functions through the axial direction, which are constant, linear, and parabolic functions. The equilibrium equations are developed by Hamilton’s principles, which yields variable-coefficients differential equations. Modified differential quadrature method (DQM) is employed to discretize and mesh the spatial domain and covert the differential equations and boundary conditions to algebraic equations. Algebraic set of equations is formed as a generalized matrix eigenvalue problem, then solved to obtain buckling loads (eigenvalues) and mode-shapes (eigenvectors). Numerical results are presented to illustrate effects of gradation parameter, load types, slenderness ratio and boundary conditions on buckling loads and mode-shapes of functionally graded beams structures. This model can be applied in designing of space-shuttle, spacecraft, nuclear structure, and naval structure subjected to distributed in-plane axial load.

From Basic Particle Gradation Parameters to Water Retention Curves and Tensile Strength of Unsaturated Granular Soils

Abstract The long-debated effective stress definition of unsaturated soils is believed to be correlated to suction, the degree of saturation, and the less mentioned interfacial areas. The tensile s...

Determination of soil permeability coefficient following an updated grading entropy method

This paper presents a critical review of the grading entropy approach of permeability-coefficient predictions (k P) for coarse-grained soils. The approach applies the grading entropy theory to particle-size distributions (PSDs), such that the entirety of each gradation curve can be interpreted as a single point on a grading entropy chart, plotting its normalised entropy increment (B) against relative base grading entropy (A) values. Published data sets of measured permeability-coefficient (k M) values for saturated compacted silty sand, sand and gravel materials are examined to understand the dependence of A and B on various gradation parameters and the void ratio (e). In particular, log k M negatively correlates with log B and positively correlates with log A and e (log e). As such, power functions of the form [Formula: see text] prove statistically superior, noting that the fitting coefficient C 1 to C 4 values are specific to the PSD range and densification (compaction) states investigated for the permeability tests. Recommendations are given for increasing the predictive power, including separate models for well-graded and poorly graded materials and the addition of a particle shape factor and specific surface parameters in the regression correlation.

An Empirical Model for Estimation of Permeability of Porous Media based on its Gradation Parameters

In the present study the hydraulic conductivity of the porous media has been related to its gradation parameters. Nine cohesion-less soils of different gradations were tested in a constant head permeameter. A low head of water, standardised to viscosity at 20°C, was used to avoid the turbulence. It was observed that the hydraulic conductivity varied significantly with respect to the gradation parameters. The empirical model developed on the basis of this study can be helpful for more rational estimation of the flow through non-cohesive porous media on the basis of its gradation characteristics.

Effect of Gradation on the Compactability of Coarse-Grained Soils

The optimal gradation for coarse-grained soil used in earth-rockfill dams is an essential design index when determining the compactability of coarse-grained soil. With the optimal gradation, coarse-grained soil can be rolled to the maximum of dry densities among all gradations under the same compaction effort. Accordingly, this research introduced a gradation equation with the gradation parameters b and m and the maximum particle size dmax to establish a quantitative description of the gradation curve. From the results of the maximum dry density tests, the maximum dry density ρmax is found to show a parabolic curve relationship with a parameter called gradation area S, which is defined as the area surrounded by the gradation curve. If the maximum particle size is a constant, the optimal gradation area, S0, has the same value for coarse-grained soils with different shapes or different parent rocks, whereas S0 linearly decreases with the increase in ln dmax. Furthermore, if dmax is known, the optimal gradation area S0 can be evaluated by the proposed linear equation. Findings support a feasible method for designing the optimal gradation distribution in laboratory tests and in-situ.

Relating gradation parameters to mechanical and drainage performance of unbound granular materials

Abstract The drainage performance of unbound granular material (UGM) is an important consideration in pavement design because premature failures can occur due to the presence of excess moisture in UGM layers. Recently, transportation agencies have been evaluating their granular base and subbase drainage and mechanical performance to ensure sufficient drainage capacity while maintaining adequate structural support to produce more sustainable pavement structures. Relating performance to UGM construction specification requires accurate characterization of physical and gradation parameters and their effects on the mechanical and drainage performance of UGM. These evaluations led to an update of the specification requirements of UGM in many jurisdictions including Manitoba. In this study, resilient modulus and constant head hydraulic conductivity tests were performed to characterize the mechanical and drainage performance of nine UGM samples. The laboratory test results were also used to investigate the reliability of the estimated hydraulic conductivity from the Moulton prediction model, and from the Enhanced Integrated Climatic Model (EICM). Test results showed an improvement in resilient modulus and drainage quality for samples in gradation bands that specify larger maximum aggregate size and limited fines. A statistical analysis of the test results showed that D10 larger than 0.2 mm and D60 larger than 8 mm would guarantee higher stiffness and better drainage performance with a time-to drain of less than 5 days for typical pavement cross-sections and a resilient modulus value exceeding 200 MPa. The Moulton prediction model was found to provide a better approximation of hydraulic conductivity of the materials included in this study, while the EICM model was found to significantly overestimate the hydraulic conductivity for most of the samples.

The influence of particle shape and gradation parameters on the permeability of filter media

In the present study, an effort has been made to determine the effect of shape of filter media particles and their gradation on its permeability. Six different shapes of the graded filter particles, ranging from rounded to flat, were used in the study. Experiments were carried out to assess the variation of permeability with respect to the various shape parameters, viz. sphericity, roundness, shape factor, flatness ratio, elongation ratio, angularity index and the gradation parameters, for each group of the material. A model on the basis of experimental data, obtained in the study was developed which takes into account the variation of the above mentioned shape and gradation parameters for estimation of the permeability through filter media.

Static stability and of symmetric and sigmoid functionally graded beam under variable axial load

This manuscript presents impacts of gradation of material functions and axial load functions on critical buckling loads and mode shapes of functionally graded (FG) thin and thick beams by using higher order shear deformation theory, for the first time. Volume fractions of metal and ceramic materials are assumed to be distributed through a beam thickness by both sigmoid law and symmetric power functions. Ceramic–metal–ceramic (CMC) and metal–ceramic–metal (MCM) symmetric distributions are proposed relative to mid-plane of the beam structure. The axial compressive load is depicted by constant, linear, and parabolic continuous functions through the axial direction. The equilibrium governing equations are derived by using Hamilton\'s principles. Numerical differential quadrature method (DQM) is developed to discretize the spatial domain and covert the governing variable coefficients differential equations and boundary conditions to system of algebraic equations. Algebraic equations are formed as a generalized matrix eigenvalue problem, that will be solved to get eigenvalues (buckling loads) and eigenvectors (mode shapes). The proposed model is verified with respectable published work. Numerical results depict influences of gradation function, gradation parameter, axial load function, slenderness ratio and boundary conditions on critical buckling loads and mode-shapes of FG beam structure. It is found that gradation types have different effects on the critical buckling. The proposed model can be effective in analysis and design of structure beam element subject to distributed axial compressive load, such as, spacecraft, nuclear structure, and naval structure.

Design criteria of protective filters based on particle shape and gradation parameters

This study presents design criteria of protective filters for different shapes of filter material and subsequently the effect of shape parameters of filter particles on its design. The filter-base combination tests have been conducted in the laboratory for different shapes of filter material, i.e., elliptical, sub-rounded, irregular and elongated. The shape parameters considered in the study are sphericity, shape factor, flatness ratio and elongation ratio. It was observed that the design criteria varied with the shape of filter particles even if the gradation of the filter material was similar. The design criteria in the form of empirical equations have been developed on the basis of D15 of filter mass, d85 of base, permeability (k) of filter mass and shape parameters of filter mass.

The influence of particle shape and gradation parameters on the permeability of filter media

The influence of particle shape and gradation parameters on the permeability of filter media

Design criteria of protective filters based on particle shape and gradation parameters

Design criteria of protective filters based on particle shape and gradation parameters

Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models

This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded (FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS structure manufactured by porous functionally graded materials.

A tool to design rutting resistant asphalt mixes through aggregate gradation selection

This work focuses on the proposition of a simple tool to evaluate the quality of the grain size distribution and its potential to produce rutting resistant asphalt mixes. The tool is based on the hypothesis of the existence of a main aggregate structure responsible for absorbing and transmitting stresses without developing plastic deformation. Two parameters were proposed in this paper to characterize such a structure: α and C ratios. The first characterizes the degree of interlocking of this structure, called the Dominant Aggregate Size Range (DASR), while the latter is related to the amount of relatively bigger particles within this structure. The Flow Number (FN) was adopted as an indicator of the rutting resistance of 27 investigated asphalt mixes, varying in grain size distribution, aggregate origin, binder type, and binder content. The proposed parameters α and C are established as characteristic parameters of the aggregate skeleton of the asphalt mix, and are well correlated with FN, indicating they have the potential for being useful tools. However, they do not capture the importance of the asphalt binder for the rutting resistance. A third index, κ, is then established as a characteristic parameter of the asphalt mix associated with the rutting resistance. It is a combination of the gradation parameters (α and C), binder content and binder viscosity. An excellent correlation was observed between the FN and the κ index. Finally, criteria for the κ index were suggested as a function of traffic level, as it is conventionally done for FN values. Results from this work contribute to the development of rational tools to design resistant and stable aggregate gradation compositions for higher quality pavements.

Applications of a gradation equation in coarse-grained soils

The gradation equation is used to mathematically express the particle size distribution (PSD) of soils. In this paper, a simple and practicable gradation equation and its applications to coarse-grained soils are discussed. First, the proposed equation can be used as an analytical technique for computing particle breakage factors. Closed forms for two widely used breakage factors are derived and demonstrated using a series of test data on the particle breakage of rockfill materials. Second, two particle size reduction techniques are derived and described by the proposed gradation equation. It is believed that the quantitative relationship between the gradation parameters before and after size reduction could be used to quantitatively and systematically study the particle size reduction effect. In addition, the proposed gradation equation can be used to design specific PSDs for the soils used in discrete-element method analyses and laboratory tests. For example, it is convenient in terms of designing the PSD with a certain coefficient of uniformity, coefficient of curvature and/or specified particle sizes.

Unloading analysis of elastically and plastically graded hemispherical contact with rigid flat

Abstract The present work puts forward a finite element based loading and unloading analysis of radially functionally graded flattening hemispherical contact. Two types of gradations are used viz. elastic gradation, where modulus of elasticity and tangent modulus (for bilinear isotropic hardening) is varied keeping the yield strength fixed and plastic gradation, where yield strength is varied keeping the modulus of elasticity and tangent modulus fixed. Loading and unloading analysis is performed for different values of elastic and plastic inhomogeneity parameters and their effects on different contact parameters are analyzed. Effect of gradation on deformation behavior and stress distribution while loading and unloading of elastically and plastically graded hemisphere are discussed. During the unloading process, secondary plastic flow was also observed and discussed for different gradation parameters. Loss of energy of the material during loading-unloading due to plasticity is also analyzed in connection with gradation parameters.

Estimation of Unsaturated Hydraulic Conductivity of Granular Soils from Particle Size Parameters

Estimation of unsaturated hydraulic conductivity could benefit many engineering or research problems such as water flow in the vadose zone, unsaturated seepage and capillary barriers for underground waste isolation. The unsaturated hydraulic conductivity of a soil is related to its saturated hydraulic conductivity value as well as its water retention behaviour. By following the first author’s previous work, the saturated hydraulic conductivity and water retention curve (WRC) of sandy soils can be estimated from their basic gradation parameters. In this paper, we further suggest the applicable range of the estimation method is for soils with d10 > 0.02mm and Cu < 20, in which d10 is the grain diameter corresponding to 10% passing and Cu is the coefficient of uniformity (Cu=d60d10). The estimation method is also modified to consider the porosity variation effect. Then the proposed method is applied to predict unsaturated hydraulic conductivity properties of different sandy soils and also compared with laboratory and field test results. The comparison shows that the newly developed estimation method, which predicts the relative permeability of unsaturated sands from basic grain size parameters and porosity, generally has a fair agreement with measured data. It also indicates that the air-entry value is mainly relative to the mean grain size and porosity value change from the intrinsic value. The rate of permeability decline with suction is mainly associated with grain size polydispersity.

Dynamic analysis of elastically and plastically graded spherical and cylindrical contact

A dynamic analysis of a hemispherical and cylindrical contact, material properties of which are graded elastically and plastically along the radius, is presented. The static force–displacement behavior of a hemisphere and a semi-cylinder in contact with a rigid flat is obtained using finite element software. The force–displacement is used in a further dynamic analysis for undamped-free as well as for forced-damped vibration of the contact interface. For the undamped free vibration, variation of natural frequency w.r.t. initial displacement is furnished for different values of elastic and plastic gradation parameter. In addition, variation of maximum initial displacement for contact loss is also demonstrated. The forced-damped vibration characteristics of the spherical and cylindrical contact interfaces are presented in the form of frequency response curves with jump up and jump down frequencies. Spherical and cylindrical contact interfaces are found to exhibit softening and hardening type nonlinearity, respectively.

Experimental Investigation of the Influence of Gradation Parameters on Atterberg Limits of Soil

Experimental Investigation of the Influence of Gradation Parameters on Atterberg Limits of Soil