Dense Packing Model Research Articles

Approaches for predicting the soil-water characteristic curves of compacted quartz sand based on particle packing theory

The soil-water characteristic curve (SWCC) is an important basis for describing hydraulic properties, which is closely related to environmental problems such as the migration of toxic substances from groundwater and soil. The SWCC models vary considerably with respect to the void ratio or bulk density. However, the void ratio and bulk density of the same soil change at different depths or positions within a flat space. Accurate simulation or calculation requires a precise SWCC, but measuring every SWCC under each density or void ratio condition is difficult. In this study, two particle packing models, the Kwan model and the modified linear packing density model (MLPDM), were introduced into the van Genuchten (VG) model to predict the SWCC for soil at the minimum void ratio (the maximum dry density). Then, the prediction method of the SWCCs for the same soil with different densities or void ratios was given. A series of laboratory tests using quartz sand mixtures were conducted to verify the accuracy of two extended models (the K-VG model and the M-VG model). For the K-VG model, the average RMSE was 0.020. For the M-VG model, the average RMSE was 0.017. In general, the SWCCs predicted by the two extended models were consistent with the measured values.

Evaluation of three packing density models on reference particle-size distributions

Evaluation of three packing density models on reference particle-size distributions

Development of low carbon engineered cementitious composite (ECC) using nano lime calcined clay cement (nLC3) based matrix

The construction industry is responsible for around 5% of total CO2 emissions globally. As a result, recent research is focused on the sustainability aspects of construction materials. Engineered cementitious Composites (ECC) are high-performance fiber reinforced composites with improved ductility and tensile strength but utilize higher cement content, raising concerns about their sustainability. In this study, nano-lime and calcined clay are combined with cement to develop a high strength sustainable nano lime calcined clay cement (nLC3) based Engineered Cementitious Composite (ECC). Initially, the packing density model was employed to develop a high strength nLC3-based matrix by combining the particle packing models and chemical compatibility while keeping costs to a minimum. Micromechanical modeling was then applied to determine the critical volume of fibers for the novel matrix using single fiber pullout tests and matrix toughness tests. According to the micromechanical model, the critical volume fraction is found to be 1.93% for the nLC3 mix. This was further confirmed by casting dog bone samples containing 2% fibers by volume which confirmed strain hardening response. The uniaxial test results indicated a strength of around 5.85 MPa in tension and 51 MPa in compression with about 3% tensile strain. These results are comparable to conventional ECC and better than previously developed LC3 based ECC. This study reveals that nLC3-based ECC is a more sustainable composite as compared to conventional ECC mix without any compromise on strength and cost.

Development of a sustainable alkali activated ultra-high performance concrete (A-UHPC) incorporating recycled concrete fines

This study assesses the properties of alkali activated ultra-high performance concrete (A-UHPC) prepared by using recycled concrete fines (RCF) to replace mineral powder in cementitious materials. To be specific, firstly, an optimized combination of low carbon cementitious mixture and aggregates skeleton is designed based on particle dense packing model. Then, the RCF is partly employed and its effect on the hydration kinetics and microstructure development of A-UHPC are tested. The results show that the A-UHPC can exhibit excellent fresh and hardened properties when the water-binder ratio range is 0.29–0.27 and the RCF content is 10–30%. In addition, under the same water-binder ratio and RCF content, the compressive strength of A-UHPC is about 120 MPa. In addition, the carbon emission of A-UHPC prepared in this paper is only 75% of that of ordinary alkali activated ultra-high performance concrete. In general, the newly developed A-UHPC in this study can effectively reuse the recycled fines from waste concrete and provide a new building material with advanced properties, which is in line with sustainable development and low carbon management.

Estimation of voids in a multi-sized mineral aggregate for asphalt mixture using the Theoretical Packing Density Model

The asphalt mixture durability and the rutting performance are related to the design parameter called Voids in Mineral Aggregate (VMA). The main objective of this research consists in estimating VMA according to gradation variation thanks to a non-linear packing density model: the Theoretical Packing Density Model (TPDM). The TPDM is derived from the Compressible Packing Model (CPM). Data are from Vavrik’s reference experiments. The TPDM requires only two parameters: the critical cavity size ratio x0 which characterizes the size of the voids in the coarse aggregate and the compaction index K. TPDM estimates are compared with those of another model, the linear-mixture packing model, thanks to the correlation coefficient, the mean absolute error, the root mean square error and the mean square error. These four statistical indicators are worth respectively 94%, 1.50%, 0.62%, 0.38% for the TPDM and 90%, 1.68%, 0.88%, 0.77% for the linear-mixture packing model: the TPDM therefore makes it possible to reduce the most significant deviations between measurements and estimates.

Mathematical modeling of the metrical parameters of hexagonal close-packed metalls

The electronic, magnetic, mechanical and other properties of crystalline substances are due to the feature of their structure — the periodicity and symmetry of the lattice, therefore, the determination of the metrical parameters is an important stage in the study of the characteristics of such materials. The paper considers a number of metals having a crystal lattice of the hcp structural type (hexagonal close packing) – beryllium, cerium, cobalt, dysprosium, erbium, gadolinium, hafnium, holmium, lanthanum, lutetium, magnesium, neodymium, osmium, praseodymium, rhenium, ruthenium, scandium, terbium, titanium, thallium, thulium, yttrium, zirconium. The paper shows the application of the annealing simulation algorithm to find the metric parameters of the materials under consideration using the dense packing model, which is widely used in crystallographic calculations. The own software implementation of the annealing simulation algorithm presented in the paper makes it possible to determine the coordinates of the atoms included in the unit cell of the crystal lattice, to calculate the lattice constants and the packing density of atoms in the cell of the crystal of the hcp structural type, using the given chemical formula and space symmetry group. These structural characteristics can be used as input parameters in modeling the electronic, magnetic, and other properties of the considered materials. The paper compares the values of the crystal lattice constants obtained as a result of numerical simulation with published data.

Evaluation of three non-linear packing density models on micropowder mixtures

The formulation of powders often requires an optimized packing density of the granular skeleton which takes into account the desired properties. More accurate than the conventional linear models, three non-linear packing density models are evaluated from published data on binary or ternary mixtures of alumina powders, glass microbeads, siliceous microaggregates: the Compressible Packing Model (CPM), the 3-parameter Particle Packing Model (3PPM), the Theoretical Packing Density Model (TPDM). Depending on the models, they involve a compaction index K and certain particle interactions: the loosening effect a and possibly the critical cavity size ratio x0 from which it appears, the wall effect b and the wedging effect c. The CPM (with a, b, K), by incorporating only 2 interaction functions for a and b, reduces its versatility but is efficient for siliceous. The 3PPM (with a, b, c), by incorporating 9 interaction functions, adapts well to the various micropowders with however a lower performance for the siliceous for which the packing densities predicted in “compacted” conditions are lower than in “uncompacted” conditions. The TPDM (with a, b, K, x0) is effective for all types of micropowders and generates the best statistical indicators.

A low-carbon alkali activated slag based ultra-high performance concrete (UHPC): Reaction kinetics and microstructure development

Ultra high performance concrete (UHPC) is a cement-based material with great development prospects. However, the production of cement will produce a large amount of CO 2 , which does not conform to the current global trend of energy conservation and emission reduction, and limits the further development of UHPC. One of the ways to further develop UHPC is to reduce the carbon emissions in the production process of UHPC. The aim of this study is to develop a low-carbon alkali activated slag based Ultra-High Performance Concrete (A-UHPC) with ultra-low moisture content. Firstly, based on the particle dense packing model, an optimized combination of low-carbon cementitious mixture and aggregates skeleton is designed. Then, the effects of moisture content on the macro-properties, hydration mechanism and micro-mechanism of the developed A-UHPC are studied. The experimental results show that the fresh performance and macroscopic mechanical properties of A-UHPC are advanced at low moisture content. When the water-binder ratio is 0.29, the compressive strength at 28 d is the highest, reaching 118 MPa. Besides, low moisture content A-UHPC also shows good microscopic properties: its hydration degree can reach 62.58% and the longest molecular chain length of the polymer is about 4.74. In general, the developed A-UHPC can meet the requirement of high performance and low CO 2 emission simultaneously, which could be one of the most suitable choices to achieve the goal of “Carbon peak and Carbon neutral” in the near future. • A novel method for designing a low carbon UHPC is presented. • The newly developed UHPC exhibits admirable ecological value. • Mineral powder and alkali-activator are adopted in UHPC. • Low moisture content A-UHPC is developed. • 5.The effect of water on the macro and micro properties of A-UHPC is studied.

Development of a rapid hardening ultra-high performance concrete (R-UHPC): From macro properties to micro structure

The aim of this study is to propose a design and optimization method for developing an Ultra-High Performance Concrete (UHPC) with rapid setting and hardening characteristics. Firstly, based on response surface approach, an optimized cementitious mixture mainly composed by alumina cement and gypsum is obtained. Then, based on the particle dense packing model, the particle dense packing skeleton of UHPC is designed. After that, the effect of water and steel fibre contents on the properties of the developed UHPC matrix are investigated. The obtained experimental results show that when the gypsum substitution is 15%, the 3 h strength develops fastest, reaching 55 MPa, while the later strength can be continuously enhanced to 81 MPa at 7 days. Moreover, compared with the reference group without fibre, 2.5% (by volume) steel fibre can improve the 3 h and 28d compressive strength of the newly designed UHPC by 157.0% and 46.1%, respectively. In general, the developed UHPC has advanced mechanical properties and durability both at super early period and later stages, which is promising to be well utilized in construction rapid reparation field.

Cement Paste Mixture Proportioning with Particle Packing Theory: An Ambiguous Effect of Microsilica

Recently, the research of innovative building materials is focused on applying supplementary materials in the form of micro- and nanopowders in cementitious composites due to the growing insistence on sustainable development. Considering above, in paper, a research on the effect of microsilica and SiO2 nanoparticles addition to cement paste, designed with Andreasen and Andersen (AA) packing density model (PDM), in terms of its physical and mechanical properties was conducted. Density, porosity, compressive strength, hardness, and modulus of indentation were investigated and compared regarding different amount of additives used in cement paste mixes. Microstructure of the obtained pastes was analyzed. The possibility of negative influence of alkali-silica reaction (ASR) on the mechanical properties of the obtained composites was analyzed. The results of the conducted investigations were discussed, and conclusions, also practical, were presented. The obtained results confirmed that the applied PDM may be an effective tool in cement paste design, when low porosity of prepared composite is required. On the other hand, the application of AA model did not bring satisfactory results of mechanical performance as expected, what was related, as shown by SEM imaging, with inhomogeneous dispersion of microsilica, and creation of agglomerates acting as reactive aggregates, what as a consequence caused ASR reaction, crack occurrence and lowered mechanical properties. Finally, the study found that the use of about 7.5% wt. of microsilica is the optimum in regards to obtain low porosity, while, to achieve improved mechanical properties, the use of 4 wt. % of microsilica seems to be optimal, in the case of tested cement pastes.

The Theoretical Packing Density Model (TPDM): A versatile model for estimating the minimum void ratio of binary soil mixtures.

Understanding the behavior of sand-fines mixtures and assessing their shear strength or permeability require knowledge of the influence of fine particles content on the minimum void ratio. The latter is often evaluated using empirical methods or models using parameters without physical significance. Validated for both ordered and disordered packings and for concrete mixtures, the Theoretical Packing Density Model (TPDM) is tested for predicting the minimum void ratio on binary sand-fines mixtures, whatever the fines content. It requires only two parameters: the critical cavity size ratio x0 from which the loosening effect occurs and the compaction index K describing the packing efficiency. Previously collected data from 30 binary soil mixtures including river, lake, mountain and crushed sands representing 285 individual specimens for which minimum void ratios are available, were used. The coefficient of determination provided by the TPDM is equal to 0.968 on average, and greater than 0.99 for 30% of the mixtures. Thanks to the compaction index K, the mathematical model is therefore capable to capture the non-linear behavior of the void ratio variation with respect to the solid volume fraction of fine particles. Finally, a method is proposed to approximate the value of the critical cavity size ratio x0 to be used as a function of the combination of the shapes of coarse and fine particles.

A novel design of low carbon footprint Ultra-High Performance Concrete (UHPC) based on full scale recycling of gold tailings

This paper presents a feasible way to design a low carbon footprint Ultra-High Performance Concrete (UHPC) with gold tailings based on the idea of full scale recycling. Due to the fact that the particle size distribution of the recycled gold tailings is normally wild, from micrometer to millimeter, it could be utilized to replace powders and aggregates in UHPC simultaneously, which can get rid of sieving process and improve the recycling efficiency. Therefore, in this study, a particle dense packing model is firstly employed to design the UHPC matrix with gold tailings, based on the full scale recycling point of view. Then, the fresh and hardened properties of the newly developed UHPC are investigated, including flowability, compressive strength, hydration kinetics, durability and microstructure. The tested results indicate that the idea of full scale recycling can guarantee a relatively high long-term compressive strength, low DRCM, and low leaching toxicity for UHPC. Additionally, the environmental evaluation further proves that the developed UHPC is a green building material with advanced properties and simple preparation process.

Design of Concrete Mix Proportion Based on Particle Packing Voidage and Test Research on Compressive Strength and Elastic Modulus of Concrete

According to the basic principle of dense packing of particles, and considering the interaction between particles, a dense packing model of granular materials in concrete was proposed. During the establishment of this model, binary particle packing tests of crushed stone and sand were carried out. The fitting analysis of the test results determines the relationship between the particle size ratio and the remaining volume fraction of the particle packing, and then the actual void fraction of the particle packing was obtained, based on which the water–binder ratio was combined to determine the amount of various materials in the concrete. The proposed concrete mix design method was used to prepare concrete, and its compressive strength and elastic modulus were tested experimentally. The test results show that the aggregate volume fraction of the prepared concrete increased, and the workability of the concrete mixture with the appropriate amount of water reducing agent meets the design requirements. When the water–binder ratio was 0.42, 0.47, or 0.52, the compressive strength of the concrete increased compared with the control concrete, and the degree of improvement in compressive strength increased with the decrease in water–binder ratio; when the water-binder ratio was 0.42, 0.47, or 0.52, the static elastic modulus of the concrete increased compared with the control concrete, and the degree of improvement in elastic modulus also increased with the decrease in water–binder ratio. The elastic modulus and compressive strength of the prepared concrete have a positive correlation. Findings show that the concrete mix design method proposed by this research is feasible and advanced in a sense.

Free volume evolution dominated by glass forming ability determining mechanical performance in Zr Ti65-Be27.5Cu7.5 metallic glasses

The shear deformation and fracture behaviors of Zr x Ti 65- x Be 27.5 Cu 7.5 metallic glasses (MGs) were systematically investigated in the range x = 20, 25, 30, 35, 40, 45, 50 at% under multi-axial loading mode by small punch test (SPT). Results show that enhanced plasticity can be obtained in MGs with composition ranging from 30 to 45 Zr at%, which is attributed to the large free volume dependent on their better glass forming ability (GFA). It is reasonably concluded that the total free volume consists of two parts: intrinsic free volume ( V 0 ) and excess free volume ( V G ). Intrinsic free volume, involved in an ideal amorphous structure, is defined as the free volume of MGs undergoing fully structural relaxation, which depends on the atomic size of each element. On the basis of atomic dense packing model, intrinsic free volume of the studied MGs is basically same due to a little difference in the atomic size between Zr and Ti. Excess free volume is crucially dominated by the GFA of MGs. In the case of little difference in atomic size of Zr and Ti, the MGs with large GFA possess a much looser atomic stacking structure, leading to the larger content of excess free volume. The large content of free volume not only favor the better atomic mobility, but also facilitate the nucleation of multiple shear bands, which can dramatically improve the plasticity of MGs. Thus, the studied MGs with Zr content ranging from 30 to 45 at% possess the larger content of total free volume than that with 20, 25 and 50 Zr at% due to their better GFA, depicting the enhanced plasticity induced by the initiation and interaction of multiple shear bands. In addition, the MGs with large content of free volume exhibits the lower driving force of shear bands nucleation, showing a soft state.

Packing potential index for binary mixtures of granular soil

Packing procedure is the mechanical process of forming a packing of soil particles, such as funnel pouring, tamping, rodding, pluviation, compaction, vibration, compression, etc. For a sand-silt mixture, packing procedure and particle shape have significant effects on the density of the binary mixture. However, these two factors have not been considered in most of the existing particle packing density models. Thus, the existing particle packing density models are not applicable to sand-silt mixtures. In this paper, we aim to study the packing procedure and particle shape effects on density of binary mixtures. We firstly define a packing potential index, which is a measure of volume reduction potential due to mixing of two components of a binary mixture system under a packing procedure. To understand the nature of packing potential index, we compare the packing potential indices of 24 different types of mixtures collected from the literature; the 24 types of mixtures were formed by two different types of packing procedure (i.e., for achieving minimum and maximum void ratios). It is found that the packing potential index is nearly independent of packing procedure but significantly dependent on the compound particle shapes of a mixture. Then, we mathematically link the packing potential index to the particle interaction parameters used in the particle packing density models. And we analyze the data to discuss the effect of packing procedure on the void ratios of sand-silt mixtures. We then propose an approach within the framework of particle packing density model to predict the void ratios of sand-silt mixtures under different packing procedures with the consideration of particle shape effect.

Development of Ultra High Performance Concrete Using Fly Ash

The experimental work presented in this article examines the possibility of lowering the economic cost of UHPC. The UHPC were designed using the Linear Packing Density Model. After 7 days, the UHPC compressive strength exceeded 120 MPa. Level of compressive strength after 90 days reaching 150 MPa had been obtained with a lower dose of cement (700 kg/m3) and with the use of secondary raw materials (fly ash), without the use of dispersed reinforcement. The successful design and production proved that the use of secondary raw materials is possible, thereby decreasing the economic cost of UHPC production.

Study of the linear and nonlinear packing model based on mixing of quartz sand

Packing density is an important engineering behavior aspect of the soil. The models in this experiment were compared using laboratory test packing data and published spherical particle packing data. The results show that the deviation between measured and predicted values of the nonlinear model is lower than that of the linear model. The root mean square error (RMSE) of the nonlinear packing model ranged from 0.01 to 0.06, considerably less than that of the linear packing model. The value of the wall effect for each of the models is similar, but variation of the loosening effect is large based on a comparison of the empirical parameter of the linear packing density model (LPDM), compressible packing model (CPM), Kwan model (KM) and modified Kwan model (MKM). When the characteristic diameter ratio is larger than 0.2, the wedging effect parameter becomes constant.

Development of ecological strain-hardening cementitious composites incorporating high-volume ground-glass pozzolans

A novel strain-hardening cementitious composite (SHCC) incorporating high-volume ground-glass pozzolans (HVGP) has been developed by coupling particle packing optimization with micromechanical tailoring. For the former, the compressible packing density model was adopted, while for the latter, single-fiber pull-out and fracture mechanics tests were conducted to compile model input parameters. Ground-glass pozzolans also known as glass powder (GP) at up to 100% replacement of fly ash (FA) were attempted. The resulting HVGP-SHCC formulations have self-consolidating ability and exhibited up to 75 MPa compressive strength, 9–15 MPa flexural capacity, 3–6 MPa tensile strength, up to ≈3% tensile strain capacity, and a significantly improved durability (up to 80% enhancement in electrical bulk resistivity). Results reveal that the compactness-based formulation of HVGP-SHCC yielded composites exhibiting higher strength than conventional SHCC containing high-volume fly ash (HVFA) with similar water-to-binder ratio while demonstrating acceptable tensile strain capacity and far better durability aspects. Research outcomes shape a forward step in the development of greener high-performance construction materials necessary for sustainable and resilient concrete infrastructures.

Eco-friendly polymers mortar for floor covering based on dredged sediments of the north of France

The onshore management of marine and river sediments represents economic, environmental, and societal issues; these materials are considered as wastes after dredging. In the framework of the SEDIPLAST regional project, dredged sediments, which are considered as non-inert waste according to European regulation, are recovered as mineral aggregates in thermosetting polymeric matrix to formulate polymer mortars in the field of floor coverings. The formulations are optimized using the Packing Density Model, to determine the optimum density of the mixtures, thus allowing having the high mechanicals characteristics of material. These formulations are evaluated by mechanical, thermal, and chemical tests according to the French classification of durability which characterizes the soil of a locality according to its use (UPEC). The results showed that the polymer mortars including dredged sediments have excellent physical, mechanical, and thermal properties, such as low voids content and excellent chemical resistance properties. Finally, SEM observations of different mixtures allowed to give an explanation of the results observed in macroscopic scale.

5D Model Theory for the Creating of Life Forms

Based on the Fermat’s Last Theorem and the Po, P1 projections from the 4th space coordinate to the time variable for Po and to the remaining 3D space variables for P1, the carbon 12 nucleus is shown explicitly as given by the hard-sphere dense packing model that also satisfies the Gell-Mann standard model. It is through these that C12 is a vital element in all biomaterials, and all proteins as well as the Nitrogenous bases in DNAs, are of hexagon geometric structures. Furthermore, the unique presence of a 3D × 1D space void within the C12 nucleus provides for the monopole Boson field tunneling to occur, giving rise to the enormous variety spectra in the DNA of life forms. In addition, on the surface of the bio cells, the carbon valence band p electron excitation into the empty conduction band separated by a bandgap G, can result in HTC Excitonic induced superconductivity binding gaps from the Excitonic spectra, which match part of those of the DNA and thus produce the self-grow mechanism of numerous different cells in a life form.