Minimum Void Ratio Research Articles

A Review of Particle Packing Models and Their Applications to Characterize Properties of Sand-Silt Mixtures

This paper reviews particle packing models and explores their application in geotechnical engineering, specifically for sand-silt mixtures. The review covers key models, including limiting case, linear, and non-linear packing models, focusing on their mathematical structures, physical principles, assumptions, and limitations through the concept of excess free volume. The application of particle packing models in geotechnical engineering is explored in characterizing the properties of sand-silt mixtures, offering insights into maximum, minimum, and critical void ratios and inter-granular void ratio, and the prediction of mechanical properties.

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.

Impact of initial gradation on compaction characteristics and particle crushing behavior of gravel under dynamic loading

Gravel is a widely used construction material due to its versatility and cost-effectiveness. However, gravel particles are prone to crushing under dynamic loading, causing changes in gradation. The evolution of gradation and its effects on physical properties are not well understood. This study investigates the physical properties of gravel, such as dry density, void ratio, and relative crushing index, under different initial gradations (uniformity coefficient, Cu), using surface vibration compaction tests. A hyperbolic relationship was established between initial Cu and dry density, showing that an increase in Cu can result in a decrease in the void ratio and an increase in the coordination number until stabilization. Particle crushing increases with higher initial Cu, correlating quantitatively with relative crushing indexes. Maximum dry density, minimum void ratio, and fractal dimension also correlate with these relative crushing indexes, suggesting intrinsic relationships among these properties and particle crushing. The size effect can be eliminated by establishing empirical relationships between crushing parameter and particle size.

Estimating Thaw Settlement of Coarse-Grained Permafrost Sediments

Thaw settlement, a frequently reported issue for infrastructure built on permafrost, contributes to high maintenance costs, reduced life cycles, and compromised serviceability of infrastructure. This paper presents a new method to estimate the thaw settlement in coarse-grained permafrost sediments, crucial for northern infrastructure planning. Utilizing available test results from the Canadian Arctic, an overview of the existing data for coarse-grained permafrost sediments is presented. The proposed method uses input parameters derived from particle size distribution to estimate the minimum void ratio of thawed sediments. The minimum void ratio is then used to infer the thawed void ratio, enabling the calculation of thaw strain. The effectiveness of the approach is confirmed by validating predicted thaw strains against measured values for over 60 permafrost samples. A comparison with existing empirical methods shows improved accuracy and reduced bias, further supporting the applicability of the approach. Additionally, an average thawed void ratio assigned to seven groups of granular soils proved valuable for predicting thaw strain when only visual descriptions of sediments are available. Tailored for granular materials and utilizing easily obtainable index properties, this approach provides a reliable and cost-effective method for predicting thaw settlement, benefiting engineers and planners in infrastructure development.

Liquefaction resistance and small strain stiffness of silty sand: Effects of host sand gradation and fines content

In this paper, a well designed experimental study comprising undrained cyclic triaxial and bender element tests was carried out on five sand-silt mixtures with three grain size ratios (Rd) and three sand uniformity coefficients (Cus). The results reveal that at given fines content (FC) and void ratio, the liquefaction resistance (CRR) of the mixtures decreases as Rd increases from 9.7 to 27.8 or Cus from 1.50 to 4.46, and the CRR of the mixture at the highest Rd or Cus becomes as low as nearly 50% of that at the lowest Rd or Cus. The equivalent relative density (Dr*) based on the binary packing theory can be utilized to capture the coupled effects of host sand gradation and FC on the CRR of sand-silt mixtures. A novel finding is that a universal relationship exists between the liquefaction resistance and the shear modulus normalized by the minimum void ratio function of host sand (GN') for different FCs, initial effective confining pressures, sample preparation methods (SPMs), and host sand gradations. Based on the comprehensive laboratory test data, the empirical CRR15-GN' correlation is proposed and further adjusted for the field liquefaction triggering analysis based on the shear wave velocity (Vs). Soil can be considered non-liquefiable when its equivalent shear wave velocity exceeds 225 m/s or the applied cyclic stress ratio (CSR) is below 0.088. Comparisons with the previously established liquefaction triggering boundary curves validate the applicability of the proposed curve for initial evaluation of the liquefaction resistance of sandy soils, indicating laboratory studies can complement in-situ investigations for Vs-based liquefaction assessment.

A new procedure for characterizing the critical intergranular contact state of non-plastic sand – fines mixed materials

A key and urgent scientific issue is how to characterize the complex intergranular contact state and mechanical behavior evolution of sand–fines mixed materials and then show how this state contributes to the static and dynamic properties of such materials. Both theoretical analyses and experimental data suggest that the mixes have different intergranular contact states as the fines content (FC) increases, and the mixed materials can be classified as sand-like, in-transition, or fines-like. The capability of the Rahman semi-empirical formula to predict the threshold fines content FCth—which distinguishes the regime of “fines in sand” (sand-dominated behavior) from that of “sand in fines” (fines-dominated behavior)—is verified using the basic material and mechanical properties of mixed materials from the literature. Developed from the method for determining the theoretical minimum void ratio, a new method that allows unified characterization of the critical intergranular contact state parameters FCin-min and FCin-max for in-transition soils is established based on the binary packing model, and FCin-min and FCin-max can be determined simply through explicit expressions that use some material physical indices of pure-sand and pure-fines materials. The proposed procedure offers significant advantages for evaluating the critical intergranular contact state and mechanical properties of sand–fines mixed materials in geotechnical engineering practice.

Modelling Water Absorption Index and Compressive Strength of Paving Stone Composites with Polyethylene Terephthalate (PET) as Total Binder Replacement

Packing density method of mix design of concrete is new method to design different types of concrete. The mix design obtained from the packing density method has suitable workability, maximum packing density and minimum voids ratio. The geometrical characteristics like shape, size and proportion of fine aggregate and coarse aggregate affect packing density. The objective of this research is to study the mix design of concrete using packing density method and develop the correlation between bulk density, packing density and voids ratio. In this work large number of trail to decide the proportion of aggregate for that optimum bulk density and packing density calculated for different varying proportion of 20 mm: 12.5 mm coarse aggregate (i.e. 90:10, 80:20,70:30, 65:35, 60:40 and 50:50) and for varying proportion coarse aggregate: fine aggregate (i.e. 90:10, 80:20, 70:30, 60:40, 55:45 and 50:50). To finalize the mix design using packing density method also varies the percentage of excess cement paste (i.e. 5%, 7%, 9%, 10%, 11% and 12%). Tests were performed for the properties of fresh concrete like workability test (Slump cone) and hardened concrete like compressive strength, split- tensile strength, pull-out test, rebound hammer and flexural Test etc. tests were determined at 7, 14 and 28 days. The obtained results for above mentioned test using packing density method at 9% of excess cement paste are satisfying the standard results.

Prediction model for small-strain shear modulus of non-plastic fine–coarse-grained soil mixtures based on extreme void ratios

The small-strain shear modulus G0 is a fundamental parameter for characterizing the dynamic behavior of soils. In this study, bender element tests were performed to investigate how the effective confining stress σ'c, relative density Dr, void ratio e, and a wide range of fines content FC (0%–100%) influence the G0 of soil mixtures containing both fine and coarse grains. The results show that under the same e and σ'c, G0 first decreases and then increases with increasing FC. Furthermore, as characteristic state parameters, the extreme void ratios (i.e., the maximum void ratio emax and the minimum void ratio emin) reflect comprehensively the particle size distribution and shape of fine–coarse-grained soil mixtures. Under the same σ'c, the lower limit of G0 (G0min) decreases with increasing emax and the upper limit (G0max) decreases with increasing emin, and the extrapolated upper and lower limits of the normalized G0/(σ'c/Pa) show a negative power-law relationship with emin and emax, respectively. Empirical formulas are established for the G0max and G0min of fine–coarse-grained soil mixtures, and G0 under various Dr can be interpolated according to G0min (for Dr = 0) and G0max (for Dr = 1). Finally, a G0 prediction model that offers reasonable characterization of fine–coarse-grained soil mixtures with different FC is established based on emin and emax.

Evaluating Sand Particle Surface Smoothness Using a New Computer-Based Approach to Improve the Characterization of Macroscale Parameters

The analysis of sands, and the foundation systems with which they interact, are largely dependent on macroscale behavioral parameters that represent the aggregated response of several microscale characteristics. This research paper examines the influence of surface texture, or smoothness, on the behavior of sands. The challenge of estimating or measuring smoothness, due to its microscale feature domain, is addressed through an examination of six artificially graded sand specimens. These specimens are evaluated both visually and numerically to characterize their surface smoothness. The first approach described is a simple visual method that uses a smoothness scale consistent with those of roundness and sphericity. This method, which can be performed with a tool as simple as a hand lens, evaluates a group of representative particles collectively. The second approach is also a visual evaluation, but it utilizes images obtained via scanning electronic microscopy, traditional optical microscopy, and newer low-cost digital microscopes that can be rapidly connected to a smartphone or laptop. To validate these visual estimates, a novel third approach is introduced. This approach is a more objective numerical analysis measurement technique that enables rapid and economic quantification of smoothness. This technique may assist both practitioners and academics in their understanding of the macroscale response of coarse-grained soils. In addition to the visual methods, this research also conducted several laboratory index tests to observe the mechanical behavior of the specimens, considering their particle shape and surface smoothness properties. The results indicate that angular sands have greater minimum and maximum void ratios, a larger difference between the minimum and maximum void ratios, greater critical state friction angles, and greater flow rates through an orifice of fixed size. When adjusted for surface smoothness using the proposed approach, the behavior of the sands—particularly the limit void ratio results—appears to be more predictable in some cases. These results provide additional evidence of particle smoothness contributing to the strength behavior of sand, which may be particularly useful in the domains of slope stability, land reclamation, soil–structure interaction, and soil dynamics.

Influence of the particle morphology and internal porosity characteristics of coral sand in the South China Sea on its limit void ratio

An essential physical parameter for describing the characteristics of cohesionless soil is the limit void ratio. A type of cohesionless soil made up of pieces of coral skeleton is known as coral sand. The limit void ratio of the aggregate will be significantly impacted by its distinct particle morphology and internal pores. The influence of particle morphology and internal pores on the limit void ratio of coral sand is investigated in this paper based on the quantitative evaluation of particle morphology and internal pores. The comparison test with natural quartz sand, artificial broken quartz sand, glass balls, and other loose aggregates reveals the impact of mineral composition on aggregates' limit void ratio. The findings indicate that: (1) the roundness of sand particles increases with particle size. (2) The roundness and internal porosity of the sample show an upward trend with an increase in the content of cube-shaped particles. (3) The internal porosity of particles is controlled by the shape of the particles. The internal porosity of cube-shaped particles is the highest, with an average internal porosity of 20.19%, followed by bar-shaped particles, and the lowest in flake-shaped particles. (4) The particle size will not affect the limit void ratio. The limit void ratio of quartz sand and glass ball has a linear negative correlation with roundness, the limit void ratio of coral sand is affected by roundness and internal porosity together, and internal porosity has a significantly greater impact than roundness. (5) Coral sand also largely follows the linear relationship between maximum void ratio and minimum void ratio which is based on terrigenous cohesionless soil.

Accurately Predicting Quartz Sand Thermal Conductivity Using Machine Learning and Grey-Box AI Models

The thermal conductivity of materials is a crucial property with diverse applications, particularly in engineering. Understanding soil thermal conductivity is crucial for designing efficient geothermal systems, predicting soil temperatures, and assessing soil contamination. This paper aimed to predict quartz sand thermal conductivity by using four mathematical models: multiple linear regression (MLR), artificial neural network (ANN), classification and regression random forest (CRRF), and genetic programming (GP). A grey-box AI method, GP, was used for the first time in this topic. Seven inputs affecting thermal conductivity were evaluated in the study, including sand porosity, degree of saturation, coefficient of uniformity, coefficient of curvature, mean particle size, and minimum and maximum void ratios. In predicting thermal conductivity, the MLR model performed poorly, with a coefficient of determination R2 = 0.737 and a mean absolute error MAE = 0.300. Both ANN models using the Levenberg–Marquardt algorithm and the Bayesian Regularization (BR) algorithm outperformed the MLR model with an accuracy of R2 = 0.916 and an error of MAE = 0.151. In addition, the CRRF model had the best accuracy of R2 = 0.993 and MAE = 0.045. In addition, GP showed acceptable performance in predicting sand thermal conductivity. The R2 and MAE values of GP were 0.986 and 0.063, respectively. This paper presents the best GP equation for evaluating other databases. Additionally, the porosity and saturation of the sand were found to have the greatest impact on the model results, while coefficients of curvature and uniformity had the least influence. Overall, the results of this study demonstrate that grey-box artificial intelligence models can be used to accurately predict quartz sand thermal conductivity.

Monotonic and Cyclic Simple Shear Response of Well-Graded Sandy Gravel Soils from Wellington, New Zealand

In the 2016 Kaikoura earthquake, liquefaction of gravelly soils from reclaimed fills occurred in CentrePort, Wellington, New Zealand. This study presents constant volume monotonic and cyclic simple shear tests on well-graded gravel with sand collected from CentrePort. A large-scale cyclic simple shear device is utilized to evaluate the monotonic, cyclic, and postcyclic responses of the sandy gravel soils. Specimens prepared at various relative densities were subjected to a vertical effective stress of 100 kPa and then monotonically and cyclically sheared. After the cyclic loading, the postcyclic response was evaluated, including volumetric compression or monotonic shear with or without dissipation of excess pore water pressure. Shear wave velocity was measured before and after the cyclic loading. The results show that the well-graded sandy gravel has a high potential for liquefaction, with higher relative density specimens having higher liquefaction resistance. Postcyclic volumetric strain is primarily correlated with density and maximum shear strain during cyclic loading. Postcyclic reconsolidation causes densification of the liquefied specimens, resulting in higher monotonic shear resistance, while postcyclic monotonic shear without dissipation of excess pore water pressure reveals that substantial shear strain is required to develop the shear resistance. Shear wave velocity was significantly reduced after liquefaction, but recovered to slightly higher than its precyclic shear values after reconsolidation. Compared to other gravelly and sandy soils, the well-graded sandy gravel showed a similar or slightly higher liquefaction resistance than gap-graded and uniform gravels. Moreover, the well-graded sandy gravel had a relatively lower ultimate postcyclic volumetric strain due to a small variation between its maximum and minimum void ratios. The results advance our understanding of the liquefaction resistance and subsequent postcyclic responses of the well-graded sandy gravel soils.

Прочностные характеристики массива мелкозернистого песчаного грунта с вертикальными армоэлементами из крупного заполнителя

This work's main objective was to increase the value of the coefficient of friction between soil grains in the test specimen by adding coarse gravel columns to the fine, sandy soil. In this regard, it was determined that a soil's lowest void ratio should be used as a measuring criterion because it matches the crucial requirement of an independent friction angle from soil gradation, all of the results above were calculated using the outcomes of a laboratory test method. Pressure addition was used to determine the relationships between a mixture with a low void ratio and the critical state or high coefficient of friction angles. Determining the strength characteristics of sand-gravel mixtures may be helped by the linkages. The riverbanks of the Tigris, which had previously been subject to similar cracks and collapses, served as the location for the collection of samples for the purpose of this research.
 The completion of the study and examination, it was discovered that the soil is composed of river sediments and that it has the potential to be categorized as soil that is constructed of fine sand. It is generally acknowledged that shear loads are a significant element that contributed to the demise of numerous riverbanks. In this particular field of research, a variety of coarse aggregate column widths and aggregate sizes used to increase the friction angle of soil are investigated via direct shear testing.
 When analyzing the qualities of soil, the minimal void ratio is important, Particle size distributions and particle shapes influence their relationship to compressive characteristics, permeability, and shear strength of the soil. While previous studies have modeled the minimal void ratio in terms of the impact of particle size distributions, they have largely disregarded the role that particle shape might play in this parameter. This work examines the effects of three different sizes of coarse aggregate on the minimal void ratio with respect to particle size distributions. Experiments have shown that when the number of fine particles increased the minimum void ratio reduced. The more irregularity there was in the particle shapes, the more difficult it was for particles to make touch with one another, and the more space there was between them. Diagrams depicting the connection between shear strength, angle of friction, and particle size distribution were created from experimental data.

Effects of intergranular friction and grain size distributions on the initial void ratio of granular sample

This paper investigates the influence of intergranular friction and grain size distributions on the initial void ratio of a granular sample subjected to isotropic compression loading. In the field of geomechanics, besides the loading path and evolution of microscopic properties, the initial void ratio is a crucial and key factor that governs the mechanical behavior of geomaterials. By using Discrete Element Model (DEM) performed on an idealized 2D assembly of disks, this study demonstrates that the initial void ratio can be affected by several parameters during isotropic compression stage. By varying a wide range of intergranular coefficients of friction and grain size distributions, our numerical results suggest that increasing the intergranular coefficient of friction during the isotropic compression phase leads to looser samples. Furthermore, when the diversity of grain sizes is rich, smaller grains can move and occupy voids, thereby increasing the density of the granular sample. A power-lawrelationship is then proposed that connects the minimum void ratio and the diversity degree of the sample.

Morphology and fines type effect on packing of binary soils

Three sands with different particle shapes were mixed with non-plastic fines and plastic fines (clay), respectively, in an entire fines content from 0 % to 100 %. Test results on determining the maximum and minimum void ratios show that both the particle shape of host material and the plasticity of fines can delay the onset of the threshold fines content. For a given fines type in binary soils, the threshold fines content decreases linearly with increasing overall regularity of host material, which proves the feasibility of overall shape parameter in describing soil properties. Meanwhile, the linear equation considering two parameters was derived from test data to evaluate the variation of the maximum and minimum void ratios with increasing fines content by volume for sand-fines mixtures, and the effects of shape of sand and plasticity of fines on the two parameters were investigated. Moreover, non-linear or higher degree equations considering two boundary conditions may have a better performance on describing the variation, but some limitations still exist.

Performance analysis of thermal cloak with porous silicon structure

Porous materials with micro/nanoscale pore size are widely used in various emerging fields such as thermal insulation outer layer of buildings and personal thermal management devices for their low density, high surface area, and perfect thermal properties. In our previous study, a nanoscale thermal cloak was constructed by a porous silicon structure and its cloaking performance was explored by the ratio of thermal cloaking. However, the effects of factors such as void ratio and dynamic temperature on the cloaking efficiency have not been explored. Therefore, in this work, by fixing the void ratio of the functional region and changing the void ratio of the minimum cell, three nanoscale thermal cloaks are constructed. Their cloaking effects at constant and dynamic temperatures are explored using perfect silicon thin films as a comparison. Cloaking can be produced at both temperature boundaries, and the smaller the minimum cell void ratio, the better the cloaking effect. Finally, the mechanism of the effect of the void ratio on the cloaking effect is explained by the phonon localization theory, and the smaller the minimum cell void ratio, the stronger the phonon localization. Our research can promote the development of nanoscale thermal cloaks and the engineering application of porous materials.

A Unified Formula for Small-Strain Shear Modulus of Sandy Soils Based on Extreme Void Ratios

Small-strain shear modulus (G0) is a fundamental property required in dynamic analyses. For sandy soils, G0 may be affected strongly by particle characteristics such as uniformity coefficient (Cu), mean particle size (d50), fines content (FC), and particle shape. Based on an extensive experimental study of the mechanical behavior of coral sands, this paper proposes a new formula for predicting G0 for sandy soils with various Cu, d50, FC, and particle shapes. A notable feature of the new formula is the use of the extreme void ratios (maximum void ratio emax and minimum void ratio emin) as the indexes, which were shown to be able to account for the effects of the various factors in a simple yet collective manner. Power-law correlations were established between the minimum small-strain shear modulus G0min and emax as well as between the maximum small-strain shear modulus G0max and emin. The wide applicability of this formula was validated further using extensive data from the literature from resonant column, bender element, and torsional shear tests on siliceous, calcareous, and coral sandy soils.

Assessment of Poorly Compactable Sands by Recycling and Recompaction: Experimental Program and Packing Particle Analysis.

Compaction is a common ground improvement technique based on the densification of soils for an energy level and optimum water content, mainly influenced by the particle size and curve gradation. Poorly compactable sands, characterized as cohesionless, fine and uniformly graded, are a challenge for earthworks since compaction is not effective due to the lack of a larger range of particle sizes to infill the voids and the compaction energy is not relevant either. These characteristics are common to other materials, i.e., desert sand, industrial or mining by-products or quarry fines, which are mostly discarded to landfill and replaced by proper soils, causing serious environmental issues. To enlarge the technical feasibilities of poorly compactable sands, reducing construction waste and raw material consumption, a mechanical stabilization, based on a repetitive series of recycling and recompaction without binder, is experimentally explored. The behavior observed is also analyzed from reported correlations and a packing particle approach, attending to densification stage, saturation degree, recompaction series, coordination number and packing density. The improvement achieved is moderate and dependent on the cycles applied, showing a characteristic repetitive pattern in the compaction curve, and approaching the estimated minimum void ratio and the theoretical maximum packing possibilities without degradation of the material.

A quantitative evaluation method for granular skeleton state of binary soils at arbitrary relative density

The granular skeleton state relates closely to the mechanical behavior of granular soils but its characterization remains an open challenge. This study aims to develop a novel method to quantify the skeleton state of binary granular soils with arbitrary relative density Dr. Inspired by a linear correlation between the maximum and minimum void ratios, the dual-skeleton packing model was extended to incorporate the effect of Dr. A standard procedure of determining the dual-skeleton index ψ at arbitrary Dr was proposed. Furthermore, a series of numerical binary soil samples with 27 PSDs were simulated in multiple Dr via discrete element method (DEM). The results indicated that the granular skeleton state experienced a typical three-phase evolution pattern of “coarse-dominated → transitional → fine-dominated” with increasing fc. Through the calculated ψ value, critical fc values of phase transition in skeleton state evolution for samples with multiple Dr and the ratio of maximum to minimum particle diameter Rd were unveiled. The micro-mechanical behaviors were observed to be strongly related to the variation of ψ value. Furthermore, a quantitative correlation between ψ and the stress contribution of fine particles was revealed. The simulation results demonstrated the dual-skeleton index ψ can serve as an indicator to characterize the micromechanical behavior of granular media.

The Effect of Fines Content on Compressional Behavior When Using Sand–Kaolinite Mixtures as Embankment Materials

In South Korea, Honam High-Speed Railway has a relatively large residual settlement issue and high fines content has been pointed out as one of the causes. Design guidelines regulate not to use soils containing fines content higher than 25%. However, there is no background information on the effect of fines content on settlement. Therefore, this paper aims to investigate compressional behavior according to fines content using sand and kaolinite. Oedometer test results showed that the compression index is lowest with fines content of 15% to 20% at which the mixture produced maximum density. The optimum fines content for inducing low settlement would be 15% to 20% for the sand–kaolinite mixture. Transition fines content (TFC), which shows sand-like to claylike behavior, was observed to have between 21% and 26% of fines content. Critical fines content (fcrit) where a minimum void ratio occurs was estimated as 21.67%. These behavioral changes appear when fines content is greater than the optimum fines content. SEM also shows that the kaolinite particles were overlapped, creating flat surfaces with a fines content higher than 30%, and showing clay-like behavior. Based on the analysis results, engineers can simply identify the behavior of embankment materials to ensure optimum fines content and consequently minimize long-term settlement potential.