Extreme Void Research Articles

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.

New empirical equations for limiting void ratios as function of particle morphology properties of sand-fly ash binary assemblies

ABSTRACT The objective of this research is to develop novel empirical equations to predict the extreme void ratios of sand-fly ash mixtures. These equations rely on multiple variables derived from the particle morphology properties of three different types of sandy materials. These sands are mixed with varying fractions of spherical fly ash particles, ranging from 0% to 30% fly ash content. High-quality microscope images of individual particles are used to determine the particle morphology properties. The analysis of the results confirms that combining these particle morphology properties (Acom, Scom, ARcom, Cxcom, and ORcom) provides suitable factors for predicting the extreme void ratios of the examined sand-fly ash mixtures. Furthermore, the study clearly demonstrates the significant influence of particle morphology on the packing density of the materials. The developed multi-variable functions can be systematically employed to predict the limit void ratios of sand-fly ash mixtures commonly encountered in various geotechnical engineering applications.

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.

The critical state line of nonplastic tailings

The probability of failure of tailing dams and associated risks demand improvements in engineering practice. The critical state line provides a robust framework for the characterization of mine tailings. New experimental data for nonplastic platinum tailings and a large database for tailings and nonplastic soils (grain size between 2 and 500 μm) show that the critical state parameters for nonplastic tailings follow the same trends as nonplastic soils as a function of particle-scale characteristics and extreme void ratios. Critical state lines determined for extreme tailings gradations underestimate the range of critical state parameters that may be encountered in a tailings dam; in fact, mixtures with intermediate fines content exhibit the densest granular packing at critical state. The minimum void ratio emin captures the underlying role of particle shape and grain size distribution on granular packing and emerges as a valuable index property to inform sampling strategies for the assessment of spatial variability. Mineralogy does not significantly affect the intercept Γ100, but it does affect the slope λ. The friction coefficients M of tailings are similar to those of other nonplastic soils; while mineralogy does not have a significant effect on friction, more angular grains lead to higher friction coefficients.

Exploring the effect of 3D grain shape on the packing and mechanical behaviour of sands

This paper investigated the dependence of three-dimensional grain shape characteristics on particle size by applying X-ray micro-computerized tomography. A series of packing and triaxial shearing experiments are performed, which suggest that the macroscale behaviour of sands at different scales of stress states progressively correspond to the characteristic scales of the microscale morphological descriptors of particles. That is, the packing behaviour are more reliant on grain aspect ratio (AR), whereas the critical state mechanical behaviour are more reliant on grain sphericity. As the AR of particulates increases, the extreme void ratios and packing index decrease. The shearing friction angles at the critical state decrease as the sphericity of grains increases and the intercept void ratios become smaller. The drained peak friction angles and maximum friction angles of undrained stable and strain-hardening specimens of angular sands are larger than those of rounded sands at the same state parameter level because the interlocking of angular sands with many projecting corners is stronger than that of rounded sands during shearing. At the same initial state level, rounded sands are more susceptible to softening and liquefaction than angular sands under undrained conditions, because smooth corners permit easier grain rotations in undrained unstable specimens.

The influence of particle characteristics on the index void ratios in granular materials

The goal of this paper is to assess the effects of particle and specific gravity characteristics (e.g. shape, size, and specific gravity) on the limiting void ratios emax and emin of granular matter. To assess the effect of specific gravity, two different types of materials—glass beads and natural sands—were used. Particle characteristics such as roundness (R), sphericity (S) regularity (ρ), the average of R and S, were calculated through image analysis techniques after obtaining high-quality microscope images of individual grains. The German DIN standards were strictly followed to determine the extremities of the void ratio. Experimental data were used to investigate the effects of the particle characteristics on the relative density of soils. The results show the significant effect of the mean grain size (D50) on the extreme void ratios of poorly graded glass as well as the significant effect of Cu but negligible effect of D50 on the extreme void ratios of sand. The effect of the specific gravity of the materials was also examined. The results were used to develop models dependent on both particle shape and specific gravity, which were validated by comparison with results of previous studies.

Re-recognizing the impact of particle shape on physical and mechanical properties of sandy soils: A numerical study

The particle shape created by geological processes is an essential characteristic that determines the physical and mechanical properties of sandy soils. However, the nature of the arbitrary shape and the individual volume of particles in natural sand have been given scant regard. In this study, we constructed a particle flow code (PFC) model using a number of clumps with random irregular shapes (called “Irreg-Sam”), and simulated direct shear tests on silica sand. Further, particle shapes were investigated via a series of numerical tests on Irreg-Sams and comparative models with rounded particles (called “Reg-Sam”). The results indicate that Irreg-Sam can form a lower minimum void ratio and interval of extreme void ratios than Reg-Sam. Conversely, Reg-Sam has a greater peak shear strength than Irreg-Sam when the normal stress is less than 200 kPa. However, there was no noticeable difference in the critical shear strengths of these two samples. Because of the higher dilatancy angle under relatively low stress levels, sand with irregularly shaped particles will exhibit a greater peak shear strength than sand with rounded particles. The nature of the arbitrary shape and the individual volume of particles in sandy soils were found to be two important factors that cannot be ignored when studying the effect of particle shape. This research will facilitate better understanding of the role of particle shapes in sandy soils.

Reliability and applicability of the Krumbein-Sloss chart for estimating geomechanical properties in sands

This paper describes the reliability of the Krumbein-Sloss chart in estimating the particle shape parameter. Despite its simplicity and subjectivity in choosing roundness and sphericity, its applicability has not yet been completely validated. We compare the computed shape parameters of four different sands from 2D microscopic images with estimated values from the chart by a questionnaire study. The survey results show that the roundness and sphericity tend to be overestimated and underestimated, respectively, regardless of the participants' expertise on shape analysis. We validate the reliability of a previous regression in literature for extreme void ratios and newly propose the correlation of critical state void ratio based on roundness and particle gradation. It underscores that the Krumbein-Sloss chart based estimation can be statistically and partially reliable and still applicable in not only estimating shape parameters and but also correlating them with geotechnical properties.

Relation between the critical state friction angle of sands and low vertical stresses in the direct shear test

In this study, the critical state friction angle in a direct shear box was tested at vertical effective stresses between 4 kPa and 150 kPa for seven sands of different origins. The results show a stress dependency on the angle of friction at low vertical stresses, and that the critical state friction angle decreases with increase in the vertical effective stress. The largest drop occurs for vertical effective stresses between 4 kPa and 50 kPa and varies between 4° and 10° depending mostly on the shape of the sand particles and the difference in the extreme void ratios.

Comparison of Methods for the Measurement of the Angle of Repose of Granular Materials

Abstract The angle of repose—the maximum angle that allows a heap of soil to remain stable without failing—is an important property of soils and affects the safety and costs of projects such as slopes or retaining walls. But several methods have been proposed to measure it, which might produce confusion in practice and research. The angles of repose obtained using six different methods for six different sands are compared here in order to quantify and explain the differences and determine some of the factors that influence the angle’s value. The results show that the highest values are obtained with the ASTM International and Cornforth methods, followed by scoop deposition (6 % smaller), the Santamarina and Cho dry method (12 % smaller), and the cone lifting method (35 % smaller). Both the cone lifting method and the Santamarina and Cho wet method produce segregation of the finer particles for sands having a specific gravity greater than 2.7 and a difference of extreme void ratios larger than 0.3.

Large scale structure simulations of inhomogeneous Lemaître-Tolman-Bondi void models

We perform numerical simulations of large scale structure evolution in an inhomogeneous Lema\^{\i}tre-Tolman-Bondi (LTB) model of the Universe. We follow the gravitational collapse of a large underdense region (a void) in an otherwise flat matter-dominated Einstein--de Sitter model. We observe how the (background) density contrast at the center of the void grows to be of order one, and show that the density and velocity profiles follow the exact nonlinear LTB solution to the full Einstein equations for all but the most extreme voids. This result seems to contradict previous claims that fully relativistic codes are needed to properly handle the nonlinear evolution of large scale structures, and that local Newtonian dynamics with an explicit expansion term is not adequate. We also find that the (local) matter density contrast grows with the scale factor in a way analogous to that of an open universe with a value of the matter density ${\ensuremath{\Omega}}_{M}(r)$ corresponding to the appropriate location within the void.

A Brief Analysis of Sister Carrie’s Character

Carrie is always dreaming while the rocking chair is rocking again and again, this is the deep impression on us after we read Sister Carrie which is the first novel of Theodore Dreiser. In this novel the protagonist Sister Carrie is a controversial person. This paper tries to analyze the character of Sister Carrie in order to find out why what she has finally achieved is just extreme void and unhappiness, and shed light on how the author calls warmly for human intuitive knowledge, attacks vigorously the society of money omnipotent, and further more exposes bourgeois society’s darkness.

Characterization of Liquefaction Susceptibility of Sands by Means of Extreme Void Ratios and/or Void Ratio Range

The liquefaction susceptibility of various graded fine to medium saturated sands are evaluated by stress controlled cyclic triaxial laboratory tests. Cyclic triaxial tests are performed on reconstituted specimens having global relative density of 60%. In all cyclic triaxial tests, loading pattern is selected as a sinusoidal wave form with 1.0 Hz frequency and effective consolidation pressure is chosen as 100 kPa. Liquefaction resistance is defined as the required cyclic stress ratio causing initial liquefaction in 10 cycles during the cyclic triaxial test. The results are used to draw conclusions on the effect of the extreme void ratios and void ratio range on the liquefaction resistance of various graded sands.

A divided Universe: red and blue galaxies and their preferred environments

(Summary) Making use of scaling relations between the central and the total galaxy luminosity of a dark matter halo as a function of the halo mass, and the scatter in these relations, we present an empirical model to describe the luminosity function (LF) of galaxies. We extend this model to describe relative statistics of early-type, or red, and late-type, or blue, galaxies, with the fraction of early type galaxies at halo centers, relative to the total sample, determined only by the halo mass and the same fraction in the case of satellites is taken to be dependent on both the halo mass and the satellite galaxy luminosity. This simple model describes the conditional luminosity functions, LF of galaxies as a function of the halo mass, measured with the 2dF galaxy group catalog from cluster to group mass scales. Using 2dF measurements, we extract information related to conditional mass function for halos from extreme voids to dense regions in terms of the galaxy overdensity. We also calculate the probability distribution function of halo mass, as a function of the galaxy overdensity, and use these probabilities to address preferred environments of red and blue galaxies. Our model also allow us to make predictions, for example, galaxy bias as a function of the galaxy type and luminosity, the void mass function, and the average galaxy luminosity as a function of the density environment.