Global Void Research Articles

The 9th Victor de Mello lecture: reflections and speculations

The paper reviews the published literature on some aspects of fabric and particle behaviour in cohesionless soils. It uses insights from Discrete Element Modelling and Microcomputed Tomography to speculate on reasons for the difference in behaviour observed between moist tamped and sedimented sands at the same global void ratio and stress state. It is suggested that inhomogeneities in the form of macrovoids in moist tamped samples trigger localisation, collapse and the development of a local scale chain reaction. It questions whether a similar sequence applies at the field scale and whether expansive partial drainage influences the rate of propagation of the chain reaction. The paper offers reasons why the use of critical state based on moist tamped samples to assess the stability of tailings, may not be the best approach, and suggests that identifying instability lines for sedimented samples at appropriate void ratios and principal stress directions, may be preferable. Critical state reflects behaviour at large strains where initial and evolving inhomogeneities affect identification of relevant void ratios; instability lines reflect behaviour at small strains where inhomogeneities probably initiate collapse. The paper emphasises the importance of spatial variations in local void ratios in loose material, the importance of anisotropy of collapse potential and of load-controlled rather that strain-controlled shearing.

Small-strain shear modulus and liquefaction resistance of calcareous sand with non-plastic fines

Incorporation of non-plastic fines can dramatically affect the liquefaction resistance and stiffness of sands. In this study, the aim is to evaluate the influence of non-plastic fines on the liquefaction resistance and small-strain shear modulus of calcareous sand under cyclic loading. Forty-seven sets of undrained cyclic triaxial tests and companion bender element tests are conducted on reconstituted specimens. The cyclic behaviour of clean sand and silty sand with varying fines content is examined with respect to the global void ratio, relative density and granular skeleton void ratio. The findings demonstrate that the microscopic contacts between coarse and fine grains have a significant impact on the macroscopic behaviour of sand–fines mixtures. The experimental findings are evaluated using the equivalent granular skeleton void ratio, which has been recognised as a suitable parameter to describe the overall effect of fines. The findings on calcareous sand with fines are supplemented and compared with published data in accordance with the semiempirical simplified approach for liquefaction triggering based on shear wave velocity.

Equivalent state parameter dependency on gradation properties of medium sand-fines mixtures

Multiple studies confirm that determining the liquefaction resistance of sand-silt mixtures is more intricate compared to pure sand. Furthermore, it has been observed that the global void ratio fails to accurately predict the behavior of silty sand soils due to the fines particles, which can occupy voids between sand grains without significantly contributing to resisting external forces. To address this, a new parameter called equivalent void ratio (e*) has been proposed to better forecast the response of medium sand-fines mixtures. To investigate this further, a series of compression triaxial tests were conducted on mixtures comprising medium sand with low plastic fines. These mixtures were prepared in the laboratory with an initial relative density and subjected to varying confining pressures. The test results were utilized to assess the undrained shear strength of medium sand-silt mixtures based on the equivalent void ratio (e*) and to establish the equivalent granular steady-state line, which serves as a reference for calculating the equivalent state parameter (ψ*). Analysis of the obtained data suggests a correlation between the equivalent void ratio (e*) and the equivalent state parameter (ψ*) with the grading characteristics (such as D10, D50, Cu, D10R, D50R, and CUR) of the medium silty sand.

Undrained shear behavior of silty sand with a constant state parameter considering initial stress anisotropy effect

Field observations in sedimentation and erosion-prone areas indicate that most natural sand deposits may contain a certain amount of non-plastic fines and are often under anisotropic stress conditions. A series of triaxial compression tests were performed on clean and silty sand with fines content fc ranging from 0 to 20% at an initial mean effective stress of p0′ = 100 kPa and varying consolidation conditions to understand the impact of initial stress anisotropy on undrained shear behavior. The results indicate that the state parameter ψ is a superior predictor for characterizing the responses of sand-fines mixtures compared to the global void ratio and relative density. A comparison of the behavior of clean and silty sand with a constant ψ (= − 0.03) confirms that the sample with 10% fc exhibits the strongest dilation and greatest shear resistance, irrespective of the consolidation conditions. It is also demonstrated that the initial stress anisotropy with a comparably higher static stress ratio ηs typically diminishes the shear strength of mixtures. However, the influence of initial stress anisotropy on soil stiffness is not unilateral. The sample consolidated to a negative ηs is stiffer than that under isotropic consolidation, while the presence of a positive ηs leads to a decrease in the secant Young's modulus.

Probabilistic fatigue strength assessment of cross-ply laminates: Exploring effects of manufacturing defects through a two-scale modeling approach

The study presents a two-scale modeling approach allowing for an efficient fatigue strength evaluation on a macro scale considering a micro-mechanical defect characterization of a Carbon Fiber Reinforced Polymer (CFRP) material. The modeling approach integrates a macro model with the effective elastic properties from micro-mechanical simulations considering voids. This enables the analysis of defects’ influence on material fatigue strength using a probabilistic weakest link approach. A CFRP laminate with a cross-ply layup was investigated. Two simulation case studies demonstrate the effect of void content and size on the characteristic fatigue strength. An experimental investigation was conducted testing the laminates in tension–tension fatigue verifying the predicted numerical behavior. The numerical models identify a difference in the characteristic fatigue strength consistent with the fatigue test results. It is numerically concluded that the investigated CFRP material’s fatigue strength is affected by the presence of voids and even with only a slight difference in the global void volume fraction a scatter in fatigue strength is identified.

Experimental study on monotonic to high-cyclic behaviour of sand-silt mixtures

The naturally deposited soil usually does not consist of pure coarse or fine-grained soil but of a mixture of both. The mechanical behaviour of a saturated fine sand mixed with varying amounts of low-plastic fines was evaluated by monotonic as well as high-cyclic triaxial tests. The test results were used to conclude on the effect of fines content on the critical state, phase transformation line, secant Young’s modulus, the residual strain accumulation as well as strain amplitude during drained cycles of the mixtures in relation to the global void ratio as well as to the equivalent void ratio. It was found that while the choice of void ratio definition is important for the uniqueness of the critical void ratio, both approaches can be used as state variables for the phase transformation line. However, some seemingly contradictive results are found from the drained high-cyclic tests. Eventhough, an increase of the residual strain accumulation with decreasing fines content compared at the same initial equivalent void ratio is rendered by the laboratory data, a unique and on fines content independent relationship between εacc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon ^{\\rm{acc}}$$\\end{document} could be established only with respect to the initial global void ratio.

Earthquake-induced large deformations and failure mechanisms of silty sands in sloped ground conditions

In practical engineering, sand deposits or fills usually contain fines and are subjected to cyclic shear stresses induced by earthquakes, traffic, or waves which are superimposed on the initial static shear stress in natural or artificial slopes or beneath existing structures. To explore the combined and complex effect of an initial static shear stress and fines content of non-plastic silty sands on their deformation characteristics, pore pressure generation, and liquefaction susceptibility, the results of a comprehensive experimental program of cyclic simple shear (SS) tests are presented. Test conditions cover different fines contents fc (0-40%), initial void ratios e0, and initial static shear stress ratios (factor α=0-0.30). The observed types of failure are divided into four cyclic patterns: flow liquefaction, limited flow liquefaction, cyclic mobility, and plastic strain accumulation, depending on the initial state of the specimens and cyclic loading characteristics. Moreover, the threshold fines content (fthre), denoting the specific value of the fines content at which the behavioral properties of the mixture are reversed, is not affected by α level, and a practically unique value of around 24.5% is identified. The Kα values of sand-silt mixtures measured under cyclic simple shear loading would either increase or decrease with an increasing initial static shear level based on the initial global void ratio and fines content of mixtures; in particular, for a given initial global void ratio, the reduction of cyclic resistance due to the addition of non-plastic fines (fc < fthre) is much more pronounced as α increases. Finally, the larger the initial shear stress, the smaller the cyclic pore-water pressure (PWP) measured at failure. Therefore, a modified stress-based PWP generation model is proposed to predict the cyclic residual excess pore pressures developed under various initial static shear stress conditions in non-plastic silty sands in a satisfactory way.

Global void ratio of municipal solid waste for compression indices estimation.

Compressibility is one of the important engineering properties of municipal solid waste (MSW) affecting the stability and functionality of a landfill. Although the correlations between MSW properties and compression parameters have been established, they either have low accuracy and small datasets or are only limited to a few specific landfills in a region. In this study, a new method using the initial global void ratio (e0*) of MSW to estimate the compression indices is developed based on a comprehensive MSW dataset. The dataset consists of 124 sets (91 laboratory and 33 field) of MSW compression results obtained from 44 studies in 13 countries with different income levels and climate conditions. We categorized MSW as a ternary mixture with biodegradable (B), reinforcing (R), and inert (I) fractions, and suggested average specific gravity values (Gs,B=1.20, Gs,R=1.07, and Gs,I=2.64), respectively. The e0* values were calculated using the initial dry unit weight (γd,0) and ternary composition of MSW. The correlations between the e0* and the immediate compression index, secondary compression index induced by mechanical creep, and secondary compression index induced by bio-compression of MSW were evidently established. The results are applicable to the MSW with B=0-79.2%, R=0-54.0%, I=2.8-100.0%, and γd,0=2.0-14.2 kN/m3. A simple flowchart was established to estimate the compression indices and strains of MSW disposed on in landfills and dumpsites in countries with different income levels.

In-situ three-dimensional investigation on micro ductile fracture mechanism of mild steel

In this paper, in-situ micro-computed tomography (micro-CT) experiments were performed on mild steel samples under monotonic tension using X-ray microscopy. A three-dimensional (3D) visualization model was reconstructed and the characteristics of void evolution under different strain states, such as void distribution, void shape, void growth and void coalescence, were quantitatively analyzed from a 3D perspective. It is found that void growth mainly depends on the stress state, while void coalescence is controlled by the stress state and intervoid spacing. The critical intervoid spacing for void coalescence occurring at the post-necking stage was given. Two stages of void coalescence, local coalescence and global coalescence, were found during void evolution. Local void coalescence was first observed at a strain of 10.02%, well before necking, but has a negligible effect on the overall void evolution. Global void coalescence was developed after the formation of a strain localization band dominated by large coalesced voids in the necking region. The propagation of fine cracks between voids along the strain localization band leads to the formation of macroscopic ductile cracks. Overall, the micro ductile fracture of mild steel is triggered by the combined effects of multiple damage mechanisms rather than independent competition.

Effects of particle morphology on pore structure and SWRC of granular soils

Given grain-size distribution (GSD) and relative density, the soil–water-retention curve (SWRC) of granular soils can be straightforwardly predicted. However, the evolution of SWRC with different particle morphologies under the same GSD is still unclear. To solve this fundamental problem, herein, four sand analogues with different particle shapes under the same GSD were produced by three-dimensional printing. The SWRCs and the pore structure at mesoscale were synergetically measured by using nuclear magnetic resonance (NMR) technology and hydraulic properly analyser water potential meter. The relationship between particle morphology and SWRC was quantitatively analysed, and the soil pore structure evolution under different particle morphology was clearly observed. Compared with round particle shape soils, soils with the same GSD but higher degree of angularity were found to have a subtle higher air-entry value (AEV) at a given relative density, even though the global void ratio is larger. NMR results indicate the pore structure of specimens with different particle morphology is similar. The pore volume is increased with angularity while the maximum pore throat shows an opposite trend. The difference in maximum pore throat is the fundamental reason for the variation in AEV, highlighting the importance of particle morphology on soil–water-retention behaviours.

The Effect of the Nonplastic Fines on the Cyclic Resistance of the Saturated Sand-Fines Mixtures

A series of undrained cyclic triaxial tests were carried out to study the nonplastic fines on the cyclic behaviour of saturated sand-fines mixtures. The influences of the fines content (FC), global void ratio (e), and relative density (Dr) were considered. The results show that the cyclic resistance ratio (CRR) of the mixtures firstly decreases and then increases, finally stabilizing with increasing FC when the samples are prepared at a constant Dr. The CRR reaches its minimum when the FC is 20%. However, the CRR decreases and then increases with increasing FC when the samples are prepared at a constant e. The CRR reaches its minimum when the FC is at 30%. The CRR of the mixtures increases with increasing Dr when the FC is given. A single Dr or e cannot describe the dense state of the mixture effectively. A new index, Dr/e, is proposed in this study to describe the dense state of the mixtures. A semiempirical model is proposed to evaluate the CRR of the mixtures using the parameters of Dr/e and FC of the mixture based on the back analysis method. The applicability of the model is verified by the test data from this study and other scholars. In addition, the parameters of Dr/e and FC of the mixture can be obtained from basic geotechnical tests, which is convenient for the application of the model.

Use of Combined Static and Dynamic Testing to Quantify the Participation of Particles in Stress Transmission

A number of research studies have recognized that not all particles in a sand specimen are active in stress transmission, particularly in the case of gap-graded soils. This has implications for the use of the global void ratio (e), and variables/parameters that depend upon e, to predict the influence of the state on the mechanical behavior of gap-graded soils. This study explores the possibility of comparing the shear stiffness determined in dynamic wave propagation tests (Gdyn) with stiffness values determined in small-strain probes (Gsta) to assess the extent to which all the particles in a specimen are actively engaged in stress transmission. The idea is initially developed using three-dimensional discrete element method simulations and considering ideal specimens. The practical application of this approach is then tested in a series of drained triaxial compression tests. The numerical studies considered both specimens with continuous, linear particle size distributions as well as gap-graded soils. The results show that the ratio Gsta/Gdyn may be associated with the ratio between the bulk density calculated considering only the stress transmitting particles, ρm, and the bulk density calculated considering all particles, ρ. The ratio ρm/ρ is determined by the proportion of inactive particles, which varies with the proportion by mass of finer particles in the soil (Ffiner) for gap-graded soils. The relationship between Gsta/Gdyn(e) and Ffiner enables a qualitative assessment of the proportion of inactive particles. The corresponding experimental test results show a similar but weaker correlation between the ratio of Gsta/Gdyn and Ffiner, this weaker correlation may be attributed to the differences between the simulations and the experimental conditions. However, despite the challenges with experimental implementation, the data presented here support the idea that it may be possible to qualitatively estimate the proportion by volume/mass of inactive particles in physical samples by comparing the stiffness results of static and dynamic testing.

Multiscale analysis of the Reynolds stress, dissipation, and subgrid-scale tensor in turbulent bubbly channel flows: Characterization of anisotropy and modeling implications

A direct numerical simulation database of bubbly channel flows at friction Reynolds number 180 and with three different global void fractions has been used to perform a multiscale analysis of the anisotropy of the Reynolds stress tensor, the dissipation tensor, and the subgrid-scale (SGS) tensor in order to characterize the turbulence for a wide range of scales down to the smallest structures occurring in the flow. Based on the hypothesis of Kolmogorov, the non-linear turbulent energy transfer is expected to result in a loss of directional information such that, for a sufficiently high Reynolds number, the small-scale turbulence is expected to be isotropic and universal. The present analysis reveals that the presence of the bubbles increases the anisotropy of the flow which persists down to the smallest scales of motion, even for the dissipation and SGS tensor. This has implications for the complete landscape of turbulence modeling approaches ranging from large eddy simulation, over hybrid approaches to Reynolds averaged Navier–Stokes based modeling.

Comprehensive laboratory study on stress–strain of granular soils at constant global void ratio: combined effects of fabrics and silt content

Comprehensive laboratory study on stress–strain of granular soils at constant global void ratio: combined effects of fabrics and silt content

Effect of particle gradation on the triaxial test of soil using three-dimensional DEM analysis

Numerical simulation of triaxial test are carried out for soil specimens with varying particle size by DEM analysis under the flexible boundary. For the purpose, soil state characteristics such as shear band formation, variation law and the difference between the global void ratio and the local void ratio are particularly focused. Results shows that the shear band of multi-graded specimen is more difficult to create, but it is thicker than that of single-graded specimen. Overall void ratio changes mostly due to particle movement at the shear band and independent to particle gradation. The shear strength of the multi-graded sample is better than that of the single-graded specimen.

DISTRIBUTION AND EVOLUTION OF FREE VOLUME OF ELLIPSOIDAL PARTICLE SYSTEMS DURING SHEARING

Granular material is a complex multi-body interaction system which is composed of a large number of discrete particles and their surrounding free volume. Although the correlation between free volume and the mechanical properties as well as the deformation characteristics of granular materials has been proved, the local free volume of non-spherical particles is not fully understood at present due to the difficulties in characterizing. In this paper, the combined finite and discrete element method (FDEM) is used to simulate the triaxial tests of ellipsoidal particles with different principal axis lengths, and the Set Voronoi tessellation method is applied to construct the Voronoi cells of the particles during shearing. The statistical distribution and evolution of the local free volume of the granular systems during shearing are analyzed, and the influence of particle shape on the evolution of free volume is studied. Our results show the anisotropy of Voronoi cells gradually increases during shearing, and the degree of anisotropy increase will be intensified with the increase of particle shape asphericity, which means the granular assembly with a larger asphericity will experience more intense rearrangement during shearing. The local void ratio of ellipsoidal particle systems with different asphericity statistically complies with a k-gamma distribution, which is controlled by the global void ratio of granular assembly and not affected by particle shape and shear state. The local void ratio fluctuations follow an Asymmetric Laplace Distribution (ALD), and its asymmetric parameter which has a linear relationship with the global void ratio of granular assembly describes the competition between contraction and dilatation of local free volume.

Influence of manufacturing-induced defects on the fatigue performances of autoclave moulded laminates

In the present work, cross-ply and multidirectional laminates were produced by autoclave moulding. Changes in the process parameters led to different microstructural features in terms of fibre volume fraction, global void content, and void size. Fatigue tests revealed a strong influence of the microstructure on the long-term performances of the laminates, in terms of life to crack initiation, crack propagation, crack density evolution and associated stiffness drop. A criterion recently proposed by the authors to predict the formation of the first fatigue cracks accounting for the actual material microstructure, including voids, was then validated on the new experimental data. The results show the need to properly account for the manufacturing induced defects for a more efficient and safer design of composite parts, and remark the necessity of developing models that link manufacturing process parameters, micro-scale morphology, and mechanical performances to enable a cost-effective production that maximizes the performance/cost ratio.

Intergranular void ratio and undrained monotonic behavior of Chlef sand containing low plastic fines

Stability analysis of soils prone to static liquefaction based on their monotonic undrained shear strength characteristics is an indispensable challenge in earthquake geotechnical engineering. This paper presents a laboratory study on the static behavior of Chlef sand–silt mixtures (with a silt content fc range from 0 to 50%); under low confining pressures. The experimental program includes undrained triaxial monotonic tests which were carried out for five types of samples, consolidated under different confining pressures (σʹc = 20, 50, 100, 150, and 200 kPa). On the samples preparation, the dry pluviation funnel has been used with a medium relative density (Dr = 60%). Main results obtained indicate that the fines content and initial confining pressure have a significant influence on instability stress and steady-state ratios of sand–silt mixtures. Moreover, the obtained data confirm the existence of a simple correlation between undrained instability stress, steady-state ratios, fines content, void ratios, and effective confining pressure. From the results obtained, nevertheless it can be concluded that the global void ratio does not represent the actual behavior of the soil under study, and the undrained residual strength decreases with a logarithmic manner with the increase of the intergranular void ratio, and a similar trend is occurring with the fine content of the sand–silt mixtures up to 50% as well.

Pore Space and Fluid Phase Characterization in Round and Angular Partially Saturated Sands Using Radiation-Based Tomography and Persistent Homology

The multiphase flow transport properties find ubiquitous applications in partially saturated granular media, particularly in the vadose zone due to alternate drying and wetting cycles. The spatial heterogeneity in the degree of saturation at the pore scale has a significant impact on the transport properties of the porous materials. In the present work, three-dimensional (3D) computed tomography (CT) images of the two-phase flow experiments are used to visualize and investigate the pore space and fluid phase microstructure of sands with rounded and angular grain morphology. The dual image modality utilizing X-rays and neutrons is used to obtain 3D information on the arrangement of solids and water in a sand sample. Advanced analysis of the experimental data is carried out using a mathematical framework known as persistent homology. This approach allows quantification of geometry as well as connectivity of pore space and fluid phase directly from the CT images with powerful implications in exploring pore-scale physics of multiphase granular materials. Persistent homology predicted percolation length of 52.5 µm and 41.86 µm consistent with the hydraulic conductivity measurements for rounded sand and angular sand, whereas the value of global void ratio equal to 0.512 and 0.69, respectively, suggests the contrasting response. The fluid distributions obtained from numerical predictions using the pore morphology method (PMM) are compared with results from experiments utilizing persistent homology. These results demonstrate the need for incorporating pore-scale physics in boundary value problems related to multiphase flow in granular materials.

Influence of Particle Size Distribution on the Proportion of Stress-Transmitting Particles and Implications for Measures of Soil State

It is generally accepted that the use of void ratio and bulk density as measures of soil state have limitations in the case of gap-graded soils because the finer grains may not transmit stress. However, no research has explored systematically whether this issue also emerges for soils with continuous gradings. Building on a number of experimental and discrete-element method (DEM) studies that have considered the idea of an effective void ratio for gap-graded or bimodal soils, this paper extended consideration of this concept to a broader range of particle-size distributions. By exploiting high-performance computers, this study considered a range of ideal isotropically compressed samples of spherical particles with linear, fractal, and gap-graded (bimodal and trimodal) particle-size distributions. The materials’ initial packing densities were controlled by varying the interparticle coefficient of friction. The results showed that even for soils with continuous particle-size distributions, a significant proportion of the finer particles may not transmit stress, i.e., they may be inactive. Drawing on ideas put forward in relation to gap-graded soils, both a mechanical void ratio and mechanical bulk density that consider the inactive grains as part of the void space were determined. Even for the linear and fractal gradings considered here, the difference between the conventional measures and the mechanical measures was finite and density dependent. The difference was measurably larger in the looser samples considered. These data highlight a conceptual/fundamental limitation of using the global void ratio as a measure of state in expressions to predict granular material behavior.