Fabric Anisotropy Research Articles

Role of particle shape in sheared granular media: Roundness and elongation

Particle shape is an intrinsic characteristic of soil particles that significantly influences mechanical responses. In this investigation, a meticulously calibrated and validated two-dimensional discrete element method (DEM) model of a biaxial shearing test was employed to simulate the shearing response of forty distinct particle shapes. The systematic evolution of particle roundness (R) and aspect ratio (AR) was achieved by utilizing idealized polygonal-shaped particles, aiming to comprehend their effects on the macro and micromechanical behaviors of granular materials. The results suggest that a reduction in R limits free rotations and enhances interlocking, thereby promoting relatively stable force transmission between particles and leading to a monotonic increase in shear strength. However, this effect diminishes as particles become more elongated. Conversely, a decrease in AR from 1.0 (increased elongation) constrains particle rotations, increases the coordination number, and enhances fabric anisotropy initially resulting in increased overall shear strength, reaching a maximum before exhibiting a decreasing trend, indicative of non-monotonic variation. For high elongations, notable fabric anisotropy impedes clear force transmission between particles thus facilitating interparticle sliding and overall strength diminishes. The extent to which AR impacts depends on the angularity feature of particles. Finally, a nonlinear equation has been proposed to predict the variation in critical state shear strength of granular samples, based on the R and AR values of the constituent particles.

Influence of inherent anisotropy on the mechanical properties of normally consolidated clays with a wide range of plasticity indices

Inherent (fabric) anisotropy is one of the most important properties of earthen materials which has a significant influence on their strength and stiffness characteristics. In this study, a comprehensive series of unconfined and constrained compression tests is performed on normally consolidated (NC) clay samples with different plasticity indices to examine the effect of inherent anisotropy on their mechanical characteristics. Accordingly, several cylindrical clay samples with different proportions of kaolinite and bentonite are reconstituted at a wide range of deposition angles and then subjected to both unconfined and constrained compressive loadings. According to the experimental results, for a clay sample with a particular plasticity index, the highest and lowest values of the unconfined compressive strength (UCS), the secant modulus (E50), and the constrained Young's modulus (Eoed) are observed to be associated with the deposition angles of 0o and 90o, respectively. The results also show that at a certain bedding plane angle, the sample containing 30% bentonite (PI = 110%) exhibits the highest UCS, E50, and Eoed values. Several practical empirical correlations are developed to estimate the strength and stiffness properties of NC clays using their plasticity indices and bedding plane directions. Scanning Electron Microscopy (SEM) analysis is also conducted to explore the microstructure of samples containing varying percentages of kaolinite and bentonite.

Particle morphology and principal stress direction dependent strength anisotropy through torsional shear testing

The major principal stress direction angle (ασ) experienced by granular soils varies widely in engineering, causing different strengths. However, how particle morphology affects the strength anisotropy behavior under different ασ remains unclear. To address this gap, this study performed drained hollow cylinder torsional shear tests under different ασ on six granular materials with distinct morphologies. Results highlight the significant dependence of peak strengths of granular materials on both particle morphology and ασ. Increasing particle shape irregularity and surface roughness leads to a considerable enhancement in peak strength, while this peak strength significantly degrades with increasing ασ. Materials with more irregular shapes were found to have a more pronounced strength anisotropy. Furthermore, the initial fabric of particle packings, derived from three-dimensional X-ray microtomography, was used to interpret microscopic mechanisms behind the morphology-dependent strength anisotropy. Irregular-shaped materials display broader preferred particle orientations and higher initial fabric anisotropy compared to relatively regular-shaped materials. This higher morphology-induced fabric anisotropy contributes to strength anisotropy, and a correlation was established for describing this trend. Additionally, an anisotropic failure criterion incorporating fabric anisotropy was developed to characterize the strength envelope for granular materials with diverse shapes.

Understanding the influence of drained cyclic preloading on liquefaction resistance of sands using DEM-clump modeling

The soils in situ are subjected to various types of preloading histories. Extensive work has been devoted to understanding the impact of undrained preloading with different strain histories on the reliquefaction resistance of sands. This study primarily examines the effects of drained cyclic preloading histories on the liquefaction resistance of soils using DEM-clump modeling. The effects of preloading stress path and preloading deviatoric stress amplitude on the drained cyclic behavior and subsequent undrained liquefaction response are discussed. Moreover, the evolution of two microscale descriptors, including coordination number Z and fabric anisotropy degree ac, during the total process is analyzed. The results demonstrate that a smaller preloading stress amplitude and an increasing preloading cycle generally increase the liquefaction resistance of sandy soils. In comparison, a larger preloading stress amplitude significantly reduces the liquefaction resistance. We also reveal that drained cyclic preloading histories induce soil samples with different relative densities and fabrics. The relationship between relative density and liquefaction resistance of soils is not unique. Essentially, Z and ac are good indexes for determining the liquefaction resistance of soils with various drained cyclic preloading histories. The primary objective of this study is to elucidate the micromechanical effects of drained cyclic preloading on the liquefaction resistance of sandy soils.

DEM study of structuralized cemented slopes under excavation conditions

Structuralized cementation has emerged as a promising method for reinforcing excavated slopes. The Discrete Element analysis is conducted on the structuralized cemented slopes under excavation with its validity verified through centrifuge model tests. The results indicate that structuralized cemented slopes exhibit progressive failure from the bottom to the top under excavation conditions. As the slope elevation decreases, the failure mode transitions from tension failure to shear failure, due to the presence of tensile stress only in the upper part of the slope. Microscopically, structuralized cementation prevents contact breakage, reducing fabric anisotropy and the variation of contact orientation from the vertical direction. Macroscopically, it increases the safety limit of slopes. The significant coupling between fabric evolution localization and local failure explains the failure mechanism of structuralized cemented slopes under excavation conditions. Increasing the size of the solidification zone reduces the localization extent of fabric evolution, thereby reinforcing the slope.

Influence of Anisotropic Consolidation on the Instability of Loose Granular Soils Under Undrained and Drained Loading

Previous studies, mostly experimental, have reported conflicting observations on the effect of the initial anisotropic consolidation stress ratio (η<sub>0</sub>) on the stress ratio at the onset of instability (η<sub>f</sub>) for drained and undrained loading that involve static liquefaction. They indicate that as η<sub>0</sub> increases, η<sub>f</sub> could decrease, increase, or remain invariant, albeit without providing potential mechanistic factors. In this study, the anisotropic critical state theory (ACST) is used to investigate potential factors, including compressibility, state, and fabric anisotropy, that can explain the influence of η<sub>0</sub> on η<sub>f</sub> under undrained and drained loading. The assessments consider numerical simulations with the ACST-based SANISAND-F model, insights from SANISAND-F based instability criteria, the instability surface concept, and available experimental observations. Our findings show that compressibility and fabric anisotropy (and its evolution) are key factors in explaining the influence of η<sub>0</sub> on η<sub>f</sub>. In particular, the results show that if fabric evolution is not substantial, an increase in η<sub>0</sub> decreases η<sub>f</sub> for materials with significant compressibility, whereas the effect of η<sub>0</sub> in low compressibility materials is minimal. On the other hand, for materials that promote fabric evolution, the results suggest that the effect of fabric changes counteract compressibility effects, potentially increasing η<sub>f</sub>.

Micro‐Mechanical Analysis for Residual Stresses and Shakedown of Cohesionless‐Frictional Particulate Materials Under Moving Surface Loads

AbstractResidual stresses and shakedown have been successfully presented by two‐dimensional numerical experiments based on the discrete element method (DEM), wherein a cohesionless‐frictional material under moving surface loads was replicated through irregular‐shaped particles. With surface loads below the shakedown limit, both permanent deformations and residual stresses cease to accumulate and the numerical structure shakes down after a number of load passes. Corresponding micro‐mechanical analyses indicate that strong forces and normal forces make a dominant contribution to residual stresses. Besides, averaged magnitudes of interparticle forces and corresponding total contact numbers initially change with load passes, and their final variation trends will differ as the structure shakes down or not. Furthermore, polar distributions of interparticle forces and contacts have been presented, and variations of their preferential orientations were emphasised. Lastly, the fabric tensor and anisotropy of resultant forces were studied, presenting the anisotropy weakening of macro‐stress fields, induced by developments of residual stresses.

Exploring the influence of fabric anisotropy on the active failure of shield tunnel through DEM

Exploring the influence of fabric anisotropy on the active failure of shield tunnel through DEM

Exploring the Effects of Initial Fabric Anisotropy due to Preshearing Stress History in Different Directions on the Undrained Behavior of Loose Sands

Exploring the Effects of Initial Fabric Anisotropy due to Preshearing Stress History in Different Directions on the Undrained Behavior of Loose Sands

Hypoplastic constitutive model of inherently anisotropic sand

The modeling of anisotropic sand has always been a challenging and prominent issue in geotechnical constitutive research. This paper presents a hypoplastic constitutive model for inherently anisotropic sand. An anisotropic state variable A, which is defined by the joint invariants of the stress and fabric tensor, is introduced to account for the fabric anisotropy. This form of A can be referred to as a re-arrangement that allows for easier calibration. And this modification leads to the anisotropic contraction of the failure surface. The softening parameter in the critical state line is revised from a fixed to a state-dependent type, for achieving unified simulations of monotonic sand mechanical behaviour under different drainage conditions and within a wide range of stress levels and densities. Simulations of various monotonic element tests show that the salient features of inherently anisotropic sand, including barotropy, pyknotropy, strain softening, and dilatancy, can be well captured. Particularly, we make the first attempt to simulate pure stress-controlled true triaxial tests using hypoplastic constitutive under both drained and undrained conditions. Moreover, we provide a method to further optimize the flow direction by introducing an exponential formula.

Instability of binary mixtures subjected to constant shear drained stress path: Insight from macro and micro perspective

AbstractLoose granular materials may also exhibit instability behaviors similar to liquefaction under drained conditions, commonly referred to as diffuse instability, which can be studied through constant shear drained (CSD) tests. So far, the research on CSD in binary mixtures is still insufficient. Therefore, a series of numerical tests using the discrete element method (DEM) were conducted on binary mixtures under CSD path. The possible model of instability is categorized into type I and type II, type I instability occurs prior to reaching the critical state line (CSL), whereas type II instability occurs after exceeding the CSL. The study analyzes the macroscopic instability behavior and the impact of fine content (FC) on macroscopic instability behavior. The numerical results show that as FC increases, the slope of the instability line (IL) increases initially and then falls in the p‐q plane. In the e‐p plane, the IL decreases initially and then ascends. The instability type of the binary mixtures is influenced not only by relative density but also by FC. The stability index increased first and then decreased with the increase of FC. The microscopic origin of binary mixtures instability is explored by investigating the fabric‐stress relationship. The collapse of the weak contact sub‐network triggers the specimen instability, while the strong contact sub‐network dictates the difficulty of achieving instability. FC influences the evolution of fabric anisotropy of the strong and weak contact networks, thereby controlling the macroscopic instability behavior of binary mixtures.

Confinement effect of geocell on the mechanical characteristics of reinforced sand subgrade

Geocell has a confinement effect, limiting the deformation of soil and enhancing the strength of reinforced soil, and has a wide range of application prospects in traffic transportation subgrade engineering. To investigate the confinement effect of geocell on the mechanical characteristics of reinforced sand subgrade, this paper analyzes the macro-mechanical properties of reinforced sand subgrade using triaxial tests, investigates the micro-reinforcement mechanism employing discrete element method (DEM)-based simulations. The potential macro–micro linkages are studied. The experimental results revealed that the volumetric strain of the geocell-reinforced samples increased with the material’s elastic modulus, exhibiting a shear shrinkage phenomenon. The deformation pattern of the reinforced samples presented “segmental deformation,” which differed from that of the unreinforced sand samples. The geocell enhanced the cohesion intercept of the sand samples while having a minimal impact on friction angle. Through the analysis of numerical simulation results, it was found that the geocell constrained the displacement of the soil particles, altering the shear band development trend of the sample and resulting in “segmental deformation”. The geocell facilitated the concentration of force chains, enhancing their stability and resulting in improving the strength in the macro. Additionally, it was observed that the confinement effect of the geocell significantly reduced the fabric and force anisotropy of the granular soil, promoting consistent vertical alignment of force chains. This, in turn, enhanced the vertical force transmission capacity of the sample, explaining the micro-mechanism by which the confinement effect of the geocell increases the peak shear strength of the samples.

Effects of fabric anisotropy on the small-strain shear modulus of granular materials

Effects of fabric anisotropy on the small-strain shear modulus of granular materials

Strength and fabric anisotropy of granular materials under true triaxial configurations using DEM

This paper investigates the strength and fabric anisotropy of granular materials under true triaxial configurations using the discrete element method. A clump logic based on the multi-sphere approach was utilized to replicate realistic particle shapes. The evolutions of deviatoric stress and volumetric strains were found to be independent of mean effective stress, and intermediate principal stress parameter (b). From a macroscopic viewpoint, all samples exhibited initial strain hardening followed by softening behaviour, stabilizing at large deviatoric strains due to the dense state of assemblies. The peak state friction angles showed dependency on the b-value, aligning closely with experimental findings. Microscopic parameters such as mechanical coordination number and sliding fraction were found to be approximately independent of b-values. Additionally, non-coaxiality was observed for various b-values except for specific shear modes, aligning with previous findings using spherical particles. These results highlight the capability of clumped particles to simulate the true mechanical behaviour of granular materials and contribute to our understanding of their complex response under different loading conditions.

Modeling of the Particle Abrasion Process and a Discrete Element Method Study of Its Shape Effect.

This study introduces a novel method for particle abrasion derived from fundamental natural phenomena and mechanical principles, allowing precise control over the degree of abrasion and more accurately mimicking natural processes. The method's validity is confirmed using a specific shape index. Through conventional triaxial tests, the mechanical behavior of granular aggregates with varying degrees of abrasion was analyzed. The findings indicate that increased particle abrasion leads to a decrease in the average coordination number and sliding amount, while the rotation amount increases. This suggests an inverse relationship between the degree of abrasion and the structural stability and interlocking of the particle aggregate. The fabric anisotropy of the system is mainly attributed to the anisotropy of the contact normal force, which decreases as particle abrasion increases. The partial stress ratio of the particle system is influenced by fabric anisotropy and remains independent of particle shape. Additionally, the internal friction angle may be overestimated in conventional triaxial tests.

Unravelling the mechanics of knitted fabrics through hierarchical geometric representation

Knitting interloops one-dimensional yarns into three-dimensional fabrics that exhibit behaviour beyond their constitutive materials. How extensibility and anisotropy emerge from the hierarchical organization of yarns into knitted fabrics has long been unresolved. We seek to unravel the mechanical roles of tensile mechanics, assembly and dynamics arising from the yarn level on fabric nonlinearity by developing a yarn-based dynamical model. This physically validated model captures the mechanical response of knitted fabrics, analogous to flexible metamaterials and biological fibre networks due to geometric nonlinearity within such hierarchical systems. Fabric anisotropy originates from observed yarn–yarn rearrangements during alignment dynamics and is topology-dependent. This yarn-based model also provides a design space of knitted fabrics to embed functionalities by varying geometric configuration and material property in instructed procedures compatible to machine manufacturing. Our hierarchical approach to build up a knitted fabric computationally modernizes an ancient craft and represents a first step towards mechanical programmability of knitted fabrics in wide engineering applications.

Examining the adaptive elastic anisotropy of granular materials

Changes of granular material anisotropy with stress are a function of numerous microscale attributes, such as contact network, particle size uniformity and shape. Such influences are often represented with fabric variables. Although multiple choices for fabric exist, the question of which variable best explains why and how granular materials adapt to stress is still open. In this study, the effectiveness of different fabric variables in tracking stress-induced anisotropy is compared. The analysis is restricted to a simple, yet fundamental, range of behavioir: elastic deformation. Both particle-scale simulations and continuum analyses are deployed. Analyses based on the discrete-element method (DEM) reveal that, depending on the contact behaviour, anisotropy may emerge even if the topology of the grain contact network is unchanged. The inspection of these results through a continuum-scale hyperelastic constitutive law further reveals that the computed trends cannot be captured without an evolving fabric variable. A comparison between such fabric and multiple microstructural indicators extracted from DEM simulations suggests that elastic stress-induced anisotropy is primarily a manifestation of changes in the anisotropic particle contact area distribution in response to the current magnitude and orientation of force chains. These results not only offer opportunities to enhance current continuum elastic models for granular materials, but can also be used to design testing strategies quantifying changes in fabric anisotropy through multi-scale measurements.

Patchwork structure of continental lithosphere captured in 3D body wave images of its anisotropic fabrics

This paper presents an overview of research conducted for more than five decades around Vladislav Babuška and collaborators on large-scale seismic anisotropy in tectonically different regions of continental lithosphere in Europe. A wide range of independent data sets and methods are covered. It also briefly touches laboratory measurements of velocity anisotropy on rock samples from the crust and the upper mantle, and emphasizes the importance of considering anisotropy in studies of the Earth structure. The anisotropy is responsible for even larger velocity variations than those due to composition of the most abundant upper mantle rocks (peridotites). The large-scale in-situ measurements of the upper mantle anisotropy capture fabrics of the mantle lithosphere, and enables mapping lateral changes in its structure. The joint inversion/interpretation of the teleseismic body-wave anisotropic parameters, such as variations of directional terms of relative travel time residuals of P waves, shear-wave splitting or the coupled anisotropic-isotropic teleseismic P-wave tomography, image the continental lithosphere as a mosaic of anisotropic domains. Each of the domains has its own thickness and fossil fabric characterized by tilted symmetry axes. We map boundaries of the domains in dependence on the fabric changes. The boundaries can be either narrow and steep or broader and inclined, with an offset relative to boundaries of the related crustal bocks, which can reach several tens of kilometres. This overview presents the European lithosphere-asthenosphere boundary (LAB) and shows examples of anisotropic fabrics of the mantle lithosphere domains and their boundaries in different parts of the European plate.

Analyzing the mechanical behavior of granular materials: A multi-morphological approach using spherical harmonics and LS-DEM

This paper investigates the micro-to-macro response of granular materials influenced by multi-scale morphological characteristics using spherical harmonics and LS-DEM. Our simulation results reveal that particle elongation plays the primary role in governing the shear strength and dilatancy, with surface roughness also affecting these macroscopic behaviors of non-elongated assemblies while marginally influencing elongated assemblies. At the microscale, more elongated particles with a higher degree of roughness present a stronger interlocking effect. Furthermore, we quantitatively establish a connection with the system stress ratio through the stress-fabric-force (SFF) relationship, enabling us to comprehend the shape-dependent macroscopic shear strength from microscopic anisotropy perspectives. Our results indicate that more elongated and rougher particles lead to a more significant fabric anisotropy at the critical state. Additionally, a mechanics-based shape parameter, known as rotational resistance angle, is found to correlate linearly with the critical shear strength of all explored assemblies, which can be explained by the microscopic linkage between all partitioned anisotropy components and the adopted shape parameter.

Maximum shear modulus anisotropy of rooted soils

The maximum shear modulus (G0(ij)) of rooted soils is crucial for assessing the deformation and liquefaction potential of vegetated infrastructures under seismic loading conditions. However, no data or theory is available to account for the anisotropy of G0(ij) of rooted soils. This study presents a new model that can predict G0(ij) anisotropy of rooted soils by incorporating the projection of the stress tensor on two independent tensors that describe soil fabric and root network. Bender element tests were conducted on bare and vegetated specimens under isotropic and anisotropic loading conditions. The presence of roots in the soil increased G0(VH) at all confining pressures (p′), as well as G0(HH) and G0(HV) at low p′. However, the trend was reversed at higher p′ because the roots reduced the effects of confinement on G0(ij) by replacing stronger soil–soil interfaces with weaker soil–root interfaces. Roots made the soil fabric and G0(ij) more anisotropic. The proposed model can effectively predict the observed anisotropy of G0(ij) under isotropic and anisotropic loading conditions. The new model also offers a new method for determining the fabric anisotropy of sand based on the anisotropy of shear modulus.