Fabric evolution of granular assembly under K0 loading/unloading

This study attempted to investigate the fabric evolution in K₀ loading/unloading. The work made use of a field simulator to control K₀ loading/unloading in large specimens prepared by air‐pluviation. In each loading stage, wave velocities along various propagation directions were measured. On the basis of the theories of micro‐mechanics and wave propagation, the microscopic parameters of the granular assembly were back calculated to investigate the fabric evolution of granular soil during K₀ loading/unloading. In this study, the Geometric fabric was modelled by fabric tensors of ranks 2 and 4. The comparison of calibrated results using ranks 2 and 4 revealed the advantage of the usage of rank‐4 fabric tensor in modelling fabric evolution in spite of its complexity. By comparing relative magnitudes of vertical and horizontal components of geometric fabric, it was demonstrated that relative constraint in lateral directions increased during K₀‐unloading in order to maintain a K₀ condition. It revealed that fabric evolution was responsible for a higher K₀ in unloading than K₀ in loading. Copyright © 2003 John Wiley & Sons, Ltd.     

Constitutive modeling of inherent anisotropy in a strain space multiple mechanism model for granular materials

Consideration of fabric anisotropy is crucial to gaining an improved understanding of the behavior of granular materials. This paper presents a constitutive model to describe the sand behavior associated with fabric anisotropy within a framework of a strain space multiple mechanism model. In the proposed model, a second-order fabric tensor is extended by incorporating a new function that represents the effect of inherent (or initial fabric) anisotropy, along with three additional parameters: two of them, a₁ and a₂ , control the degree of anisotropy, and the second mode of inherent anisotropy can be expressed by introducing the parameter a₂ as well as the first mode by the parameter a₁ . The third parameter, θ₀ , expresses the principal direction of inherent anisotropy (eg, the normal vector direction of bedding planes relative to horizontal axis). The formulation of the dilative component of dilatancy (ie, positive dilatancy) is also extended to consider the effect of inherent anisotropy based on the interlocking mechanism. Experimental data on the complex anisotropic responses of Fraser River sand and Toyoura sand under monotonic loading is used to validate this model. The proposed model is shown to successfully capture anisotropic responses, which become contractive or dilative depending on different principal-stress directions, with a single set of anisotropy parameters; thus, the model is considered to possess the capability to simulate the anisotropic behaviors of granular materials. In addition to different loadings on the same fabric, the effects of different fabric anisotropies upon the sand behavior under the same loadings are also investigated.     

On statistical description of stress and fabric in granular materials

The notion of overall macroscopic stress in granular masses is examined from a fundamental point of view by a statistical consideration of the contact forces that are transmitted by the contacting granules at the microscale. This examination leads in a natural way to relations between the macroscopic stress and the resulting granular fabric. The overall stresses are expressed in terms of the contact forces in two different but complementary ways: (1) by a statistical averaging over the sample volume of contact forces and “branches” which are vectors connecting the centroids of two contacting granules; and (2) by defining the overall tractions transmitted across an interior imagined plane as the sum of the contact forces which represent the mechanical effect of granules on one side of a unit area of this plane, upon those on the other side. Conditions under which the two representations of overall stresses are equivalent, are examined in detail. In addition, explicit results are given, which, define stresses in terms of the fabric and other microstructural characteristics of the granular mass.     

Rapid estimation of maximum and minimum void ratios of granular soils

Maximum and minimum void ratios (e_max and e_min) of granular soils are commonly used as indicators of many engineering properties. However, few methods, apart from laboratory tests, are available to provide a rapid estimation of both e_max and e_min. In this study, we present a theoretical model to map the densest and the loosest packing configurations of granular soils onto the void space. A corresponding numerical procedure that can predict both e_max and e_min of granular soils with arbitrary grain size distributions is proposed. The capacity of the proposed method is evaluated by predicting the maximum and minimum void ratios of medium to fine mixed graded sands with different contents of fines. The influence of the grain size distribution, characterized quantitatively by uniformity parameter and the fractal dimension, on e_max and e_min is discussed using the proposed method. Moreover, application of this method in understanding the controlling mechanism for the void ratio change during grain crushing is presented.

     

Fabric evolution within shear bands of granular materials and its relation to critical state theory

In an effort to study the relation of fabrics to the critical states of granular aggregates, the discrete element method (DEM) is used to investigate the evolution of fabrics of virtual granular materials consisting of 2D elongated particles. Specimens with a great variety of initial fabrics in terms of void ratios, preferred particle orientations, and intensities of fabric anisotropy were fabricated and tested with direct shear and biaxial compression tests. During loading of a typical specimen, deformation naturally localizes within shear bands while the remaining of the sample stops deforming. Thus, studying the evolution of fabric requires performing continuous local fabric measurements inside these bands, a suitable task for the proposed DEM methodology. It is found that a common ultimate/critical state is eventually reached by all specimens regardless of their initial states. The ultimate/critical state is characterized by a critical void ratio e which depends on the mean stress p, while the other critical state fabric variables related to particle orientations are largely independent of p. These findings confirm the uniqueness of the critical state line in the e ? p space, and show that the critical state itself is necessarily anisotropic. Additional findings include the following: (1) shear bands are highly heterogeneous and critical states exist only in a statistical sense; (2) critical states can only be reached at very large local shear deformations, which are not always obtained by biaxial compression tests (both physical and numerical); (3) the fabric evolution processes are very complex and highly dependent on the initial fabrics. Copyright © 2010 John Wiley & Sons, Ltd.     

Elastic shear stiffness anisotropy and fabric anisotropy of natural clays

Natural clays usually show anisotropic stiffness due to their deposition process and anisotropic in situ stress state. The stiffness anisotropy depends on both of the stress anisotropy and fabric anisotropy, while the latter can be quantified by the stiffness anisotropy at isotropic stress states. This paper measures the K₀ value (i.e., stress anisotropy) and elastic shear stiffness anisotropy of natural Shanghai clay in a triaxial apparatus with horizontal and vertical bender elements. The results show that the K₀ value of Shanghai clay lies in the range of 0.40–0.66, and an empirical equation is proposed to estimate the K₀ value based on the plasticity index and initial void ratio. The fabric anisotropy of natural Shanghai clay lies in the range of 1.2–1.4 with a stronger fabric in the horizontal plane. Moreover, the experimental data of the stiffness anisotropy and fabric anisotropy of different clays in the literature are reviewed and analyzed. It reveals that the stiffness anisotropy generally increases, while the fabric anisotropy remains nearly the same during K₀ consolidation. For normally consolidated clay, the fabric anisotropy generally lies in the range of 1.1–1.7. For overconsolidated clays, the fabric anisotropy generally increases as the overconsolidation ratio increases. Empirical equations are proposed to approximately estimate the fabric anisotropy of clays based on its stress normalized elastic shear stiffness.

     

Magnetic fabrics and rock magnetism of Proterozoic dike swarm from the southern São Francisco Craton, Minas Gerais State, Brazil

Magnetic fabric and rock magnetism studies were performed on 32 mafic dikes of a Proterozoic dike swarm from the southern São Francisco Craton (SFC; Minas Gerais State, SE Brazil). Magnetic anisotropies were determined by applying anisotropy of low-field magnetic susceptibility (AMS) and anisotropy of remanent magnetization (ARM). The latter was performed imposing both anhysteretic (total (AAR) and partial pAAR)) and isothermal remanence magnetizations (AIRM). Partial anhysteretic remanence anisotropy was performed based on remanent coercivity spectra from a pilot specimen of each site. In most sites, AMS is dominantly carried by ferromagnetic minerals, however, in some sites, the paramagnetic contribution exceeds 70% of bulk susceptibility. Rock magnetism and thin section analysis allow classifying the dikes as non-hydrothermalized and hydrothermalized. Magnetic measurement shows that the mean magnetic susceptibility is usually lower than 5×10⁻³ (SI). Ti-poor titanomagnetites up to pure magnetite pseudo-single-domain (PSD) grain sizes carry the majority of magnetic fabrics for non-hydrothermalized dikes whereas coarse to fine grained Ti-poor titanomagnetites carry the majority of magnetic fabrics for hydrothermalized dikes.Three primary AMS fabrics are recognized which are coaxial with ARM fabric, except for two dikes, from both non-hydrothermalized and hydrothermalized dikes. Normal AMS fabric surprisingly is not dominant (31%). The parallelism between AMS, pAAR_0–30, pAAR_30–60 and pAAR_60–90 fabrics in the hydrothermalized dikes indicates that magnetic grains formed due to late-stage crystallization or to remobilization of iron oxides due to hydrothermal alteration after dike emplacement have acquired a mimetic fabric coaxial with the primary fabric given by coarse-grained early crystallized Ti-poor titanomagnetites. This fabric is interpreted as magma flow in which the analysis of K_max inclination permitted the inference that the dikes were fed by horizontal or subhorizontal fluxes (K_max<30°). Intermediate AMS fabric is the most important (41%) in the investigated swarm. It is interpreted as due to vertical compaction of a static magma column with the minimum stress along the dike strike. ARM determinations for these sites also remained intermediate except for two dikes. In one of them, AIRM fabric resulted in normal AMS fabric while for the other AAR fabric resulted in inverse AMS fabric. A combination of AMS and ARM fabrics suggest that magmatic fabric for both dikes were overprinted by some late local event, probably related to Brasiliano orogenic processes after dike emplacement. InverseInverse AMS fabric is a minority (four dikes). ARM determinations also remained inverse suggesting a primary origin for inverse AMS fabric.     

Magnetic fabrics, rock magnetism, cathodoluminescence and petrography of apparently undeformed Bambui carbonates from São Francisco Basin (Minas Gerais State, SE Brazil): An integrated study

Magnetic measurements were performed on apparently undeformed limestones and carbonate shales from 44 sites in nearly horizontal stratigraphic layers mainly from the basal units of the Neoproterozoic Bambui Group in the southern part of the São Francisco Basin. Rock magnetism, cathodoluminescence, transmitted and reflected light microscopy analyses reveal that there is a mix of ferromagnetic minerals, mainly magnetite and pyrrhotite, in most sites. In some sites, however, the ferromagnetic minerals are magnetite and hematite. Fine-grained pyrrhotite and pyrite accompany rare fine-grained graphite and probably amorphous carbon in some of stylolites, while pyrrhotite is also present as larger interstitial masses in coarse-grained domains outside, but close to the stylolites. Magnetic fabrics were determined applying both anisotropy of low-field magnetic susceptibility (AMS) and anisotropy of anhysteretic remanence magnetization (AAR). The AAR tensor was less well defined than the AMS fabric due to the low ferromagnetic mineral content. The analysis at the individual-site scale defines three AMS fabric types. The first type (two sites) shows K_min perpendicular to the bedding plane, while K_max and K_int are scattered within bedding plane itself. This fabric is usually interpreted as primary (sedimentary-compactional), typical of totally undeformed sediments. The second type shows the three well-clustered AMS axes with K_min still perpendicular to the bedding plane. This fabric is the most important since it was found in the majority of the sites. The third type (two sites) is characterized by well-clustered K_max in the bedding plane, while K_min and K_int are distributed along a girdle. The second and third fabric types are interpreted as combinations of sedimentary-compactional and tectonic contributions at the earliest, and at a slightly later stage of deformation, respectively. AMS represents the contribution of all the rock-forming minerals, while AAR isolates the contribution of remanence-bearing minerals from the matrix minerals. However, rock magnetism shown that anhysteretic remanence only reaches grains with coercivity < 100 mT because the maximum AF in the majority of the available instruments is 100 mT. Therefore, hematite and pyrrhotite probably do not contribute to AAR, which is due to the shape-preferred orientation of magnetite grains. For some sites, the AMS and AAR fabric orientations are different, mainly with respect to the lineation orientations (K_max and A_max, respectively). In general, K_max is well developed and follows the trend of the main regional thrusts, fold axes and faults generated in the first deformational phase, while A_max follows both this trend and that of structural lineaments formed during the second deformational phase. These deformation phases arose from the compression, which occurred during the evolution of the Brasília fold belt during the last stages of the Brasiliano event. The magnetic fabrics of the apparently undeformed Bambui limestones are typical of very weakly deformed sediments, in which the depositional-compaction fabric has been partly overprinted by a tectonic one, with minimum susceptibility direction remaining perpendicular to bedding. This result is in agreement with the textures given by the petrographic observations.     

Analysis of deformation fabric in an Alkaline Complex (Koraput): Implications for time relationship between emplacement,fabric development and regional tectonics

The Koraput Alkaline Complex (KAC) lies on the NE-SW trending Sileru Shear Zone (SSZ) separating the Proterozoic Eastern Ghats Province from the Archaean Indian craton. The core of the KAC is made of hornblende gabbro, which is rimmed by a band of nepheline syenite in the east and syenodiorite in the west. The timing of magmatism with respect to the SSZ is disputed. The KAC was deformed during emplacement, and a magmatic foliation related to the syn-emplacement deformation, D ₁ , is present in the gabbroic core. The dominant D ₂ -related field fabric strikes NESW and is penetrative in parts of the gabbro and marginal lithologies. E-W trending D ₃ shear zones cut across the complex. Distinct textural domains resulted from strain partitioning during deformation. Parts of the complex with magmatic textures constitute Domain-1, while D ₂ and D ₃ fabric zones comprise Domains-2 and 3 respectively. Temperatures in the KAC initially decreased following D ₁ , but increased through D ₂ and D ₃ . Anisotropy of magnetic susceptibility (AMS) studies show that the magnetic fabric generally follows S ₁ in Domain-1. While the magnetic fabric in Domain-2 is dominantly parallel to S ₂ , some of it parallels S ₁ . The latter is a relict D ₁ fabric that is recognized from AMS analysis but is obliterated in the field, which confirms that the KAC pre-dates the SSZ. The response of magnetic fabrics to temperature and implications of the study for Indo-Antarctica amalgamation are discussed.     

A critical state sand plasticity model accounting for fabric evolution

Fabric and its evolution need to be fully considered for effective modeling of the anisotropic behavior of cohesionless granular sand. In this study, a three‐dimensional anisotropic model for granular material is proposed based on the anisotropic critical state theory recently proposed by Li & Dafalias [2012], in which the role of fabric evolution is highlighted. An explicit expression for the yield function is proposed in terms of the invariants and joint invariants of the normalized deviatoric stress ratio tensor and the deviatoric fabric tensor. A void‐based fabric tensor that characterizes the average void size and its orientation of a granular assembly is employed in the model. Upon plastic loading, the material fabric is assumed to evolve continuously with its principal direction tending steadily towards the loading direction. A fabric evolution law is proposed to describe this behavior. With these considerations, a non‐coaxial flow rule is naturally obtained. The model is shown to be capable of characterizing the complex anisotropic behavior of granular materials under monotonic loading conditions and meanwhile retains a relatively simple formulation for numerical implementation. The model predictions of typical behavior of both Toyoura sand and Fraser River sand compare well with experimental data. Copyright © 2013 John Wiley & Sons, Ltd.     

Constitutive modelling of granular materials using a contact normal-based fabric tensor

This paper presents a fabric tensor-based bounding surface model accounting for anisotropic behaviour (e.g. the dependency of peak strength on loading direction and non-coaxial deformation) of granular materials. This model is developed based on a well-calibrated isotropic bounding surface model. The yield surface is modified by incorporating the back stress which is proportional to a contact normal-based fabric tensor for characterising fabric anisotropy. The evolution law of the fabric tensor, which is dependent on both rates of the stress ratio and the plastic strain, rules that the material fabric tends to align with the loading direction and evolves towards a unique critical state fabric tensor under monotonic shearing. The incorporation of the evolution law leads to a rotational hardening of the yield surface. The anisotropic critical state is assumed to be independent of the initial values of void ratio and fabric tensor. The critical state fabric tensor has the same intermediate stress ratio (i.e. b value) and principal directions as the critical state stress tensor. A non-associated flow rule in the deviatoric plane is adopted, which is able to predict the non-coaxial flow naturally. The stress–strain relation and fabric evolution of model predictions show a satisfactory agreement with DEM simulation results under monotonic shearing with different loading directions. The model is also validated by comparing with laboratory test results of Leighton Buzzard sand and Toyoura sand under various loading paths. The comparison results demonstrate encouraging applicability of the model for predicting the anisotropic behaviour of granular materials.

     

Unravelling the tectonothermal evolution of reworked Archean granulite facies metapelites using in situ geochronology: an example from the Gawler Craton,Australia

The use of in situ geochronological techniques allows for direct age constraints to be placed on fabric development and the metamorphic evolution of polydeformed and reworked terranes. The Shoal Point region of the southern Gawler Craton consists of a series of reworked granulite facies metapelitic and metaigneous units which belong to the Late Archean Sleaford Complex. Structural evidence indicates three phases of fabric development with D₁ retained within boudins, D₂ consisting of a series of upright open to isoclinal folds producing an axial planar fabric and D₃ composed of a highly planar vertical high‐strain fabric which overprints the D₂ fabric. Th–U–total Pb EPMA monazite and garnet Sm–Nd geochronology constrain the D₁ event to the c. 2450 Ma Sleaford Orogeny, whereas the D₂ and D₃ events are constrained to the 1730–1690 Ma Kimban Orogeny. P–T pseudosections constrain the metamorphic conditions for the Sleafordian Orogeny to between 4.5 and 6 kbar and between 750 and 780 °C. Subsequent Kimban‐aged reworking reached peak metamorphic conditions of 8–9 kbar at 820–850 °C during the D₂ event, followed by high‐temperature decompression to metamorphic conditions <6 kbar and 790–850 °C associated with the development of the D₃ high‐strain fabric. The P–T–t evolution of the Shoal Point rocks reflects the transpressional exhumation of lower crustal rocks during the Kimban Orogeny and the development of a regional ‘flower structure’.     

Investigation of influence of particle characteristics on the non‐coaxiality of anisotropic granular materials using DEM

As a result of deposition process and particle characteristics, granular materials can be inherently anisotropic. Many researchers have strongly suggested that the inherent anisotropy is the main reason for the deformation non‐coaxiality of granular materials. However, their relationships are not unanimous because of the limited understanding of the non‐coaxial micro‐mechanism. In this study, we investigated the influence of inherent anisotropy on the non‐coaxial angle using the discrete element method. Firstly, we developed a new discrete element method approach using rough elliptic particles and proposed a novel method to produce anisotropic specimens. Secondly, the effects of initial specimen density and particle characteristics, such as particle aspect ratio A _m, rolling resistance coefficient β , and bedding plane orientation δ , were examined by a series of biaxial tests and rotational principal axes tests. Findings from the numerical simulations are summarized as follows: (1) the peak internal friction angle ? _p and the non‐coaxial angle i both increase with the initial density, A _m and β , and they both increase initially and then decrease with δ in the range of 0–90°; (2) among the particle characteristics, the influence of A _m is the most significant; and (3) for anisotropic specimens, the non‐coaxial angle can be calculated using the double slip and rotation rate model. Then, an empirical formula was proposed based on the simulation results to depict the relationship between the non‐coaxial angle and the particle characteristics. Finally, the particle‐scale mechanism of non‐coaxiality for granular materials was discussed from the perspective of energy dissipation. Copyright © 2016 John Wiley & Sons, Ltd.     

Average properties of ellipsoidal fabrics: Implications for two- and three-dimensional methods of strain analysis

Many rocks contain ellipsoidal objects (such as pebbles or reduction zones) which display a variety of shapes and orientations. In deformed rocks such objects may be used for strain analysis by using the concept of an average ellipsoid (here called the “fabric ellipsoid”). Two fabric ellipsoids are defined which are the results of two different algebraic averaging processes. During deformation of ellipsoidal distributions, the fabric ellipsoids change as if they were themselves material ellipsoids and are therefore of fundamental importance in strain analysis.In most studies to date, such 3-D fabric ellipsoids have been obtained from 2-D average ellipses determined on section planes cut through the rock sample. Previous work has assumed that the average ellipses will approximate to section through a single fabric ellipsoid. I show here that this is not the case as sectioning introduces a systematic bias into the section ellipse data. This bias is distinct from the statistical errors (due to finite sample size and measurement errors) discussed in other work and must be considered in any method of strain analysis using section planes.     

Micromechanical inspection of incremental behaviour of crushable soils

In granular soils grain crushing reduces dilatancy and stress obliquity enhances crushability. These are well-supported specimen-scale experimental observations. In principle, those observations should reflect some peculiar micromechanism associated with crushing, but which is it? To answer that question the nature of crushing-induced particle-scale interactions is here investigated using an efficient DEM model of crushable soil. Microstructural measures such as the mechanical coordination number and fabric are examined while performing systematic stress probing on the triaxial plane. Numerical techniques such as parallel and the newly introduced sequential probing enable clear separation of the micromechanical mechanisms associated with crushing. Particle crushing is shown to reduce fabric anisotropy during incremental loading and to slow fabric change during continuous shearing. On the other hand, increased fabric anisotropy does take more particles closer to breakage. Shear-enhanced breakage appears then to be a natural consequence of shear-enhanced fabric anisotropy. The particle crushing model employed here makes crushing dependent only on particle and contact properties, without any pre-established influence of particle connectivity. That influence does not emerge, and it is shown how particle connectivity, per se, is not a good indicator of crushing likelihood.

     

Evolution of induced fabric in a strain space multiple mechanism model for granular materials

The strain space multiple mechanism model idealizes the behavior of granular materials based on a multitude of virtual simple shear mechanisms oriented in arbitrary directions. Within this modeling framework, the virtual simple shear stress is defined as a quantity that depends on the contact distribution function as well as the normal and tangential components of inter‐particle contact forces, which evolve independently during the loading process. In other terms, the virtual simple shear stress is an intermediate quantity in the upscaling process from the microscopic level (characterized by the contact distribution and inter‐particle contact forces). The stress space fabric (i.e. the orientation distribution of the virtual simple shear stress) produces macroscopic stress through the tensorial average. Thus, the stress space fabric characterizes the fundamental and higher modes of anisotropy induced in granular materials. Comparing an induced fabric associated with the biaxial shear of plane granular assemblies obtained via a simulation using Discrete Element Method to the strain space multiple mechanism model suggests that the strain space multiple mechanism model has the capability to capture the essential features in the evolution of an induced fabric in granular materials. Copyright © 2012 John Wiley & Sons, Ltd.     

Effects of soil fabric on behaviors of granular soils: Microscopic modeling

The effects of initial soil fabric on behaviors of granular soils are investigated by using Distinct Element Method (DEM) numerical simulation. Soil specimens are represented by an assembly of non-uniform sized spheres with different initial contact normal distributions. Isotropically consolidated triaxial compression loading and extension unloading in both undrained and drained conditions are simulated for vertically- and horizontally-sheared specimens. The numerical simulation results are compared qualitatively with the published experimental data and the effects of initial soil fabric on resulting soil behaviors are discussed, including the effects of specimen reconstitution methods, effects of large preshearing, and anisotropic characteristics in undrained and drained conditions. The effects of initial soil fabric and mode of shearing on the quasi-steady state line are also investigated. The numerical simulation results can systematically explain that the observed experimental behaviors of granular soils are due principally to their conditions of the initial soil fabric. This outcome provides insights into the observed phenomena in microscopic view.