Fabric Evolution Research Articles

A hypoplastic model for granular soils incorporating anisotropic critical state theory

SummaryIt is well known that soil is inherently anisotropic and its mechanical behavior is significantly influenced by its fabric anisotropy. Hypoplasticity is increasingly being accepted in the constitutive modeling for soils, in which many salient features, such as nonlinear stress‐strain relations, dilatancy, and critical state failure, can be described by a single tensorial equation. However, within the framework of hypoplasticity, modeling fabric anisotropy remains challenging, as the fabric and its evolution are often vaguely assumed without a sound basis. This paper presents a hypoplastic constitutive model for granular soils based on the newly developed anisotropic critical state theory, in which the conditions of fabric anisotropy are concurrently satisfied along with the traditional conditions at the critical state. A deviatoric fabric tensor is introduced into the Gudehus‐Bauer hypoplastic model, and a scalar‐valued anisotropic state variable signifying the interplay between the fabric and the stress state is used to characterize its impact on the dilatancy and strength of the soils. In addition, fabric evolution during shearing can explicitly be addressed. Modifications have also been undertaken to improve the performance of the undrained response of the model. The anisotropic hypoplastic model can simulate experimental tests for sand under various combinations of principle stress direction, intermediate principal stress (or mode of shearing), soil densities, and confining pressures, and the associated drastic effect of different principal stress orientations in reference to the material axes of anisotropy can be well captured.

3D reconstruction of fabric and metamorphic domains in a slice of continental crust involved in the Alpine subduction system: the example of Mt. Mucrone (Sesia–Lanzo Zone, Western Alps)

Geological mapping, multiscale structural analysis, and estimations of the degree of fabric evolution and of reaction progress allow the construction of a 3D quantitative model of structural and metamorphic gradients in a portion of continental crust deeply involved in the Alpine subduction system and mainly structured under eclogite-facies conditions before the continental collision. The investigated and modelled rocks outcrop in the surroundings of Mt. Mucrone, in the central Sesia–Lanzo Zone. The Geomodeller® software allowed a quantitative 3D estimation of domains characterized by homogeneous fabric evolution and metamorphic reaction progress (DFE and DRP, respectively) for two of the seven structural and metamorphic imprints detected in this area: the D2-eclogitic and D5-greenschist stages, which are the most pervasive at km scale. Such a 3D modelling clarifies mutual relationships between fabric and metamorphic gradients and indicates that: (i) DFE and DRP are closely related regardless of the rock type; (ii) the syn-deformational thermal regime can influence the degree of metamorphic transformation, if DFE remains below the 60% threshold; (iii) the phase transitions can not be properly implemented in quantitative geodynamic modelling without considering the heterogeneity of reaction progress and fabric evolution.

Integrating X-Ray Computed Tomography With Chemical Imaging to Quantify Mineral Re-crystallization From Granulite to Eclogite Metamorphism in the Western Italian Alps (Sesia-Lanzo Zone)

Metamorphic transformations and fabric evolution are the consequence of thermo-dynamic processes, lasting from thousands to millions of years. Relative mineral percentages, their grain size distribution, grain orientation, and grain boundary geometries are first-order parameters for dynamic modeling of metamorphic processes. To quantify these parameters, we propose a multidisciplinary approach integrating X-ray computed microtomography (µ-CT) with X-ray chemical mapping obtained from an Electron MicroProbe Analyzer (EMPA). We used a metapelitic granulite sample collected from the Alpine HP-LT metamorphic rocks of the Mt. Mucrone (Eclogitic Micaschists Complex, Sesia-Lanzo Zone, Western Alps, Italy). The heterogeneous Alpine deformation and metamorphism allowed the preservation of pre-Alpine structural and mineralogical features developed under granulite-facies conditions. The inferred granulitic mineral association is Grt + Bt + Sil + Pl + Qtz ± Ilm ± Kfs ± Wm. The subsequent pervasive static eclogite-facies re-equilibration occurred during the Alpine evolution. The inferred alpine mineral association is Wm + Omp ± Ky + Qtz+ Grt though local differences may occur, strongly controlled by chemistry of microdomains. X-ray µ-CT data extracted from on centimeter-sized samples have been analyzed to quantify the volumetric percentage and shape preferred orientation for each mineral phase. By combining tomographic phase separation with chemical variation and microstructures (i.e., different grain-size classes for the same phase and morphology of different pre-Alpine microdomains) the pre-Alpine mineralogical phases from the Alpine overprint have been distinguished and quantified. Moreover, the sample preserves 100% of the pre-Alpine granulite fabric, which surprisingly corresponds to less than 22% of the corresponding pre-Alpine metamorphic assemblages, while the Alpine eclogitic static assemblage corresponds to 78% though no new fabric is developed. This contribution demonstrates that the combined use of EMPA X-ray chemical mapping with the X-ray µ-CT shape analysis permits a dynamic approach to constrain the chemistry of the mineral phases linked to the development of metamorphic-related static and dynamic fabrics.

Diffuse instability of granular material under various drainage conditions: discrete element simulation and constitutive modeling

Diffuse instability is a typical failure mode of sand that occurs before the perfect plastic flow condition is attained. Whereas extensive laboratory experiments have demonstrated the macro-scale responses associated with such a failure mode, its underlying microscopic mechanism remains unclear. Therefore, no effective predictions can be made incorporating sophisticated constitutive models of sand, particularly when various drainage conditions are considered. In the present study, diffuse instability is first investigated using the discrete element method (DEM). Herein, partially drained and fully drained conditions are imposed to investigate the instability failure in proportional strain loading and constant shear drained tests, respectively. Then, both macro- and micro-scale second-order work criteria are applied to identify the occurrence of instability. Furthermore, the main features associated with the onset of diffuse instability are presented. The diffuse instability behavior of sand is observed to be closely related to its fabric evolution. Eventually, independent criteria for diffuse instability under various drainage conditions are determined considering the DEM results. In addition, a newly developed anisotropic constitutive model with a fabric evolution law is applied to simulate the mechanical behavior of sand and the instability that ensues. The model exhibits satisfactory agreement with the DEM simulation results. Overall, this study is aimed at elucidating why diffuse instability occurs prior to the plastic limit and how to predict it under various drainage conditions.

Geochemical constrains on dolomitization pathways of the Upper Jurassic carbonate rocks in the Geneva Basin (Switzerland and France)

The Kimmeridgian-Tithonian carbonate rocks of the Geneva Basin represent potential reservoirs for geothermal energy exploitation. Based on petrographic data, a previous study (Makhloufi et al. 2018) reported three different stages of dolomitization affecting these carbonate rocks, followed by dedolomitization. The present study focuses on the geochemical characterization of these stages based on O, C and Sr isotopes of dolomites and dedolomites. The oxygen isotopic values of early dolomite are depleted compared to the values of Late Jurassic marine cements. This is interpreted to reflect dolomite precipitation from an oxygen-enriched fluid, likely evaporitic. Carbon isotopic values are close to the composition of well-preserved Late Jurassic cements suggestive of abiotic precipitation. These findings are consistent with a scenario of reflux type dolomitization induced by high-frequency sea-level changes producing pulses of dolomitizing brines. Late dolomitization represents an advanced level of replacement. Isotopic data exhibits depleted oxygen composition pointing towards burial diagenesis and is interpreted as the results of shallow burial over-dolomitization. Ages provided by radiogenic strontium isotopes data are consistent with an early first stage of dolomitization followed by late burial dolomite. Dedolomitization is observed at different orders of magnitude and might results from the interaction with meteoric water initiating the dissolution of both early and late dolomites. This dedolomitization would have taken place during long-term emersion events or after the exhumation. The results presented in this work provide further understanding of the processes involved in dolomitization under the influence of high-frequency sea-level fluctuations and the evolution of dolomitic fabrics during burial.

Fabric evolution and dilatancy within anisotropic critical state theory guided and validated by DEM

Fabric, expressed by means of an evolving deviatoric fabric tensor F, plays a very important role in the anisotropic mechanical response of granular materials. The Anisotropic Critical State Theory (ACST) addresses fabric anisotropy by rendering dilatancy a function of F, in addition to other state variables. In this paper, 3D DEM is used to guide the specific grain-level definition of F, the formulation of its continuum evolution equation and its effect on anisotropic dilatancy within ACST. DEM provides stress-ratio and shear strain variations as input for ACST analytical calculations of evolving fabric tensor and dilatancy, which are then favourably compared with totally independent direct measurements of these quantities by DEM. Dilatancy is shown to be strongly affected by the contact normal-based fabric tensor Fc, whose evolution is best described by a continuum equation within ACST that includes dilatancy and a quantity related to particle orientation-based fabric tensor Fp. The aforementioned favourable comparison of the results for fabric tensor and dilatancy obtained independently by ACST and DEM, confirms the validity of the core framework of ACST irrespective of any constitutive model that addresses the deviatoric stress-strain relations.

First investigation of quartz and calcite shape fabrics in strained shales by means of X-ray tomography

We document the evolution of the 3D fabric of shale along a km-long strain gradient in the Jaca basin (Southern Pyrenees, Spain). With respect to the distance from a thrust, samples were collected in the cleavage-free domain, at the onset of the pencil-cleavage domain, within the pencil-cleavage domain and within the slaty-cleavage domain. By combining high resolution X-ray computed tomography (XCT) and energy dispersive X-ray spectroscopy (EDS), the morphology and the Shape Preferred Orientation (SPO) of thousands of quartz grains, calcite grains and pores was studied. In the least deformed samples, quartz and calcite display mean foliation parallel to bedding with comparable dispersion. In the pencil-cleavage domain, quartz foliation still follows the bedding while calcite foliation is mostly governed by cleavage. In the slaty-cleavage domain, calcite shows a much better organization, with foliation parallel to cleavage, mimicking closely the pore fabric. By contrast, the quartz shape fabric is much less defined, scattered between bedding and cleavage planes. This suggests that quartz grain act as rigid marker in the ductile matrix, while calcite grain orientation is governed by dissolution-precipitation processes.

Effect of particle flow dynamics on the fabric evolution in spherical granular assemblies filled under gravity

The evolution of contact anisotropy (or fabric) for a spherical granular assembly filled under gravity is investigated. The effect of filling positions and the particle inlet velocity on the contact anisotropy is presented. Discrete Element Method is used to generate the granular assemblies by filling the particles into a container under gravity. The contact anisotropy and the coordination number shows a strong dependence on the filling locations. However, when these assemblies with distinct initial anisotropy are subjected to uniaxial compression, their contact anisotropy approaches the same value. The initial velocity of the particles shows a significant effect on the contact anisotropy of the granular assembly. It was found that the contact anisotropy first decreases and then increases showing a zone of minimum anisotropy with increase in inlet particle velocity. Initiation of particle whirling motion was found as the reason for this zone of minima. The inlet particle velocity at which the minimum contact anisotropy is observed depends on the direction of the particle motion. The findings in this work will be useful in identifying the critical spots (with high heat or force) and in designing better granular beds with uniform distribution of fabric via filling.

Capturing transient granular rheology with extended fabric tensor relations

We present an improved continuum model for transient processes in granular simple shearing, which predicts the coupled evolution of the effective friction coefficient and fabric tensor. Specifically, the model gives the transient strength associated to the kinematics and the structure of the granular media for the quasi-static regime. The results of the continuum model were compared against molecular dynamic simulations. The comparison for the modulus and the angle of the principal directions of the fabric tensor showed a very good agreement for all the cases analyzed. The new fabric evolution model is capable of capturing the abrupt fall in the fabric modulus and in the effective friction coefficient at the beginning of reversal processes, when the network is destroyed. The model also predicts the right spin direction of the fabric angle, when the force chains move from one steady state to another, during reversal. Improvement in modeling the stress is obtained by relating the friction coefficient to the fabric and the unit shear rate tensors.

Observations on fabric evolution to a common micromechanical state at the soil‐structure interface

SummaryThe fabric plays an important role in the mechanical behavior of granular material. The aim of this paper is to investigate the evolution of fabric in a soil‐structure interface (SSI) to a large shearing in an effort to clarify whether and how this form of fabric evolution can lead to a common microstructure. Using the discrete element method (DEM), two‐dimensional (2D) numerical interface shear tests were carried out, and certain macromechanical and micromechanical properties were exploited. All samples exhibited prominently localized strain in a zone covering the structure's surface (named the localized zone), and much lower density and higher soil fabric anisotropy levels were found inside this zone than outside it. Disregarding different initial void ratios, a common critical state microstructure was observed in large shear deformations of soil samples, with essentially the same fabric arrangement in terms of contact orientation and internal force transmission. Due to the systematic forming, buckling, and collapsing of force chains, an angular zone (called an α‐zone), in which contact density was sluggish to varying degrees, appeared and extended around the main direction of the distribution of contact orientation inside the localized zone. The gradual deterioration of the force chains' stability, as a result of an increasing void ratio, seemed to drive the α‐zone's extension and lead to the rare variation of microstructures in the critical state.

Discrete element modelling of flexible membrane boundaries for triaxial tests

The discrete element modelling of triaxial tests plays a critical role in unveiling fundamental properties of particulate materials, but the numerical implementation of a flexible membrane boundary for the testing still imposes problems. In this study, a robust algorithm was proposed to reproduce a flexible membrane boundary in triaxial testing. The equivalence of strain energy enables the particle-scale parameters representing the flexible membrane to be directly determined from the real geometric and material parameters of the membrane. Then the proposed flexible membrane boundary was implemented in the context of discrete element simulation of triaxial testing and was validated with laboratory experiments. Furthermore, comparisons of triaxial tests with flexible and rigid boundaries were performed from macro-scale to meso-scale. The results show that the boundary condition has limited influences on the stress-strain behaviour but a relatively large impact on the volumetric change, the failure mode, the distribution of contact forces, and the fabric evolution of particles in the specimen during triaxial testing.

Investigation of the fabric evolution and the stress-transmission behaviour of sands based on X-ray μCT images

This paper presents the use of X-ray micro-tomography (X-ray μCT) and image processing and analysis techniques to investigate the stress transmission and buckling of inter-particle contacts within a granular material. A triaxial testing of a miniature Leighton Buzzard sand (LBS) sample was carried out with full-field in-situ X-ray μCT scanning. High-spatial-resolution CT images of the sample were acquired at several loading stages of the test. Image processing and analysis techniques were used to quantify the inter-particle contact evolution (contact gain, contact loss and contact movement), fabric, contact duration and buckling of stress-transmission contacts based on the CT images. The results indicated that contact gain and loss, and contact movement played two competing roles in determining the overall fabric evolution of the sample. Contacts with a longer duration were more likely to orient in the major principal stress direction and form a stress-transmission contact network. A gradual decrease in the buckling rate of the stress-transmission contacts was observed outside of the shear band, and a relatively stable buckling rate was observed within the shear band during the shear. The results suggested that jamming occurred outside of the shear band and that unjamming occurred within the shear band.

Necessary and sufficient conditions for reaching and maintaining critical state

SummaryAccording to classical critical state theory (CST) of granular mechanics, two analytical conditions on the ratio of stress invariants and the void ratio are postulated to be necessary and sufficient for reaching and maintaining critical state (CS). The present work investigates the sufficiency of these two conditions based on the results of a virtual three‐dimensional discrete element method experiment, which imposes continuous rotation of the principal axes of stress with fixed stress principal values at CS. Even though the fixity of the stress principal values satisfies the two analytical CST conditions at the initiation of rotation, contraction and abandonment of CS occur, which proves that these conditions may be necessary but are not sufficient to maintain CS. But if fixity of stress and strain rate directions in regard to the sample is considered at CS, the two analytical conditions of CST remain both necessary and sufficient. The recently proposed anisotropic critical state theory (ACST) turned this qualitative requirement of fixity into an analytical condition related to the CS value of a fabric anisotropy variable A defined in terms of an evolving fabric tensor and the plastic strain rate direction, thus, enhancing the two CST conditions by a third. In this way, the three analytical conditions of ACST become both necessary and sufficient for reaching and maintaining CS. In addition, the use of A explains the observed results by relating the stress‐strain response, in particular the dilatancy, to the evolution of fabric by means of the relevant equations of ACST.

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.

The Origin and Evolution of Magnetic Fabrics in Mafic Sills

Studying extinct volcanoes where erosion has exposed dykes and sills provides direct access to the fossil remnants of magma movement, however linking crystallised magma to emplacement dynamics is challenging. This study investigates how magma flow varies across the thickness of a thin (6 metres thick) mafic sill. We use a high-resolution sampling regime to measure micro-scale variations in magnetic anisotropy, which is associated with the orientation of the magnetic particles present within the crystalline rock. Fieldwork was conducted on exposed sills of the British and Irish Palaeogene Igneous Province, Isle of Skye, Scotland. Here Jurassic sedimentary rocks have been intruded by a series of sills, of picrite to crinanite composition, from the Little Minch Sill Complex (c.60 Ma). Anisotropy of magnetic susceptibility (AMS) and anisotropy of anhysteretic remanent magnetisation (AARM) signals have been used to separate a crinanite sill into distinct magnetic groupings. We identified two AMS groups (the upper and lower sill margins, and the central region) and four AARM groups (the lower margin, the middle region, a region just below the upper margin, and the upper margin). Both AMS and AARM signals originate from titanomagnetite of multi-domain or vortex-state to single-domain sized grains, respectively. The AMS and AARM fabrics are aligned with each other in the margin regions preserving a history of magma flow towards the North during initial emplacement. However, in the sill interior the magnetic fabrics are oblique to each other, thus reflecting multiple origins. We suggest the AMS fabrics have recorded magma flow during sill growth, and AARM fabrics have recorded melt percolation flow as the interstitial melt migrated upwards through a solidifying crystal mush. We demonstrate that when AMS and AARM are used in combination they enable a detailed understanding of magma flow and solidification dynamics to be obtained, from initial emplacement to solidification. Overall, our detailed sampling and analysis indicates that magnetic fabrics can be highly variable over small distances, supporting the suggestion of horizontal flow restriction and propagation path migration within growing sills, and that previous reports of magma flow and solidification dynamics based on under-sampled bodies may require reconsideration.

Anisotropic Strength of Granular Material Considering Fabric Evolution

Abstract The effect of fabric anisotropy on strength has not been considered in most strength criterions for granular material. Some criterions can describe the variation of material strength with stress-induced anisotropy, but micro-mechanism and physical meanings are undefined. Some criterions consider the effect of fabric anisotropy, but the evolution of fabric is ignored during loading by assuming a constant fabric tensor. Based on strength mechanical characteristics of granular material, in this paper, the relationship between macro stress and micro contact force of granular material is derived by micromechanics. Then, the concept of true stress tensor is proposed. An anisotropic strength criterion of granular material considering fabric evolution is established and its applicability is validated by comparing with test results for different granular materials. The analysis results indicate that the proposed anisotropic criterion can be utilized to describe the strength feature of anisotropic granular materials, which gives a way for the cause analysis of the strength of granular materials from the perspective of Microscopic mechanism.

Genetic variants implicated in the pathogenesis of delusional disorder: A systematic review of evidence-to-date

In this paper, the effects of the intermediate stress ratio, i.e., b-value (b = (σ2 − σ3)/(σ1 − σ3)), on the contact normal-based fabric evolution of granular material, are incorporated into an extant hybrid fabric evolution law. The new evolution law is validated by Discrete Element Method (DEM) simulation results under monotonic shearing with different b-values. Predictions of the proposed generalized fabric evolution law agree well with the DEM simulation results. This evolution law can be widely used for constitutive modelling of granular materials, considering the effects of b-value in a general geomechanical three-dimensional stress space.

Investigation of fabric evolution using bidirectional shear wave velocity measurements

In order to characterise fabric evolution, continuous bidirectional shear wave velocity measurements are performed in vertical and horizontal directions (V&H) on triaxial soil specimens during shearing in which two horizontal piezo-electrics were mounted on samples using a new measurement technique. The specimens are prepared by wet tamping method and then subjected to strain-controlled compressional shearing under drained and undrained conditions. The shear wave velocities of all drained specimens initially increased as the loading commenced and then converged to a unique state in both horizontal and vertical directions. The shear wave velocity of undrained specimens on the other hand, for both horizontal and vertical directions initially decreased due to the rising of the excess pore water pressure and then gradually approached a unique shear wave velocity like drained specimens. The fabric condition or stiffness in V&H directions of all the examined drained and undrained specimens at critical state are found to be unique.

Measuring the fabric evolution of particulate media during load reversals in triaxial tests

The behaviour of granular materials upon load reversal is not yet fully understood. In order to experimentally reveal the microstructure of a specimen subjected to load-unload cycles, a triaxial compression test on lentils is carried out in the x-ray scanner. Before analysing the acquired tomographies, a benchmark analysis is conducted to validate the image analysis tools that are used to extract the fabric from these images. The contact fabric evolves strongly with the shearing in the experiment on lentils. However, only very slight changes of the anisotropy within the cycles are observed.

The influence of particle-size distribution on critical state behavior of spherical and non-spherical particle assemblies

This paper presents an investigation into the effects of particle-size distribution on the critical state behavior of granular materials using discrete element method (DEM) simulations on both spherical and non-spherical particle assemblies. A series of triaxial test DEM simulations examine the influence of particle-size distribution (PSD) and particle shape, which were independently assessed in the analyses presented. Samples were composed of particles with varying shapes characterized by overall regularity (OR) and different PSDs. The samples were subjected to the axial compression through different loading schemes: constant volume, constant mean effective stress, and constant lateral stress. All samples were sheared to large strains to ensure that a critical state was reached. Both the macroscopic and microscopic behaviors in these tests are discussed here within the framework of the anisotropic critical state theory. It is shown that both OR and PSD may affect the response of the granular assemblies in terms of the stress–strain relations, dilatancy, and critical state behaviors. For a given PSD, both the shear strength and fabric norm decrease with an increase in OR. The critical state angle of shearing resistance is highly dependent on particle shape. In terms of PSD, uniformly distributed assemblies mobilize higher shear strength and experience more dilative responses than specimens with a greater variation of particle sizes. The position of the critical state line in the e–p′ space is also affected by PSD. However, the effects of PSD on critical strength and evolution of fabric are negligible. These findings highlight the importance of particle shape and PSD that should be included in the development of constitutive models for granular materials.