Fabric Anisotropy Research Articles

Hypoplastic modeling of anisotropic sand behavior accounting for fabric evolution under monotonic and cyclic loading

A unified hypoplastic model is formulated by incorporating the anisotropic critical state theory to describe the fabric effect in sand under both monotonic and cyclic loading conditions. An evolving deviatoric fabric tensor that characterizes the internal microstructure of sand is introduced into the hypoplastic model in conjunction with the intergranular strain concept. A scalar-valued fabric anisotropic variable indicating the interplay between the fabric and the loading direction is employed to account for the impact of fabric anisotropy on both the dilatancy and shear strength of sand. The model is demonstrated to be capable of simulating the anisotropic behavior of sand, using a single set of parameters under both monotonic and cyclic loading conditions, as evidenced by the satisfactory match with experimental results from various sources. In particular, by considering the influence of fabric evolution on the dilatancy of sand, the model adequately accounts for the fabric change effect and accurately captures the deviatoric strain accumulation, cyclic mobility, and the flow liquefaction phenomenon under cyclic loading condition.

3D DEM insights into the effect of particle overall regularity on macro and micro mechanical behaviours of dense sands

Particle shape affects the mechanical properties of sands, but the underlying micro-mechanisms are not yet explored, at least partially, due to difficulties in accessing the particle scale information in the laboratory. This study aims to fill this gap through DEM by proposing a general framework for DEM simulation considering realistic particle shape and grading characteristics. Within the proposed framework, the irregular sand particle is approximated by 3D clump, and numerical triaxial drained compression tests are conducted for five granular assemblies of different overall regularity. The simulated critical state friction angles of these five assemblies are consistent with those predicted by an empirical formula proposed in the literature. The simulation results demonstrate that decreasing of overall regularity enhances the interlock effect between particles, making the assembly a higher stiffness and shear strength. Moreover, among different fabric anisotropies, the anisotropies of contact normal and normal contact force fabrics contribute to about 80% of the critical shear strength regardless of the overall regularity. With the decreasing of the overall regularity, the contribution of the anisotropy of contact normal fabric increases while that of normal contact force fabric decreases. The overall regularity mainly affects the anisotropies of contact normal and shear contact force fabrics.

Multiscale modelling and analysis of footing resting on an anisotropic sand

The influence of the inherent fabric anisotropy of sand and its evolution on the footing bearing capacity and failure mechanism has been modelled and analysed with a multiscale approach that couples the finite-element method (FEM) and the discrete-element method (DEM). In this approach, the material constitutive responses are captured by DEM simulations on representative volume elements (RVEs) assigned to the FEM Gauss points. The inherent fabric anisotropy of sand is reflected by the bedding plane angle α of the RVEs composed of elliptic particles, where α measures the average angle between the long axes of the particles and the horizontal direction. The bearing capacity is found to decrease with an increasing α and the reduction can reach as high as 25%. Asymmetric deformation has been observed in the α other than 0° or 90° cases, which is mainly attributable to the different relative principal directions between the stress and the fabric at the two sides of the domain. Further multiscale analyses reveal that the load-bearing structure of the material expressed by the contact-normal-based fabric tensor is more fragile under the footing loading at one side of the domain and in larger α cases, which offers a micromechanical explanation to the observation of the asymmetric deformation and the decreased bearing capacity with increased α.

Geometrical network of granular materials under isochoric cyclic shearing

We use three-dimensional particle dynamics simulations to investigate the microstructure evolution of granular material subjected to isochoric cyclic shearing, driving the system to a liquefaction state. The cyclically sheared assembly presents a realistic macroscopic response as observed in physical experiments. By analyzing the contact network evolution in the post-liquefaction period, we show that the onset of liquefaction state is characterized by a sudden drop of coordination number and a fragile particle connectivity network. The simulation suggests a critical coordination number for exiting the liquefaction state. Evolution of fabric anisotropy combined with coordination number implies the isotropic and anisotropic gain or loss of contacts at certain durations of a post-liquefaction loading cycle.

Contact evolution in granular materials with inherently anisotropic fabric

This paper presents the results of two triaxial compression tests performed on approximately 9×103 oblate spheroids (lentils) with different initial orientations with respect to the loading axis (approximately 30° and 60°). Typical stress-strain information is complemented with x-ray tomography scans every 1 % strain. Starting from an initial labelling of particles, a new technique is used to obtain unprecedented detail of tracking of all the particles through time. This rich dataset is analysed from the perspective of inter-particle contacts (building on previous metrological work on this subject) revealing that the mean contact orientation in both samples rotates towards the direction of σ1 at a rate depending on the initial orientation. Different trends are observed for the alignment of contact orientation, with a significant evolution observed in the sample prepared at 30° which is not as pronounced as in the other sample.

Numerical and Experimental Investigation of the Opposite Influence of Dielectric Anisotropy and Substrate Bending on Planar Radiators and Sensors.

The simultaneous influences of the substrate anisotropy and substrate bending are numerically and experimentally investigated in this paper for planar resonators on flexible textile and polymer substrates. The pure bending effect has been examined by the help of well-selected flexible isotropic substrates. The origin of the anisotropy (direction-depended dielectric constant) of the woven textile fabrics has been numerically and then experimentally verified by two authorship methods described in the paper. The effect of the anisotropy has been numerically divided from the effect of bending and for the first time it was shown that both effects have almost comparable but opposite influences on the resonance characteristics of planar resonators. After the selection of several anisotropic textile fabrics, polymers, and flexible reinforced substrates with measured anisotropy, the opposite influence of both effects, anisotropy and bending, has been experimentally demonstrated for rectangular resonators. The separated impacts of the considered effects are numerically investigated for more sophisticated resonance structures—with different types of slots, with defected grounds and in fractal resonators for the first three fractal iterations. The bending effect is stronger for the slotted structures, while the effect of anisotropy predominates in the fractal structures. Finally, useful conclusions are formulated and the needs for future research are discussed considering effects in metamaterial wearable patches and antennas.

Paleostress variation during the same regional deformation in the Eastern Dharwar Craton (southern India)

The objective of this study is to evaluate progressive variation in the state of stress at ca 2.5 Ga in Hutti region of Eastern Dharwar Craton (EDC, southern India). Paleostress analysis is performed using quartz vein orientations in metavolcanic and granitoid rocks (ca 2.5 Ga) of the region. It is established that veins in the metavolcanic rocks formed during regional D3 deformation under N–S compression that is related to N–S directed far-field stress, which is also responsible for D3 folds with E-W striking axial planes in parts of the EDC. Anisotropy of magnetic susceptibility data from the granitoids yields NNW-SSE striking fabric anisotropy that developed during regional D1/D2 deformation. Paleostress analysis using veins in the granitoids of the region yields NE-SW compression. However, the kinematics of formation of these veins is shown to be compatible with dextral simple shear along pre-existing NNW-SSE oriented fabric under N–S directed D3 compression. Therefore, it is established that veins in the metavolcanic and granitiod rocks of the study area formed under the same N–S directed D3 far-field stress, an interpretation that is further supported by the similar values of stress ratio obtained from 3D Mohr circle analysis of vein data from the two lithologies. Thus, the study demonstrates that there are pitfalls in direct evaluation of paleostress using only vein orientations and that understanding kinematics of vein emplacement is critical in paleostress analysis. Our data further reveal that the granitoids were subjected to faulting during the final stages of D3 due to which the veins are displaced. Paleostress analysis using fault-slip data from the granitoids yields NNE-SSW compression. This local variation of paleostress in granitoids is due to late-D3 brittle deformation during cratonization of the Dharwar Craton at ca 2.5 Ga.

Discrete Element Modelling of the Mechanical Behavior of Sand-Rubber Mixtures under True Triaxial Tests.

Sand–rubber mixtures (SRMs) consisting of stiff sand particles and soft rubber particles are typical binary mixture materials that possess a variety of complicated properties. The complexity of the properties of sand–rubber mixtures is increased when complex stress path is involved. This study investigates the mechanical behavior of sand–rubber mixtures under generalized loading conditions using the discrete element method. A series of numerical true triaxial shear tests were conducted on pure sand and sand–rubber mixtures. The effect of rubber content and loading path on both of the macroscopic and microscopic performances of sand–rubber mixtures was investigated, and the associated microscale mechanism was also discussed. Numerical simulations show that the relationship between the peak friction angle and the intermediate principal stress ratio is influenced by the addition of rubber particles, and a suggested explanation of this phenomenon is that the rubber particles mainly affect the inherent stability of the strong network. Particle-scale observations, including the coordinate number, the proportion of strong contacts, and the fabric anisotropy, are also presented in this study. Microscopic results confirm the explanation above, and explore the force transmission characteristics of sand–rubber mixtures under generalized loading conditions. This research can provide a reference for the constitutive model development of sand–rubber mixtures.

Critical State Soil Mechanics for Cyclic Liquefaction and Postliquefaction Behavior: DEM study

Discrete-element method (DEM) simulations of three-dimensional (3D) assemblies of ellipsoid particles were used to evaluate the critical state (CS) for both drained and undrained (constant volume) conditions. A series of conventional triaxial cyclic liquefaction tests with symmetrical cyclic deviatoric stress (σd) with initial q=0 kPa were simulated to develop a relationship between the cyclic stress ratio (CSR=σd/2σ0′) and the number of cycles required for initial liquefaction (NL), where σ0′ is the mean effective normal stress at the end of consolidation. Both cyclic mobility and instability type behaviors were observed depending on the initial void ratio (e0) and σ0′. The micromechanics quantities, i.e., the coordination number (CN), von Mises fabric (FvM), fabric anisotropy intensity (αc), and stress-strain behavior, suggested that cyclic mobility and instability may depend on the phase transformation and instability state, respectively. The cyclic resistance ratio (CRR15), i.e., CSR at NL=15, showed a unique relation with the initial state parameter (ψ0), irrespective of e0 and σ0′. Two series of postliquefaction monotonic simulations with and without reconsolidation exhibited a unique CS, which perfectly matched with the original CS line. The FvM also reached a unique, narrow range at the CS. The postliquefaction settlement during reconsolidation also showed a linear relation with ψ0.

Анизотропные алюмооксидные нанопористые мембраны.

In the present study, we report the development of a new type of anodic aluminium oxide membranes. Nanoporous alumina films have been fabricated by galvanostatic two-step anodizing technique. For the 1stgroup of samples at both stages was used water solution of oxalic acid as an electrolyte; and for the 2ndgroup at the 2ndstage was used a special multicomponent electrolyte. Using atomic force microscopy, it was found that a method of barrier layer thinning “from above” in combination with chemical removal of metal enables permeable anisotropic alumina membranes fabrication.

DEM investigations of the effects of intermediate principal stress ratio and particle breakage on the critical state behaviors of granular soils

Three dimensional discrete element (DEM) analyses were performed in Particle Flow Code (PFC3D) to study the effects of intermediate principal stress ratio and particle breakage on the critical state behaviors of granular materials. The variation of intermediate principal stress ratio is achieved by increasing intermediate and major principal stresses at different ratios. The breakage of calcareous sand particles is simulated in DEM with clumped particles using the octahedral shear stress crushing criterion. The macroscopic behaviors of crushable and uncrushable particles during shearing and at the critical state are compared. It is found that intermediate principal stress ratio and particle breakage affect the dilation and peak strength but have different effects on the critical stress ratios of the assemblies. The evolutions of micromechanical parameters such as redundancy factor, fabric and force anisotropies are examined to explain the difference between the behaviors of crushable and uncrushable assemblies under different stress paths.

J2-deformation-type soil model coupled with state-dependent dilatancy and fabric evolution: multiaxial formulation and FEM implementation

In this paper, an original J2-deformation type model coupled with state-dependent dilatancy is further extended to a multiaxial stress space. Compared with most existing models, the proposed model only requires ten parameters, which can be easily calibrated, and does not involve any abstruse concepts in elastoplasticity theory. The model is then implemented into ABAQUS through a user-defined subroutine (UMAT), and the capability of the extended model in capturing the mechanical behavior of sand is demonstrated by element tests, including conventional triaxial tests and true triaxial tests. To demonstrate the robustness of the model, two typical boundary value problems are illustrated, i.e., the biaxial compression test and the strip footing test. The model is further incorporated with anisotropic critical state theory to simulate anisotropic soil behavior. The biaxial compression test with smooth and rough boundaries is simulated with the anisotropic model. The results confirm the impact of fabric anisotropy and boundary constraints on the shear strain distributions and patterns of shear bands. The simulation results show the capability of the proposed model, which can be applied in practical analyses and geotechnical engineering designs.

The role of inter-particle friction on rheology and texture of wet granular flows.

In order to get insight into the rheology and texture of rough unsaturated granular flows, we study the effects of the inter-particle friction coefficient on the macroscopic attributes and the texture variables of steady-state shearing flow of wet granular materials by relying on three-dimensional (3D) particle dynamics simulations. The macroscopic attributes are characterized by the macroscopic friction coefficient, macroscopic cohesion, and the packing fraction. The microstructural variables are characterized by the fabric and force anisotropies, the coordination number, and the stress transmission ratio. We show that the macroscopic observables behave as a function of the inertial number as a dry case for different values of the inter-particle friction coefficient. In particular, the macroscopic friction coefficient increases and the packing fraction decreases rapidly for small values of the friction coefficient, then they almost reach plateaus for higher values of the friction coefficient. Interestingly, all the macroscopic observables nicely behave as a function of the small values of the friction coefficient. Similarly, we also observe these characteristics for the fabric and force anisotropies and the coordination number as well as the stress transmission ratio which reflects the intermediate relationship between the microstructure and the mechanical behavior of such flows.

Lithospheric mantle anisotropy from local events beneath the Sunda–Banda arc transition and its geodynamic implications

Shear wave splitting analysis to characterise lithospheric mantle anisotropy has been performed to provide better knowledge about lithospheric deformation and mantle flow beneath the Sunda–Banda arc transition, Indonesia. The tectonic setting of the study area is very complex characterised by the transition from subduction along Sunda arc to collision in Banda arc. The splitting measurements show lateral and vertical variation in the fast directions of the S-waves in this region. When the splitting results are analysed through 2D delay-time tomography and spatial averaging, systematic patterns in delay times and fast polarisation become more visible. In the subduction domain, the spatial averages of fast directions are dominated by two distinct fast polarisations: perpendicular and parallel to the plate motion for shallow and deep events, respectively. The results suggest that anisotropy in this area is not only controlled by anisotropic source related to the simple mantle flow model, but also by anisotropic fabric in the mantle deformed under influence of high stresses, high water contents and low temperatures. In addition, there might also be contribution from the anisotropic body in the upper layer. In the collision domain, spatially averaged fast directions show mostly perpendicular to the plate motion for all deep levels. For shallow level in this region, this trend is mainly governed by the lithospheric deformation process due to the continent-arc collision as also shown by delay time tomographic inversion. For deeper part of the region, the result of tomographic inversion and spatial averaging reveals a high anisotropy followed by rotational pattern of fast directions in the north of Timor. We suggest that this pattern might be related to the induced mantle flow due to lateral tearing of the slab.

Research on the yield function of sand based on thermodynamics

It is well known that stress-strain relation of sand is influenced by anisotropic fabric. In this paper, the relationship between macroscopic strain and shear strain and its pore structure is established by combining micromechanical theory and pore structure tensor. It is further confirmed that the stress-induced anisotropy and dilatancy of sand are inevitable. Based on this, with the help of thermodynamic theory, the inclined elliptic yield surface function in dissipative space is built, and there are three important lines in dissipative space for the influence of anisotropic fabric, normal consolidation line, phase transition line and peak line respectively corresponding to the three characteristic lines of real stress space: normal consolidation line, phase transition line and peak line which really reflects the mechanical properties of sand, especially dense sand.

Influence of aggregate geometry and material fabric on tensile cracking in concrete

A recently developed discrete element capability is used to understand the effect of random variations in aggregate shape and size on tensile cracking in concrete. A procedure to reconstruct the three-dimensional crack surface, and characterize its tortuosity, is proposed. The role of anisotropy in the material fabric, induced by variations in aggregate shape, is studied. Both tensile and compressive strength are seen to be affected by fabric anisotropy, but to different extents and in different ways. Post-peak behaviour in tension is linked to dispersion in the local fabric, characterized by a proposed local fabric tensor. The influence of aggregate shape on fracture process zone geometry is investigated. Overall, aggregate shape appears to be the dominant factor in determining the post-peak response. However aggregate size appears to affect the tensile strength more strongly while its influence on the fracture energy is complicated and subject to two opposing trends.

Thermal cycling effects on the structure and physical properties of granular materials

Over the past two decades, various investigations have shown that the application of thermal cycles of heating and cooling to granular materials causes permanent densification. However, prior to this study, significant associated effects of thermal cycles on the structural reorganization and physical properties of granular materials remained mostly unknown. To address these elusive aspects, this paper investigates the relationship between the microstructural changes induced by thermal cycling and their influence on the physical properties of granular materials using a multiphysical and multiscale computational approach. Microstructural changes are analyzed using coupled thermo-mechanical discrete element simulations and macroscopic physical properties are upscaled using homogenization. Multiple initial porosities and particle size distributions are investigated for a large number of thermal cycles of varying amplitude. Results demonstrate significant variations in the structure and properties of granular materials. Volumetric densification and fabric anisotropy increase monotonically with the amplitude and number of cycles. Coordination number exhibits a maximum for a critical temperature amplitude established theoretically to correspond to an optimal particle rearrangement. Mechanical stiffness and thermal conductivity increase in anisotropic fashion due to stress relaxation and fabric anisotropy and typically exhibit the most variation at the critical temperature amplitude. Intrinsic permeability to fluid flow decreases isotropically and monotonically with the amplitude and number of thermal cycles due to pore volume reduction. The critical temperature amplitude provides a limit to the thermal energy that can seemingly induce optimal and permanent structural reorganizations, as well as maximum variations of specific physical properties of granular materials.

Anisotropy of elastic wave velocity influenced by particle shape and fabric anisotropy under K0 condition

Non-cohesive granular materials exhibit fabric-induced anisotropy of small-strain stiffness. The stiffness anisotropy is often measured using dynamic wave measurements in the laboratory. It is widely accepted that elastic wave velocities are influenced by stress state, while the role of particle shape in the wave velocity anisotropy, and thus the stiffness anisotropy, has not been fully understood. The difficulty arises partially from the incomplete understanding of particle-scale responses of granular materials. Considering 1D vertical compressoin with zero lateral strains (K0 condition) analogue to in-situ ground, this contribution performs wave propagation simulations using discrete element method and explores how particle shape and packing characteristics influence the anisotropy of elastic wave velocity. Sphere clumps with various aspect ratios are used. The orientation of the particle major axis is varied systematically by inhibiting particle rotation during dry-pluviation process. The simulation results reveal that the wave velocity anisotropy is largely affected by the combined effect of the particle aspect ratio and the orientation of particle major axis. Micromechanical analyses on assemblies of sphere clumps and ellipsoids shed light on the importance of the inter-particle contact stiffness, in addition to the particle aspect ratio and fabric, to determine the wave velocity anisotropy when non-spherical particles are used.

Imaging the Tectonic Grain of the Northern Cordillera Orogen Using Transportable Array Receiver Functions

AbstractAzimuthal variations in receiver function conversions can image lithospheric structural contrasts and anisotropic fabrics that together compose tectonic grain. We apply this method to data from EarthScope Transportable Array in Alaska and additional stations across the northern Cordillera. The best-resolved quantities are the strike and depth of dipping fabric contrasts or interfaces. We find a strong geographic gradient in such anomalies, with large amplitudes extending inboard from the present-day subduction margin, the Aleutian arc, and an influence of flat-slab subduction of the Yakutat microplate north of the Denali fault. An east–west band across interior Alaska shows low-amplitude crustal anomalies. Anomaly amplitudes correlate with structural intensity (density of aligned geological elements), but are the highest in areas of strong Cenozoic deformation, raising the question of an influence of current stress state. Imaged subsurface strikes show alignment with surface structures. We see concentric strikes around arc volcanoes implying dipping magmatic structures and fabric into the middle crust. Regions with present-day weaker deformation show lower anomaly amplitudes but structurally aligned strikes, suggesting pre-Cenozoic fabrics may have been overprinted or otherwise modified. We observe general coherence of the signal across the brittle-plastic transition. Imaged crustal fabrics are aligned with major faults and shear zones, whereas intrafault blocks show imaged strikes both parallel to and at high angles to major block-bounding faults. High-angle strikes are subparallel to neotectonic deformation, seismicity, fault lineaments, and prominent metallogenic belts, possibly due to overprinting and/or co-evolution with fault-parallel fabrics. We suggest that the underlying tectonic grain in the northern Cordillera is broadly distributed rather than strongly localized. Receiver functions thus reveal key information about the nature and continuity of tectonic fabrics at depth and can provide unique insights into the deformation history and distribution of regional strain in complex orogenic belts.

Rheology and granular texture of viscoinertial simple shear flows

By means of extensive particle dynamics simulations in a three-dimensional model, we analyze the rheology and granular texture in the steady-state of the viscoinertial granular flow. The interactions between dry particles are added by the theoretical description of the capillary cohesion forces and viscous forces due to the presence of the viscous liquid bridge. We show that the rheology of such flow characterized by the apparent friction coefficient and packing fraction can be nicely described as a function of the viscoinertial number combining the particle inertia and viscous stress of the liquid bridge by keeping the constant value of the liquid-vapor surface tension. Furthermore, the flow behavior can alternatively be described by the effective viscosities (normal and shear components) as a function of the imposed volume fraction, which is in good agreement with previous numerical simulations of particles immersed in a viscous fluid and experiments in dense suspensions. Interestingly, the granular texture characterized by the fabric and force anisotropies and the bond coordination number is also well-described by this modified inertial number. Remarkably, the stress transmission ratio reflects the intermediate relationship between microstructure and mechanical behavior of wet granular flow, expressed as a function of the viscoinertial number. We also find that shearing leads to variations of the compressive and tensile interactions between neighboring particles.