Anisotropic constitutive modelling of rooted soils

The dependence of the undrained behaviour of sand on the initial stress state and the orientation of principal stresses with respect to the bedding planes is assessed under generalized loading paths using hollow cylinder torsional shear tests. The undrained tests were carried out using displacement-controlled loading to confidently capture the post-peak strain-softening response. Undrained behaviour of sands under identical initial states is shown to be dependent on the direction of principal stresses, during and prior to undrained shear, in relation to the direction of bedding planes. The minimum undrained strength of the strain-softening sand is found to be highly influenced by the initial stress state (confining stress, direction of principal stresses, and static shear), even though the friction angle mobilized at the instant of minimum strength is unique. A mere rotation of principal stresses at constant deviator stress alone can lead to a strain-softening response that may culminate in limited or unlimited flow deformation. The susceptibility of sand to liquefaction due to stress rotation increases as the direction of the major principal stress approaches the orientation of the bedding plane. The potential for flow deformation is strongly dependent on the direction of the major principal stress in relation to the bedding planes, and the steady state strength is not uniquely related to the void ratio alone.Key words: liquefaction, hollow cylinder torsion test, principal stress direction, static shear, steady state strength, minimum undrained strength.

Drained triaxial compressive and extension strengths of air-pluviated sand were evaluated by means of a conventional triaxial apparatus taking into account both strength anisotropy and the effects of sample slenderness, that is, height/width or diameter ratio (H/D). The initial values of H/D employed were 2.0, 1.0, 0.5, and 0.25. The direction of the major principal stress σ1′ was either normal to or parallel to the bedding plane. It was found that the triaxial extension strength is greatly influenced by H/D. Strengths in the following four stress conditions were compared: (1) triaxial compression where the σ1′ direction is normal to the bedding plane, (2) triaxial extension where one of two σ1′ directions is normal to the bedding plane while the other is parallel to the bedding plane, (3) triaxial compression where the σ1′ direction is parallel to the bedding plane, and (4) triaxial extension where both σ1′ directions are parallel to the bedding plane. It was found that while the relative strength is a complicated function of H/D, generally the strength is the largest for the second case, intermediate for the first and fourth cases, and the smallest for the third case. This result suggests that (φ) is not a simple function of b = (σ2′ − σ3′)/(σ1′ − σ3′), which represents the relative magnitude of σ2′ against σ1′ and σ3′, but the strength anisotropy and failure mode, especially in triaxial extension, should be taken into account in a combined manner.

Computational fluid dynamics (CFD) studies provide a valuable tool for evaluating the role of hemodynamics in vascular diseases such as cerebral aneurysms and atherosclerosis. However, such models necessarily only include isolated segments of the vasculature. In this work, we evaluate the influence of geometric approximations in vascular anatomy on hemodynamics in elastase induced saccular aneurysms in rabbits. One representative high aspect ratio (AR-height/neck width) aneurysm and one low AR aneurysm were created at the origin of the right common carotid artery in two New Zealand white rabbits. Three-dimensional (3D) reconstructions of the aneurysm and surrounding arteries were created using 3D rotational angiographic data. Five models with varying extents of neighboring vasculature were created for both the high and low AR cases. A reference model included the aneurysm sac, left common carotid artery (LCCA), aortic arch, and downstream trifurcation/quadrification. Three-dimensional, pulsatile CFD studies were performed and streamlines, wall shear stress (WSS), oscillatory shear index, and cross sectional velocity were compared between the models. The influence of the vascular domain on intra-aneurysmal hemodynamics varied between the low and high AR cases. For the high AR case, even a simple model including only the aneurysm, a small section of neighboring vasculature, and simple extensions captured the main features of the steamline and WSS distribution predicted by the reference model. However, the WSS distribution in the low AR case was more strongly influenced by the extent of vasculature. In particular, it was necessary to include the downstream quadrification and upstream LCCA to obtain good predictions of WSS. The findings in this work demonstrate the accuracy of CFD results can be compromised if insufficient neighboring vessels are included in studies of hemodynamics in elastase induced rabbit aneurysms. Consideration of aspect ratio, hemodynamic parameters of interest, and acceptable magnitude of error when selecting the vascular domain will increase reliability of the results while decreasing computational time.

Many linear island chains in the Pacific appear to consist of individual volcanic shields that lie on relatively short, curved loci sometimes of sigmoidal form. These loci, in turn, lie at an angle to the directions of propagation of the chains. Those chains that now trend just south of east (the Pratt-Welker, Hawaiian, Tuamotu, and Austral chains) consist of en echelon sets of loci with right lateral (clockwise) sense of stepwise overlap, whereas the supposed older extensions of these chains that lie nearly north-south (the Emperor and Ellice-Gilbert-Marshall chains) consist of sets of loci with left lateral (counterclockwise) sense of stepwise overlap. Rift zones of isolated volcanoes in the chains, that is, those volcanoes whose local stress fields were not influenced by the buttressing effects of near-neighbor volcanoes at the time of their formation, show the same orientation as the loci. First-motion studies of earthquakes in the Pacific lithosphere to date are few in number and give a variety of solutions with inferred directions of maximum principal compression (P) nearly horizontal and trending in both northeasterly-southwesterly and northwesterly-southeasterly directions. However, the number of such solutions is small, in some cases related to edifice effects, and interpretations relating compression and dilatation to principal stress directions in magmatic source regions are open to question. We consider it likely that the dominant orientation patterns have been due to dynamic effects related to the overall kinematic patterns of Pacific plate motions. Although a large number of different factors can influence the inherent and transmitted stresses in the lithosphere, and thereby influence the locally dominant stress field, we conclude that the effective stress orientations in the very recent past and for about the last 40–50 m.y. can be considered to have been caused by dynamic forces reflected in a right lateral rotational couple acting within the plane of the Pacific plate. These forces have induced maximum (S1) principal compressional stress directions that have had surface traces trending about northwest-southeast, relating to minimum (S3) principal stress directions that have trended northeast-southwest. Prior to 40–50 m.y. ago the dominant stress orientations in the plate were caused by a tendency for left lateral stress rotations, which induced maximum (S1) principal compressional stress directions with surface traces that trended just west of north and minimum (S3) principal stress directions that trended just north of east. These data and interpretations are independent of whether or not a change in direction of motion of the Pacific lithospheric plate took place roughly at the time represented by the bends in the island chains and are also independent of arguments as to whether melting anomalies of the Pacific are rigidly fixed or whether they are better explained in terms of thermal plumes or gravitational anchors. We conclude that the trends and age correlations of volcanic loci in the Pacific accurately track and identify the evolution of states of stress in the Pacific lithosphere with time. As more age data for linear island edifices become available, it should be possible to construct a Pacific-wide chronology of volcanism independent of but similar to that developed from magnetic reversals. Further, it appears that changes in stress directions in the plate have been episodic and that they may correlate with episodic magma generation not only in the central part of the Pacific plate but also around its margins.

Recent laboratory investigations indicate that the stress-strain-strength responses of granular soils are appreciably affected by the fabric orientation of the soil relative to the frame of principal stresses. Especially, a sand specimen exhibiting a dilative response during triaxial compression may show a contractive response during triaxial extension under otherwise identical conditions. This observation is of practical importance for applications concerning essentially undrained loading conditions, because the effective mean normal stress at failure, and consequently, the shear strength, associated with an undrained contractive path are considerably lower than those following a dilative path. This raises a question about the impact of soil anisotropy on seismic performance of retaining structures subjected to active and passive earth pressures, because the directions of principal stresses in retained soils for the two cases are very different. This note presents a set of fully coupled finite-element analyses incorporating an anisotropic sand model. The analyses reveal that the impact of fabric anisotropy could be significant when the retaining structure is under passive earth pressure conditions. © 2007 ASCE.

The flame behavior and the thermal structure of gaseous fuel jets issued from rectangular nozzles of high and low aspect ratios with co-flowing air were experimentally studied. Two rectangular nozzles with aspect ratios AR = 36 and 3.27 and with side channels for co-flowing air were examined. Flame behaviors were studied by photography techniques. Flame temperatures were measured using a fine-wire thermocouple. The AR = 36 burner exhibited three characteristic flame modes: attached flame, transitional flame, and lifted flame. The AR = 3.27 burner presented three characteristic flame modes: diffusion flame, transitional flame, and triple-layered flame. High AR jets promoted entrainment and mixing in the region around the flame base, whereas low AR jets enhanced mixing in the regions along the flame edges. At low co-flows, at Rec < 1200, the low AR burner flames were shorter, but at Rec > 1200, the high AR burner flames became shorter and wider. At Rec > 950, the high AR burner recorded higher flame temperatures, compared to the low AR burner by over 100 °C. At high fuel jet Reynolds numbers and moderate co-flow, high AR burner flames presented better combustion performances when compared to low AR jet flames. The good combustion performance of the high AR jet flames was due to enhanced entrainment and mixing, which were induced by flame lifting. However, at low Rec and high co-flow, the low AR jet flames exhibited desirable flame characteristics due to improved entrainment and turbulence at the jet interfaces.

A laboratory investigation has been carried out into the effects of initial anisotropic fabric and b = (σ2'-σ3')/(σ2'-σ3') on the strength and deformation characteristics of air-pluviated Toyoura sand. Drained tests in triaxial compression (b = 0.0), in plane strain compression (b = 0.2 ~ 0.5) and in triaxial extension (b = 1.0) were performed at different directions of principal stresses with respect to the deposition direction. The strength in triaxial extension was found to be strongly influenced by failure modes. The inherent anisotropy in strength and the effects of both the parameter b and the failure mode on strength are portrayed in the form of a three dimensional surface having the axes of ϕ, b and the angles ꞷ and ξ; ꞷ and ξ represent the deposition direction with respect to the directions of σ1', σ2'and σ3'. It was found that ϕ is rather insensitive to the change in b when the one of the planes of the maximum stress obliquity is in parallel with the bedding plane. The deformation characteristics including the stress-dilatancy relation are discussed in a similar way as for ϕ.

A sequential nonlinear multiscale method for the simulation of elastic metamaterials subject to large deformations and instabilities is proposed. For the finite strain homogenization of cubic beam lattice unit cells, a stochastic perturbation approach is applied to induce buckling. Then, three variants of anisotropic effective constitutive models built upon artificial neural networks are trained on the homogenization data and investigated: one is hyperelastic and fulfills the material symmetry conditions by construction, while the other two are hyperelastic and elastic, respectively, and approximate the material symmetry through data augmentation based on strain energy densities and stresses. Finally, macroscopic nonlinear finite element simulations are conducted and compared to fully resolved simulations of a lattice structure. The good agreement between both approaches in tension and compression scenarios shows that the sequential multiscale approach based on anisotropic constitutive models can accurately reproduce the highly nonlinear behavior of buckling-driven 3D metamaterials at lesser computational effort.

Consideration of the stress ellipsoid shows that the Principal Horizontal Stress (PHS) direction may not be a determinable or particularly significant stress direction for some kinds of faults. Principal stress magnitudes, as well as principal stress directions, can play a role in fixing the orientation of PHS. The usefulness of a method for PHS location recently proposed by Lensen is questioned on this basis and also because considerable errors may arise from its application to faults for which the PHS direction is determinable. Fault dip and the angle between a fault and the greatest principal stress direction are considered important factors given insufficient attention in Lensen's analysis. An alternative method for location of stress directions is discussed briefly.

The paper presents a study of the effects of initial fabric and shearing direction on cyclic deformation characteristics such as stress-strain response, shear modulus and damping ratio from drained static cyclic tests on medium dense Toyoura sand using hollow cylinder apparatus. The apparatus allows independent control of stress components, σz, σθ, σr and τzθ, and accurate measurement of strain components, ez, eθ, er and γzθ, over a wide range of strains from 10-3% to 10%. Three methods of sample preparation, air pluviation, water pluviation and dry rodding, were employed to produce different initial fabrics. Samples were sheared cyclically in p’-constant plane along the direction of major principal stress 0° (90°), 22.5° (–67.5°) and 45° (–45°) relative to the direction of deposition. Anisotropic behaviour was observed in stress-strain response and the secant shear moduli defined separately for each direction of major principal stress. However, the equivalent shear modulus was found to be little affected by the direction of the major principal stress. In addition, the effect of initial fabrics was not significant. The same was found for the hysteretic damping ratio.

Effect of the Principal Stress Direction on Cyclic Cumulative Deformation and Pore Pressure of Soft Clay

Characterisation of the permeability of soils is of practical importance and, for cohesionless or granular soils, it can be predicted from the void ratio and the particle size distribution (PSD). However, the effect of fabric anisotropy on the permeability is rarely discussed. Restricting consideration to granular (cohesionless) soil, this study combines a variety of numerical methods to investigate (1) how the anisotropy of the permeability evolves as the soil fabric anisotropy evolves in triaxial deformation and (2) establish a link between the anisotropy of the permeability and the fabric anisotropy. The Discrete Element Method (DEM) was employed to create linearly graded virtual samples of spheres (Cu of 1 to 2). Initially isotropic sphere packings were subjected to triaxial compression or triaxial extension up to 30% of absolute axial strain to induce an anisotropic fabric. Pore Network Models (PNMs) present a computationally efficient option for simulation of flow through the pore space. A PNM models fluid flow between pores (nodes) connected by pipes (edges) whose geometry is defined by the topology of the connected pores and the mass balance equation is solved at each pore. After demonstrating the accuracy of the PNM framework adopted here, this contribution presents data from PNM simulations that used the positions of individual particles in the sheared spherical packings as input data. The fabric and permeability anisotropies during triaxial shear deformation were compared at axial strain intervals of 1%. Detailed microscale analyses suggest that the anisotropy in the permeability can be attributed to an increase in the local conductance of fluid pipes in the direction of the major principal stress, which is related to the evolution of the pore topologies during the shear deformation.

Drives to improve gas turbines efficiency have lead to an increase in firing temperatures. This increase in exhaust temperature has a negative impact upon turbine blade life. Both engineers and material scientists have produced methods to improve turbine blade life under these conditions. Cooling holes have become commonplace and use relatively cool gas to create a lower temperature barrier around a turbine blade. These cooling holes creating internal and external surfaces; a common sight of crack initiation. Directionally-solidified (DS) turbine blades have also become commonplace. These turbine blades exhibit a transversely-isotropic grain structure that improves creep strength in a desired direction. To model a component under such conditions, anisotropic constitutive models are required. In this paper, an anisotropic tertiary creep damage constitutive model for transversely-isotropic materials is given. The influence of creep-damage on general linear elasticity (elastic damage) is described by a modified Hooke’s compliance tensor. Finite element simulations of a V-notched tensile specimen are conducted to replicate a crack initiation site. A discussion on stress triaxiality, stress redistribution, and damage distribution due to anisotropy is provided.

In this study, we focused on the principal stress value and direction in weld residual stress fields. We used specimens welded under three heat input conditions, and so the weld metal of each specimen had a different solidification structure. We evaluated the principal stress value and direction of the specimens by X-ray stress measurement. In the specimen welded under the smallest heat input condition, the weld metal showed a clear difference between the maximum principal stress and the minimum principal stress. However, in the specimen welded under the largest heat input condition, the maximum principal stress and the minimum principal stress were almost the same value. The principal stress direction changed significantly and shear stress occurred at the weld metal boundary in the specimens welded under the large heat input condition. In all specimens, the principal stress direction in the base metal changed. As conclusions, when the minimum and the maximum principal stress values were almost the same, the principal stress direction changed more noticeably. Additionally, due to the influence of the edge in the base metal, the principal stress direction changed significantly regardless of the welding condition.

The influence of stresses arising from horizontal density contrasts on the orientation and relative magnitudes of principal stresses in an otherwise uniform lithospheric stress field is investigated. A simple model is constructed, in which a local deviatoric stress due to a density anomaly, embedded within or just below the lithosphere, and a regionally constant deviatoric stress field are each approximated by biaxial tensors. The net stress field is obtained from the sum of the two. Both the relative magnitudes of principal stresses and the magnitude of the angular difference in principal stress direction of the summed tensor compared with that obtained in the absence of buoyancy forces depend on two parameters. The first is the ratio τ/τ′, where τ is a measure of the magnitude of the regional deviatoric stress and τ′ is the magnitude of the stress arising from buoyancy forces associated with the density anomaly. The second parameter is the angle between the trend of the density anomaly and the direction of maximum compressional stress that obtains in the absence of any perturbation by the local buoyancy forces. The directions of the principal axes of the total stress field are found to differ by up to 90° from those of the reference stress field. The model is applied to the Transverse Ranges, California, where the observed 23° difference in orientation of principal horizontal compressive stress compared with the principal compressive stress direction in central California constrains the predicted value of τ/τ′ to be approximately −0.4. This is consistent with an independently calculated range of τ/τ′ in which τ′ is inferred from seismological constraints on the magnitude of density variations underneath the Transverse Ranges and τ is inferred from observations of heat flow along the San Andreas fault in central California. The agreement between the two estimates of τ/τ′ supports the hypothesis that the observed differences in horizontal principal stress orientation in California can be explained by the combined influence of a local negative buoyancy force under the Transverse Ranges and a regional stress field associated with transcurrent deformation within the Pacific‐North American plate boundary zone. The observed counterclockwise angular difference in principal horizontal stress direction in the Transverse Ranges compared with central California implies that the plane of maximum right lateral shear stress is also rotated counterclockwise relative to that in central California. This supports the possibility that the “big bend” in the San Andreas fault may be a consequence of the negative buoyancy forces acting in the Transverse Ranges, and not the cause of Transverse Ranges formation, as has often been assumed.