Anisotropic Elastoplastic Bounding Surface Model for Cohesive Soils

The initial stresses existing in the natural ground are anisotropic in the sense that the vertical stress is typically larger than the lateral stresses. The construction activities, such as embankments and excavation, induce anisotropy in the stress system. The stress-deformation behavior and excess pore water pressure response of soils are affected by the inherent and induced stress anisotropy. This paper presents an improved soil model based on the anisotropic critical state theory and bounding surface plasticity. The anisotropic critical state theory of Dafalias was extended into three-dimensional stress space. In addition to the isotropic hardening rule, rotational and distortional hardening rules were incorporated into the bounding surface formulation with an associated flow rule. The projection center that is used to map the actual stress point to the imaginary stress point was specified along the K0 line instead of the hydrostatic line or at the origin of the stress space. A simplified form of plastic modulus was used and the proposed model requires a total of 12 material parameters, the same number as that of the single-ellipse time-independent version of the Kaliakin–Dafalias model. The model was validated against the undrained isotropic and anisotropic triaxial test results under compression and extension shearing modes for Kaolin Clay, San Francisco Bay Mud, and Boston Blue Clay. The effects of stress anisotropy and overconsolidation were well captured by the model. The time effect was not included in the formulations presented in this paper.     

Stress-Induced Anisotropic Gma x of Sands and Its Measurement

Anisotropy in elastic shear modulus Gma x exists in most soils as the result of either anisotropic soil fabric or anisotropic stress conditions. This paper presents a theoretical and experimental study on the anisotropy in a Gma x of sand due to a K0 stress condition. Elastic shear moduli of two types of sand in multiple stress planes under a K0 condition were measured using bender elements. Stress-induced anisotropy in Gma x of the sands during loading and unloading processes and the important influential factors were investigated. An empirical relationship for the estimation of K0 was proposed based on the experimental data. Shear moduli in nonprincipal stress planes were measured and compared with the results from the theory. The influence of stress cycles on Gma x in multiple stress planes was studied.     

Elastic Anisotropic Viscoplastic Modeling of the Strain-Rate-Dependent Stress–Strain Behavior of K0-Consolidated Natural Marine Clays in Triaxial Shear Tests

This paper presents a new three-dimensional (3D) anisotropic elastic viscoplastic (EVP) model for the time-dependent stress–strain behavior of K0-consolidated marine clays. A nonlinear creep function with a limit for the creep volumetric strain under an isotropic or odometer K0-consolidated stressing condition and a nonsymmetrical elliptical loading locus are incorporated in the 3D anisotropic EVP model. An α-line defines the inclination of the nonsymmetrical elliptical loading locus in the p′-q plane and is commonly used for natural soils. All model parameters are determined from the results of one set of consolidated undrained compression tests and an isotropic consolidation/creep test. With the parameters determined, the 3D anisotropic EVP model is used to simulate the behavior of K0-consolidation tests and the strain-rate-dependent stress–strain behaviors of the K0-consolidated triaxial compression and extension tests on natural Hong Kong marine deposit clay specimens. These triaxial K0-consolidated specimens were sheared at step-changed axial strain rates from +2?to?+0.2, +20, ?2 (unloading) and +2%/h (reloading) for compression tests; or from ?2?to??0.2, ?20, +2 (unloading), and ?2%/h (reloading) for extension tests, all in an undrained condition. The simulation results of all these tests are compared with the test results. The validation and limitations of the model are then evaluated and discussed.     

Acoustic Measurements of the Anisotropy of Dynamic Elastic and Poromechanics Moduli under Three Stress/Strain Pathways

A series of triaxial compression experiments have been conducted to investigate the effects of induced stress on the anisotropy developed in dynamic elastic and poroelastic parameters in rocks. The measurements were accomplished by utilizing an array of piezoelectric compressional and shear wave sensors mounted around a cylindrical sample of porous Berea sandstone. Three different types of applied states of stress were investigated using hydrostatic, triaxial, and uniaxial strain experiments. During the hydrostatic experiment, where an isotropic state of stress was applied to an isotropic porous rock, the vertical and horizontal acoustic velocities and dynamic elastic moduli increased as pressure was applied and no evidence of stress induced anisotropy was visible. The poroelastic moduli (Biot’s effective stress parameter, α) decreased during the test but also with no evidence of anisotropy. The triaxial compression test involved an axisymmetric application of stress with an axial stress greater than the two constant equal lateral stresses. During this test a marked anisotropy developed in the acoustic velocities, and in the dynamic elastic and poroelastic moduli. As axial stress increased the magnitude of the anisotropy increased as well. The uniaxial strain test involved axisymmetric application of stresses with increasing axial and lateral stresses but while maintaining a zero lateral strain condition. The uniaxial strain test exhibited a quite different behavior from either the triaxial or hydrostatic tests. As both the axial and lateral stresses were increased, an anisotropy developed early in the loading phase but then was effectively “locked in” with little or no change in the magnitude of the values of the acoustic velocities, or the dynamic elastic and poroelastic parameters as stresses were increased. These experimental results show that the application of triaxial states of stress induced significant anisotropy in the elastic and poroelastic parameters in porous rock, while under the uniaxial strain condition the poromechanics, Biot’s effective stress parameter, exhibited the largest variation among the three test conditions.     

Transformation of retained austenite in carburized 4320 steel

A systematic study of stress-induced and thermal-induced transformation of retained austenite in carburized 4320 steel with an initial retained austenite of 35 pct has been conducted. The transformation was monitored by recording the change in volume of smooth fatigue specimens. Stress-induced transformation was studied by conducting monotonic and cyclic tests at temperatures in the range from 22 °C to 150 °C. The volumetric transformation strain was as large as 0.006 at 22 °C. The anisotropy of the transformation was such that the axial transformation strain component exceeded the diametral transformation strain component by a factor of 1.4. Thermal-induced transformation was investigated with temperature stepup tests in the range from 150 °C to 255 °C at constant stress (-500 MPa, 0 MPa, and 500 MPa) and with static tests where temperature was held constant at zero load. The maximum thermal-induced volumetric transformation strain of 0.006 was independent of stress. However, the anisotropy of the transformation strain components was dependent on stress direction and magnitude. An axial tensile stress increased the axial transformation strain relative to the diametral transformation strain. The influence of low-temperature creep(T = 150 °C) on the anisotropy of strains is noted. The differences between stress-induced and thermal-induced transformation mechanisms are discussed. Thermal-induced transformation primarily occurred at temperatures between 100 °C and 200 °C, with the rate of transformation increasing with temperature, while the stress-induced transformation primarily occurred at 22 °C, with the rate of transformation decreasing with increasing temperature. There was no stress-induced transformation above 60 °C.     

Effect of Microfabric on Mechanical Behavior of Kaolin Clay Using Cubical True Triaxial Testing

Various aspects of the mechanical behavior of kaolin clay are discussed in light of experimental observations from a series of strain controlled true triaxial undrained tests performed on cubical kaolin clay specimens with flocculated and dispersed microfabric, using a fully automated flexible boundary experimental setup with real-time feedback control system. The laboratory procedures used to prepare flocculated and dispersed microfabric specimens are presented. Mercury intrusion porosimetry is used to evaluate the pore structure of these specimens. The influence of microfabric on the consolidation behavior of kaolin clay is evaluated based on the data obtained from K0 consolidation during constant rate of strain tests and the isotropic consolidation during true triaxial tests. Undrained tests on kaolin clay show that the following vary with microfabric of specimen: The shear stiffness, excess pore pressure generated during shear, and strength and strain to failure. For both microfabrics, the observed strength behavior using cubical triaxial testing shows a similar pattern of variation with applied stress anisotropy; hence, only a marginal influence of fabric-induced anisotropy.     

Poromechanics of Anisotropic Hollow Cylinders

It has been known that inherent material anisotropy influences the mechanics of geoengineering applications. Aiming at the experimental studies associated with geoengineering applications in anisotropic materials, this paper proposes a poromechanics analysis of a fully saturated transversely isotropic hollow cylinder. Closed-form analytical solutions for the pore pressure and stress fields were derived. These solutions are obtained under various loading conditions that are encountered in laboratory testing procedures. Numerical analyses were carried out to demonstrate the material anisotropy effect on stress, displacement, and pore pressure distributions in the cylinder. It is also shown that uncertainties in the estimation or measurements of the poromechanical parameters have proven effects on the time-dependent responses of the hollow cylinder geometry during laboratory testing.     

Anisotropic Nonlinear Elastic Model for Particulate Materials

This paper presents the development of an elastic model for particulate materials based on micromechanics considerations. A particulate material is considered as an assembly of particles. The stress–strain relationship for an assembly can be determined by integrating the behavior of the interparticle contacts in all orientations and using a static hypothesis which relates the average stress of the granular assembly to a mean field of particle contact forces. Hypothesizing a Hertz–Mindlin law for the particle contacts leads to an elastic nonlinear behavior of the particulate material, we were able to determine the elastic constants of the granular assembly based on the properties of the particle contacts. The numerical predictions, compared to the results obtained during experimental studies on different granular materials, show that the model is capable of taking into account both the influence of the inherent anisotropy and the influence of the stress-induced anisotropy for different stress conditions.     

Anisotropy of the critical resolved shear stress of a superalloy containing 6 vol.% L12-ordered γ′-precipitates

Single crystals of the γ′-strengthened nickel-base superalloy NIMONIC PE16 have been compression tested in the temperature range 683–1143 K. Four different orientations of the specimens have been studied: [0 0 1].[1¯23].[011] and [1¯11]. They were either in the homogenized, single-phase state or in the peak-aged state. The critical resolved shear stress (CRSS) of the homogenized specimens was isotropic at 683 K. The CRSS of the peak-aged specimens, containing 6 vol.% of L1₂-long-range ordered γ′-precipitates of 25 nm radius, was anisotropic at 683 K and at 989 K: the [001]-orientated specimens were the softest ones, the CRSS increased as the orientation moved towards [011] or [11¯1]. This is the same orientation dependence found for the CRSS of single-phase L1₂-ordered materials. The interpretation of the anisotropy of the CRSS of NIMONIC PE16 follows that given for single-phase L1₂-long-range ordered materials.     

Stress-Strain Responses of Block Samples of Compressible Chicago Glacial Clays

This paper presents the results and analysis of a laboratory investigation of the behavior of lightly overconsolidated compressible Chicago glacial clays over a wide strain range. Each specimen was trimmed from high quality block samples taken from an excavation in Evanston, Illinois. Specimens were instrumented with three sets of bender elements and local LVDTs. After K0 consolidation to the in situ vertical effective stress of the block, drained stress probe tests were conducted. Results of bender elements tests obtained prior to stress probing show that compressible Chicago glacial clay initially is cross anisotropic. Propagation velocities measured by bender elements in axial direction after K0 reconsolidation and drained creep agrees well with the in situ shear wave velocity measured by seismic cone penetration tests. Results of drained stress probe tests are analyzed in terms of shear, volumetric and coupled stiffness, stiffness degradation, and direction of loading. The significant variability of shear, bulk and cross-coupling response depending on stress path direction and strain level provide experimental evidence that the Chicago clays are incrementally nonlinear at the strain levels investigated.     

Sand Plasticity Model Accounting for Inherent Fabric Anisotropy

A sand plasticity constitutive model is presented herein, which accounts for the effect of inherent fabric anisotropy on the mechanical response. The anisotropy associated with particles’ orientation distribution, is represented by a second-order symmetric fabric tensor, and its effect is quantified via a scalar-valued anisotropic state variable, A. A is defined as the first joint isotropic invariant of the fabric tensor and a properly defined loading direction tensor, scaled by a function of a corresponding Lode angle. The hardening plastic modulus and the location of the critical state line in the void ratio?mean effective stress space, on which the dilatancy depends, are made functions of A. The incorporation of this dependence on A in a pre-existing stress-ratio driven, bounding surface plasticity constitutive model, achieves successful simulations of test results on sand for a wide variation of densities, pressures, loading manners, and directions. In particular, the drastic difference in material response observed experimentally for different directions of the principal stress axes with respect to the anisotropy axes, is well simulated by the model. The proposed definition and use of A has generic value, and can be incorporated in a large number of other constitutive models in order to account for inherent fabric anisotropy effects.     

Elastic wave velocities in various alloy strips

The zeroth order plate mode shear wave velocity has been measured in thin strip specimens of Oriented Electrical Steel, Elinvar-Extra, and RMI 464 titanium alloy as a function of the angle between the propagation direction and the rolling direction. Also, the plane wave shear and longitudinal velocities have been measured along the normal to the rolling plane. The results in the Oriented Electrical Steel agree with the known (110)[001] texture. In the Elinvar-Extra there is a texture indistinguishable elastically from (100)[Oil], or partial (100)[011] superimposed on a random background. Different annealing temperatures following cold-rolling yield different degrees of anisotropy and different dependences (1/G)(dG/dT) of the shear modulus upon ambient temperature. At an annealing temperature of about 850‡C, (1/G)(dG/dT) evaluated near room temperature changes from positive to negative, and anisotropy becomes minimum. In the RMI 464 titanium alloy, the shear velocity anisotropy was only 1 pct in the rolling plane. Formerly with Bell Telephone Laboratories, Allen town, Pa.     

Stress Path Testing of an Anisotropic Sandstone

The Berea sandstone used in this study is transversely isotropic with respect to elastic response, with P-wave velocities of 2,160?m/s normal to bedding and 2,290?m/s parallel to bedding, a variation of only 6%. Triaxial compression and extension tests involving failure by loading and unloading were performed along the two directions of symmetry. With axial stress applied parallel to bedding, the internal friction angle was approximately 55° for compression and extension, indicating no intermediate stress effect for the linear Mohr-Coulomb criterion. However, for axial stress normal to bedding, the friction angle in compression was 50°, whereas in extension it was 44°. This anomalous behavior was attributed to strength anisotropy of the sandstone.     

Complementary Wave-Based Characterizations of Sedimentation Processes

In this paper, the sedimentation behavior of two kaolinite samples with distinct fabric associations is characterized using mechanical and electromagnetic wave-based techniques. The two different fabric formations, the edge-to-face (EF) flocculated structure (i.e., Sample A) and the dispersed and deflocculated structure (i.e., Sample B), were produced by changing the pH of the pore fluid. The anisotropy of the shear-wave velocity and DC conductivity was not observed in the sediment of Sample A because of EF isotropic fabric associations, but it was detected in Sample B as a result of face-to-face aggregation. An open card-house structure of the Sample A sediment results in a higher relaxation strength of the bulk water, Δκw owing to a higher water content; the smaller Δκw measured in the Sample B sediment indicates denser packing. In both samples, sediment consolidation gives rise to a decrease in the bulk-water relaxation strength, but an increase in the bound-water relaxation strength owing to increasing particle content. During sediment consolidation, the sediment conductivity of Sample A continuously decreases because of the reduced contribution from the fluid conductivity. In Sample B, the surface conduction overcompensates such a decreased contribution so that the sediment conductivity increases with increasing particle content.     

Evaluation of Two Homogenization Techniques for Modeling the Elastic Behavior of Granular Materials

This paper discusses the capabilities of two homogenization techniques to accurately represent the elastic behavior of granular materials considered as assemblies of randomly distributed particles. The stress-strain relationship for the assembly is determined by integrating the behavior of the interparticle contacts in all orientations, using two different homogenization methods, namely the kinematic method and the static method. The numerical predictions obtained by these two homogenization techniques are compared to results obtained during experimental studies on different granular materials. Relations between elastic constants of the assembly, interparticle properties, and fabric parameters are discussed, as well as the capabilities of the models to take into account inherent and stress-induced anisotropy for different stress conditions.     

Postcyclic Recompression, Stiffness, and Consolidated Cyclic Strength of Silt

Low plasticity silts are liquefiable and the dissipation of pore pressures after an earthquake will be accompanied by densification and compression of the soil skeleton. Anisotropic rather than isotropic stress distributions are commonly found to exist in slopes or silty fills placed under K0 conditions and this can be enhanced further by the weight of overlying structures. Compression after an earthquake generally increases soil resistance but it can still be liquefied by aftershocks. The postcyclic recompression of silt, and postdrainage monotonic and cyclic strength and stiffness have therefore been investigated with respect to the effect of initial anisotropic consolidation. The compressibilities during postcyclic recompression were similar to those for isotropic consolidation. Samples with a greater initial anisotropy had less volumetric strain but larger axial strains during postcyclic drainage. Under stress reversal conditions failure occurred as a result of the development of double amplitude cyclic strains, whereas under nonreversal conditions compressive axial plastic strain was accumulated. Postdrainage second loading cyclic strength increased with increasing anisotropy. For isotropically consolidated samples failure under reversal cyclic loading resulted in a weaker soil structure even after postcyclic reconsolidation.     

Laboratory Studies of Two Common Saprolitic Soils in Hong Kong

Two commonly encountered saprolitic soils in Hong Kong, weathered volcanic tuff (WT) and weathered granite (WG), were studied using high-quality intact samples. The intact samples exhibited quasi-preconsolidation pressure or yield stress under isotropic compression due to their bonded structures, but the yield was progressive and not abrupt. As the stress increased, significant volumetric changes were measured. These changes resembled clay-type behavior. The soils also exhibited anisotropic deformation under isotropic loading and unloading, which was associated with the features of their parent rocks. During the drained tests, shearing at the in situ stress-state produced peak strength and volumetric dilation. Undrained shearing showed complicated stress paths and dilatancy behavior in these soils. Phase transformation states and dilative shear failure were readily seen, which resembles typical sand-type behavior. Distinct shear band(s) appeared in the WT specimens during shearing, whereas a bulging type of failure appeared in the WG specimens. The soils ultimately approached the corresponding state guided by a unique critical state line, regardless of their complex initial states in relation to the bonded structure and drainage conditions.     

Acid-facilitated supramolecular assembly of G-quadruplexes in d(CGG)4

Molar [K+] induces aggregate formation in d(CGG)4, as evidenced by absorbance, circular dichroic (CD), and gel measurements. The kinetics of this transformation are extremely slow at pH 8 but are found to be greatly facilitated in acidic conditions. Kinetic profiles via absorbance or CD monitoring at single wavelength resemble those of autocatalytic reacting systems with characteristic induction periods. More than 0.8 M KCl is needed to observe the onset of aggregation at 20 degrees C and pH 5.4 within the time span of 1 day. Time-dependent CD spectral characteristics indicate the formation of parallel G-tetraplexes prior to the onset of aggregation. Despite the evidence of K(+)-induced parallel G-quadruplex and higher molecular weight complex formation, both d(TGG)4 and d(CGG)4T fail to exhibit the observed phenomenon, thus strongly implicating the crucial roles played by the terminal G and base protonation of cytosines. A plausible mechanism for the formation of a novel self-assembled structure is speculated. Aided by the C+.C base pair formation, parallel quadruplexes are initially formed and subsequently converted to quadruplexes with contiguous G-tetrads and looped-out cytosines due to high [K+]. These quadruplexes then vertically stack as well as horizontally expand via interquadruplex C+.C base pairing to result in dendrimer-type self-assembled super structures.     

Anisotropy of yielding in a Zr-2.5Nb pressure tube material

The anisotropy of yielding, as measured by the ratio of yield stress in the axial and transverse directions of Zr-2.5Nb pressure tubes used in Canada Deuterium Uranium (CANDU) nuclear reactors, was determined experimentally by testing samples in uniaxial tension. The yield anisotropy was measured in uniaxial tension in samples obtained from the three directions of a Zr-2.5Nb plate and in shear, by testing in torsion “mini” pressure tubes from the same material. From these experiments, the temperature and strain-rate dependence of the yield stress and the dependence of the anisotropy of yielding on temperature were also determined. It is shown that the yield anisotropy of pressure tube material is constant for temperatures up to about 800 K and that the strain-rate sensitivity is also constant up to about 700 K and is equal to ∼0.02. In addition, the activation energy (Q) of this material was estimated by using the temperature dependence and rate sensitivity of the yield stress. It was found to be of the same order of magnitude as that determined earlier by other investigators. A polycrystalline, nonlinear self-consistent model that takes into account the crystallographic texture of the material was used to derive the values of the critical resolved shear stress (CRSS) which are consistent with prismatic, basal, and pyramidal glide and the values of the Hill’s plastic anisotropy coefficients which are consistent with the observed anisotropy of yielding. The model provided an estimate of the complete stress tensor, describing yielding of a Zr-2.5Nb pressure tube material.     

Reynolds Stress Anisotropy in Open-Channel Flow

This paper reports the results of an experimental study characterizing turbulence and turbulence anisotropy in smooth and rough shallow open-channel flows. The rough bed consists of a train of two-dimensional transverse square ribs with a ratio of the roughness height (k) to the total depth of flow (d) equal to 0.10. Three rib separations (p/k) of 4.5, 9, and 18 were examined. Here, p is the pitch between consecutive roughness elements and was varied to reproduce the classical condition of d- and k-type roughness. For each case, two-component velocity measurements were obtained using a laser Doppler velocimetry system at two locations for p/k = 4.5 and 9: on the top of the rib and above the cavity, and an additional location for p/k = 18. The measurements allow examination of the local variations of the higher-order turbulent moments, stress ratios as well as turbulence anisotropy. Large variations of the turbulence intensities, Reynolds shear stress, turbulent kinetic energy and turbulence production are found for y1<3k. In this region, the flow is more directly influenced by the shear layers from the preceding ribs. The higher-order moments appear to be similar for all rough surfaces beyond y1 ≈ 7k. In the outer layer (y1>3k), all higher-order turbulent moments for the k-type roughness show a substantial increase due to the complex interactions between the roughness and the remnants overlying shear layers shed from succeeding ribs. Analysis of the components of the Reynolds stress anisotropy tensor shows that at p/k = 18, the flow at y1<5k tends to be more isotropic which implies that for this particular case, the effect of the roughness density could also be important. On the smooth bed, at the shallower depths, the correlation coefficient near the free surface increases and turbulence tends to become less anisotropic.