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.     

Possibility of Postliquefaction Flow Failure due to Seepage

This study examines the postliquefaction flow failure mechanism, in which shear strain develops due to seepage upward during the redistribution of excess pore water pressure after an earthquake. The mechanism is addressed as both a soil element and a boundary value problem. Triaxial tests that reproduce the stress state of a gentle slope subjected to upward pore water inflow were performed, with the results showing that shear strain can increase significantly after the stress state reaches the failure line. In addition, when subject to equivalent volumetric strain, shear strain is considerably larger in loose sand conditions than in dense sand. Compared with consolidated and drained test results, the dilatancy coefficient β, which indicates the rate of dilation, is the same as that obtained from pore water inflow tests. Torsional hollow cylinder tests were also performed to ascertain the limit of dilation of sand specimens. It was found that the β values are nonlinear in behavior. In addition, a postliquefaction flow failure mechanism based on one-dimensional consolidation theory and shear deformation behavior as a result of pore water inflow is proposed.     

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.     

Effects of Principal Stress Rotation on Permanent Deformation in Rail Track Foundations

A realistic assessment of the whole life cost of rail track foundations requires analysis of the effects of the repeated loadings applied by trains. This paper reports the effects of principal stress rotation (PSR) during cyclic loading on the permanent deformations measured in a series of hollow cylinder tests. The tests were carried out on a number of reconstituted soils selected in order to simulate foundation materials on an existing heavy haul railway line. Typical loadings and track geometry together with dynamic finite-element analyses were used to define representative stress changes to be applied to these soils, which were then tested with and without principal stress rotation during loading. It is shown that principal stress rotation has a significant and deleterious impact on permanent deformation of some materials. Therefore, it is concluded that cyclic triaxial testing, which cannot impose principal stress rotation, will not necessarily give good estimates of the long-term performance of rail track foundations. As PSR cannot be ignored when evaluating permanent displacements of rail track foundations, the use of more appropriate (realistic) testing methods such as the cyclic hollow cylinder or the cyclic simple shear apparatus is required.     

Mechanical Behavior of Metallic Hollow Sphere Materials: Experimental Study

Different from conventional metal foams, sintered metallic hollow sphere (MHS) material contains a certain volume fraction of enclosed pore space inside the spheres, as well as the interstitial porosity between the sintered neighbors, and this mixed open/closed-cell characteristic offers low density, high stiffness, and good energy absorption capacity. It is a new type of prospective light weight material for automotive and aerospace industry. In this study, the mechanical properties, especially the dynamic behaviors of the MHS materials are examined experimentally. Basic geometrical measurements reveal that the two types of MHS specimens we used were composed of randomly packed hollow spheres with uniform outer radius (0.9 and 1.5?mm) and wall thickness 0.05?mm (relative density <6%). A very long, plateau length (up to 67% nominal strain) with almost constant stress was found in quasi-static tests, indicating that they are appropriate for energy absorption applications. Dynamic tests were performed by using a modified split Hopkinson pressure bar (SHPB), and significant dynamic strength enhancements were observed. Moreover, based on the experimental observations the relevant collapse and dynamic enhancement mechanisms are discussed, whereas the localization phenomena in dynamic crushing process were revealed by using the particle image velocimetry correlation method.     

Consolidation of a Finite Transversely Isotropic Soil Layer on a Rough Impervious Base

A semianalytical solution to axisymmetric consolidation of a transversely isotropic soil layer resting on a rough impervious base and subjected to a uniform circular pressure at the ground surface is presented. The analysis uses Biot’s fully coupled consolidation theory for a transversely isotropic soil. The general solutions for the governing consolidation equations are derived by applying the Hankel and Laplace transform techniques. These general solutions are then used to solve the corresponding boundary value problem for the consolidation of a transversely isotropic soil layer. Once solutions in the transformed domain have been found, the actual solutions in the physical domain for displacements and stress components of the solid matrix, pore-water pressure and fluid discharge can finally be obtained by direct numerical inversions of the integral transforms. The accuracy of the present numerical solutions is confirmed by comparison with an existing exact solution for an isotropic and saturated soil that is a special case of the more general problem addressed. Further, some numerical results are presented to show the influence of the nature of material anisotropy, the surface drainage condition, and the layer thickness on the consolidation settlement and the pore pressure dissipation.     

In Situ Pore-Pressure Generation Behavior of Liquefiable Sand

To overcome current limitations in predicting in situ pore-pressure generation, a new field testing technique is used to measure directly the coupled, local response between the induced shear strains and the generated excess pore pressure. The pore-pressure generation characteristics from two in situ liquefaction tests performed on field reconstituted specimens are presented, including the pore- pressure generation patterns at various strain levels, the observed stages of pore-pressure generation, and pore-pressure generation curves. Comparisons of the in situ pore-pressure generation curves with data in the literature and from laboratory strain-controlled, cyclic direct simple shear tests support the in situ testing results. In addition, the effects of effective confining stress on threshold shear strain and pore- pressure generation curves are discussed. Comparisons of the rate of pore-pressure generation among the in situ tests, laboratory strain-controlled tests, and a model based on stress-controlled tests reveal that in situ pore pressures generated in reconstituted soil specimens during dynamic loading develop more similarly to those from cyclic strain-controlled laboratory testing. This observation implies that the evaluation of induced strains rather than induced shear stresses may be more appropriate for the simulation of pore-pressure generation.     

Finite-Element Analysis of Inclined Piezocone Penetration Test in Clays

A three-dimensional finite-element analysis was performed to analyze the effect of soil anisotropy on the inclined piezocone penetration test in normally consolidated clay. The piezocone penetration was numerically simulated based on a large strain formulation using the commercial finite-element code ABAQUS, and the anisotropic modified cam clay model (AMCCM) was chosen and implemented into ABAQUS through the user subroutine UMAT. For verification purposes, numerical simulations were first performed on previously conducted calibration chamber tests, and the predicted results were compared with the measured values. For different initial stress conditions and different penetration angles, the cone tip resistance profile; excess pore pressure profile at the cone tip; typical stress, strain and excess pore pressure distributions around the cone; and excess pore pressure dissipation at the cone tip are provided. This study shows that when the initial stress state is anisotropic, the soil behavior is different under different angles of penetration.     

Poromechanics Response of Inclined Wellbore Geometry in Chemically Active Fractured Porous Media

The porochemoelastic analytical models and solutions have been used to describe the response of chemically active saturated porous media such as clays, shales, and biological tissues. To date, all existing solutions are only applicable to single-porosity and single-permeability model, which could fall short when the porous material exhibits multiporosity and/or multipermeability characteristics, such as secondary porosity or fractures. This work summarizes the general linear dual-porosity and dual-permeability porochemoelastic formulation and presents the solution of an inclined wellbore drilled in a fluid-saturated chemically active fractured formation, such as fractured shale, subjected to a three-dimensional in situ state of stress. The analytical solution to this geometry incorporates coupled matrix-fracture deformation, simultaneous fluid flows, solute transports and interporosity exchanges induced by the combined influences of stress variation, fluid pressure and solute chemical salinity gradients under isothermal conditions. The fracture system is modeled as a secondary porosity porous continuum following Biot’s formulation while using mixture theory and the pore fluid is a binary solution comprised of a solvent and a solute. Results for the transient stresses and dual pore pressure distributions due to the coupled fracture and hydrochemical effects are plotted in the vicinity of the inclined wellbore and compared with the classical porochemoelastic and poroelastic counterparts. Finally, wellbore stability analyses are carried out to demonstrate applications of the solutions to field drilling operations.     

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.     

Shear Strength of Municipal Solid Waste

A comprehensive large-scale laboratory testing program using direct shear (DS), triaxial (TX), and simple shear tests was performed on municipal solid waste (MSW) retrieved from a landfill in the San Francisco Bay area to develop insights about and a framework for interpretation of the shear strength of MSW. Stability analyses of MSW landfills require characterization of the shear strength of MSW. Although MSW is variable and a difficult material to test, its shear strength can be evaluated rationally to develop reasonable estimates. The effects of waste composition, fibrous particle orientation, confining stress, rate of loading, stress path, stress-strain compatibility, and unit weight on the shear strength of MSW were evaluated in the testing program described herein. The results of this testing program indicate that the DS test is appropriate to evaluate the shear strength of MSW along its weakest orientation (i.e., on a plane parallel to the preferred orientation of the larger fibrous particles within MSW). These laboratory results and the results of more than 100 large-scale laboratory tests from other studies indicate that the DS static shear strength of MSW is best characterized by a cohesion of 15?kPa and a friction angle of 36° at normal stress of 1?atm with the friction angle decreasing by 5° for every log cycle increase in normal stress. Other shearing modes that engage the fibrous materials within MSW (e.g., TX) produce higher friction angles. The dynamic shear strength of MSW can be estimated conservatively to be 20% greater than its static strength. These recommendations are based on tests of MSW with a moisture content below its field capacity; therefore, cyclic degradation due to pore pressure generation has not been considered in its development.     

Analytic Solution for Finite Transversely Isotropic Circular Cylinders under the Axial Point Load Test

An exact solution for stress distributions within a finite transversely isotropic cylinder for the axial point load strength test (PLST) is analytically derived. Lekhnitskii’s stress function is first used to uncouple the equations of equilibrium. Two different kinds of solutions corresponding to the real and the complex characteristic roots of the governing equation of the stress function are derived. The solution type to be used for stress analysis depends on the anisotropic parameters of the cylinder. The solution for isotropic cylinders under the axial PLST is recovered as a special case. Numerical results show that the pattern of stress distribution along the line joining the point loads does not depend on the degree of anisotropy of the cylinder, but the magnitude of the stress distributions does. In particular, the local maximum tensile stress, which is located near the point loads, may be either larger or smaller than that of isotropic cylinders. In general, the maximum tensile stress inside the cylinder increases with the ratio of Young’s moduli, but decreases with both the ratio of Poisson’s ratio and the ratio of the shear moduli. If anisotropy of the cylinder is ignored, the point load strength index may be overestimated when the ratio of Young’s moduli is greater than one, or when the ratios of Poisson’s ratio or of the shear moduli is smaller than one.     

Analyses of Inclined Boreholes in Poroelastic Media

Solutions for the borehole problem based on Biot’s poroelasticity theory have shown that drilling through fluid saturated formations, gives rise to time-dependent stress and pore pressure fields in the vicinity of the borehole. As a natural consequence, borehole stability in such formations is of a time-dependent nature. However, existing analyses are based on two limiting cases viz., constant pore pressure and/or no flux boundary conditions at the borehole wall. Adding time dependency to the pore fluid boundary conditions can simulate realistic field conditions such as those observed during hydraulic fracturing, fluid injection or development of filter cake. Analytical solutions for inclined boreholes with time-dependent pore pressure and flux boundary conditions at the borehole wall are presented in this paper. Analysis is carried out for two special cases of the ramp-type pore pressure and linearly reducing flux boundary conditions. Analytical solutions are supplemented with asymptotic solutions for small and large time analysis. The effects of these conditions on stress concentrations near the borehole wall and their implications on borehole stability are examined in detail.     

Contraction, Dilation, and Failure of Sand in Triaxial, Torsional, and Rotational Shear Tests

The response of a saturated fine sand (Nevada sand No. 120) with relative density Dr ≈ 70% in drained and undrained conventional triaxial compression and extension tests and undrained cyclic shear tests in a hollow cylinder apparatus with rotation of the stress directions was studied. It was observed that the peak mobilized friction angle for this dilatant material was different in undrained and drained tests; the difference is attributed to the fact that the rate of dilation is smaller in an undrained test than it is in a drained test. Consistent with the findings of others, the material is more resistant to undrained cyclic loading for triaxial compression than for triaxial extension. In rotational shear tests in which the second invariant of the deviatoric stress tensor is held constant, the shear stress path (after being normalized by the mean normal effective stress) approached an envelope that is comparable but not identical in shape to a Mohr-Coulomb failure surface. As the stress path approached the envelope, the shear end deviatoric strains continued to increase in an unsymmetrical smooth spiral path. During the rotational shear tests, the direction of the deviatoric strain-rate vector (deviatoric strain increment divided by the magnitude of change in Lode angle) was observed to be about midway between the deviatoric stress increment vector and the normal to a Mohr-Coulomb failure surface in the deviatoric plane. The stress ratio at the transition from contractive to dilative behavior (i.e., “phase transformation”) was also observed to depend on the direction of the stress path; therefore this stress ratio is not a fundamental property. Results from torsional hollow cylinder tests with rotation of stress directions are presented in new graphical formats to help understand and interpret the fundamental soil behavior.     

Lateral Force Induced by Rectangular Surcharge Loads on a Cross-Anisotropic Backfill

This article presents approximate but analytical-based solutions for computing the lateral force (force per unit length) and centroid location induced by horizontal and vertical surcharge surface loads resting on a cross-anisotropic backfill. The surcharge loading types include: point load, finite line load, and uniform rectangular area load. The planes of cross-anisotropy are assumed to be parallel to the ground surface of the backfill. Although the presented solutions have never been proposed in existing literature, they can be derived by integrating the lateral stress solutions recently addressed by the author. It is clear that the type and degree of geomaterial anisotropy, loading distances from the retaining wall, and loading types significantly influence the derived solutions. An example is given for practical applications to illustrate the type and degree of soil anisotropy, as well as the loading types on the lateral force and centroid location in the isotropic/cross-anisotropic backfills caused by the horizontal and vertical uniform rectangular area loads. The results show that both the lateral force and centroid location in a cross-anisotropic backfill are quite different from those in an isotropic one. The derived solutions can be added to other lateral pressures, such as earth or water pressure, which are necessary in the stability and structural analysis of a retaining wall. In addition, they can be utilized to simulate more realistic conditions than the surcharge strip loading in geotechnical engineering for the backfill geomaterials are cross-anisotropic.     

Calculation of the pipeline wall thickness under internal pressure at an arbitrary law of hardening

A semianalytical solution is obtained for the problem of the deformation of a hollow cylinder (tube) subjected to internal pressure for the material that meets the Tresca plasticity condition and obeys an arbitrary law of hardening. The solution is analytical for linear hardening. This solution can be used to take into account the bearing capacity of a material in strength calculations more completely and reliably as compared to the existing techniques by choosing the cylinder wall thickness.     

Recurrent and Constructive‐Algorithm Networks For Sand Behavior Modeling

This article presents and discusses various aspects regarding the modeling of the behavior of a coarse granular material using Recurrent Neural Networks (RNNs) and Constructive Algorithms (CAs). A series of undrained triaxial tests following compression stress paths was performed to develop the database for neural network training and testing, where the relative density (Dr) and the confining effective stress (σ3) were varied. The range of (Dr) and (σ3) values was selected to have both dilatant and compressive sand behaviors. Modeling of sand behavior is done using Cascade and Jordan’s network architectures. Several input functions, learning rules, and transfer functions are utilized to evaluate their effects on the accuracy achieved by both algorithms during the training and predicting stages as well as on the time employed to perform these tasks. It is also shown that for the case of cascade networks, when the full‐size network having two outputs (pore water pressure and deviatoric stress) is divided into two networks with only one output each, the accuracy of predictions is improved appreciably. The results, in terms of pore water pressure‐stress‐strain relationships, included in this article point out the great potential RNNs and CAs have to become another class of computational tools to solve complex problems in material modeling. Thus, it is conceivable that ANNs when properly trained on a comprehensive data set could be designed to model the behavior of soil materials under a variety of initial conditions and stress path trajectories.     

Determination of Shear-Wave Velocities and Shear Moduli of Completely Decomposed Tuff

Based on theoretical derivations and considerations, five series of laboratory tests were planned to investigate and differentiate the degrees of inherent and stress-induced anisotropy, to study the effect of void ratio changes on shear-wave velocities and shear moduli, and to determine the relationship between shear-wave velocity and stress state on a completely decomposed tuff (CDT). Shear-wave velocities in three orthogonal horizontal and vertical planes [vs(hh), vs(hv), and vs(vh)] were measured in both vertically and horizontally cut block and Mazier specimens. Under isotropic stress conditions (K = 1.0), the degrees of inherent anisotropy [vs(hh)2/vs(hv)2 = Ghh/Ghv] were 1.48 and 1.36 for the block and Mazier specimens, respectively. At the anisotropic stress state (K = 0.4), the degrees of anisotropy of the block and Mazier specimens were 1.26 and 1.15, respectively, 15% reduction from the measured inherent anisotropy due to stress-induced effects. The measured higher shear-wave velocity in the horizontal plane of the CDT was confirmed by testing both vertically and horizontally cut specimens and the measured results reflect a stronger layering structure in the horizontal bedding plane of the natural material, in which K0 less than 1.0 is commonly assumed in designs. Under both isotropic and anisotropic stress states, the shear-wave velocities [vs(hh), vs(hv), and vs(vh)] of the block specimens are on average about 27% higher than those of the Mazier specimens.     

In Situ Pore Pressure Responses of Native Peat and Soil under Train Load: A Case Study

Settlement and formation of piping holes on surfaces were observed along a rail embankment subject to normal traffic load. Piezometers were installed in the native peat and soil underneath the embankment inside and outside problematic area to measure the pore pressure responses during train traffic. Peculiar pore pressure responses were observed. Cyclic pore pressures were only measured during the first 60–80?s of the 6-min train passage, and thereafter the pressures decayed rapidly to the initial values. The pore pressure changes in the shallow peat layer were lower than those in the deep soil layer. Possible mechanisms causing such peculiar pore pressure responses, surface settlement, and piping holes were explored and identified. It was found that the stiffness contrast between the stiff, upper granular fill and the soft, native peat material could lead to a redistribution of tensile stress in the granular fill layer to the peat layer due to the moving train load. This stress redistribution promotes the propensity of vertical piping in the peat layer.     

Micromechanical Basis of Concept of Effective Stress

Key developments in the concept of effective stress are surveyed with an emphasis on the ensemble averaging based micromechanical approach reported by Didwania and de Boer in 1999. Various assumptions underlying the effective stress for special cases like rigid/poroelastic solid material saturated by incompressible fluid under homogeneous conditions are elucidated. It is shown that for inhomogeneous saturated porous material the concept of effective stress needs to be generalized by introducing higher gradients of porosity, pore pressure, etc.