Cross Anisotropy Research Articles

A 3D coupled ALEM-BEM method for assessing pile mitigation performance to moving-harmonic-load induced vibrations in cross-anisotropic porous saturated media

The present investigation aims at proposing a three-dimensional ALEM-BEM coupling analytical approach to evaluate the isolation effectiveness of pile barriers in stratified cross-anisotropic porous saturated media under moving harmonic loads. The governing equations of Biot’s porous elastic theory are decoupled through an analytical layer-element method (ALEM). The pile-soil boundary equation is derived using BEM combined with a two-stage theory. Two-node beam cells are adopted to discretize the piles based on Timoshenko beam theory. The pile barrier mitigation effectiveness is obtained depending upon a vibration screening theory. After carefully validating the presented solutions by various reduced instances, the impacts of two-phase compressibility, geomaterial cross anisotropy, and load frequency on the mitigation effectiveness are analyzed. Results illustrate that the isolation effectiveness is more sensitive to the velocity in the medium with high two-phase compressibility or low cross-anisotropic coefficient. The pile screening effectiveness influenced by a high-speed load is more sensitive to the frequency.

Simplified approach to characterize anisotropic strength of granular soils

Experimental evidence shows that the strength of granular soils is significantly influenced by inherent cross anisotropy which cannot be properly described by isotropic failure criteria. This paper reviewed laboratory test results of various sands at different fabric directions. Based on the observations, this paper formulates the hypothesis that deposit plane creates a plane of weakness and the anisotropic strength of sands depends on orientations of deposit plane and failure plane. The strength decreases when orientations of deposit plane and failure plane are close to each other, and the strength increase when they diverge from each other. Then, an anisotropic failure criterion is developed based on this hypothesis and validated by available experimental data from literature. Remarkable agreements between predictions and measurements have been observed, which demonstrate validity, effectiveness, and robustness of new criterion in characterizing anisotropic strength of sands with variations of loading directions and intermediate principal stresses.

Maltese Cross Anisotropy in Antiferromagnetic State of Metallic Ho0.5Lu0.5B12 with Dynamic Charge Stripes

Maltese Cross Anisotropy in Antiferromagnetic State of Metallic Ho_0.5Lu_0.5B₁₂ with Dynamic Charge Stripes

A new approach to characterizing asphalt concrete in the linear/nonlinear small strain domain

Asphalt concrete (AC) material characterization is usually performed on laboratory prepared specimens, a procedure that does not ensure that the material tested reproduces the aggregates arrangement of the field material. Currently, field specimens are tested on cores in the Indirect Tensile Test (IDT) and on cylindrical specimens cored horizontally from relatively thick AC layers. As AC materials may exhibit cross anisotropy, testing cylindrical specimens requires two specimens, one in the vertical direction and the other in the horizontal direction. The above limitations can be overcome by testing prismatic field specimens in a triaxial cell with controllable vertical stress and confining pressure. The paper presents a study of the cross-anisotropic relations in two different specimen shapes, cylindrical and prismatic, and shows that prismatic specimens are preferred in the case of cross anisotropy. The use of the triaxial cell offers the possibility of applying different 2D stress paths and measuring the resulting 3D deformations. Creep and recovery tests on a prismatic specimen cut from a test section are conducted to illustrate the feasibility of the procedure. Before embarking in an extensive research project, six creep and recovery tests are conducted, under different stress paths that represent the closest stress/strain condition under a wheel load. The stress/strain conditions were kept within the small strain range, within the linear nonlinear stages. The linear viscoelasticity for cross-anisotropic materials is formulated, implying the derivation of four independent creep compliance functions. The test results are analyzed using numerical integration. The analyses show that the creep compliance functions vary with the stress/strain level, even in the so-called small strain range. Recommendations for further research are suggested.

Development of a modulus of subgrade reaction model to improve slab-base interface bond sensitivity

ABSTRACT In the Pavement ME Design, the modulus of subgrade reaction (k-value) is characterised by the dense liquid or Winkler model, which does not consider the interface bond within the supporting media. In this study, a modified k-value model was developed to take into account the shear interaction between concrete slab and base course. Formulation of the modified k-value model contained four steps: (a) correction of cross anisotropic base modulus; (b) development of a submodel for slab-base equivalent thickness; (c) development of a formula for slab-base interface shear bonding; and (d) determination of k-value using the calculated shear bonding and the deflection patterns of falling weight deflectometer (FWD). A large number of rigid pavement structural and strength properties and the corresponding FWD deflection patterns data were collected from the Long-Term Pavement Performance database and used to calculate the modified k-value. These were compared against the k-values using the existing ‘backcalculated best-fit approach’. The results showed that the modified k-values changed significantly due to the consideration of cross anisotropy and slab-base interface bonding. Finally, an artificial neural network (ANN) approach was employed to predict the modified k-values for the given pavement structures, layer moduli and interface bonding ratios.

INTEGRAL MECHANICAL TESTS IN THE STRENGTH CALCULATIONS OF THE MAIN PIPELINE FOR TRANSPORTATION OF OIL AND OIL PRODUCTS

Problematic issues of the current state and prospects of development of the standard, unified and special laboratory, bench and full-scale tests are considered to substantiate complex characteristics of the durability, survivability, cold resistance, reliability and safety of the elements of pipeline transport of oil and oil products are considered. These tests are linked to the stages of the pipeline life and improvement of the basic and verification methods of calculation and experimental determination of the criterial characteristics of the pipe steels, pipes and main pipelines with allowance for domestic and foreign experience. In the field of standard tests for static stretching, the experimentally obtained characteristics of the basic mechanical properties (yield strength and strength, elastic moduli) are included in the basic calculations of the static strength of newly designed and functioning pipelines. Standard tests for hardness and toughness are used to control the quality of pipe steels. The results of standard tensile tests are used to provide additional computational information regarding the estimates of ductility and degree of steel hardening upon elastoplastic deformation to get reliable verification estimates of the static strength. Unified laboratory tests are intended to refine determination of the pipeline strength taking into account the effects of 3D character of the stress state, absolute sizes of the pipeline cross section, deformation rate, anisotropy, cold resistance, corrosion and existence of welded connections. Assessment of the crack resistance of the pipe steel and pipes by criteria of linear and nonlinear fracture mechanics with allowance for technological and operational defects takes a special place in laboratory and bench tests. An emphasis is made on the domestic experience gained in the Russian system of testing the main pipelines for transportation of oil and oil products.

SWELLING ANISOTROPY OF STRAIGHT-GRAINED AND WAVY-GRAINED WOOD OF ABIES ALBA MILL.

Вивчено особливості анізотропії розбухання прямоволокнистої та хвилясто-завилькуватої деревини ялиці білої в межах радіуса та висоти стовбура. Дослідженнями охоплено ялицевий деревостан у вологій смереково-буковій суяличині Буковинських Карпат. Взірці деревини відібрано з 12 модельних дерев ялиці білої із прямоволокнистою та хвилясто-завилькуватою структурою деревини. Встановлено, що середні значення тангентального та радіального розбухання прямоволокнистої деревини є більшими від аналогічних показників хвилясто-завилькуватої. Середні значення розбухання прямоволокнистої деревини за об'ємом становить 14,2-14,3 %, а для хвилясто-завилькуватої деревини – 11,9-12,1 %. Величина поперечної анізотропії розбухання прямоволокнистої деревини є на 20 % більшою від подібного показника для хвилясто-завилькуватої деревини ялиці білої. Щільність прямоволокнистої деревини при абсолютній вологості 8 % становить 380 кг∙м-3 на висоті стовбура 1,3 м. Взірці хвилясто-завилькуватої деревини характеризуються на 21 % більшими середніми значеннями щільності деревини за абсолютної вологості 8 %. Щільність мокрої деревини змінюється від 900 до 1100 кг×м-3 за абсолютної вологості від 106 до 224 %. Встановлено істотні відмінності показників анізотропії розбухання та об'ємної маси прямоволокнистої та хвилясто-завилькуватої деревини ялиці білої.

Axisymmetric dynamic response of the multi-layered transversely isotropic medium

By virtue of the precise integration method (PIM) and the technique of mixed variable formulations, solutions for the dynamic response of the multi-layered transversely isotropic medium subjected to the axisymmetric time-harmonic forces are presented. The planes of cross anisotropy are assumed to be parallel to the horizontal surface of the stratified media. Four kinds of vertically acting axisymmetric loads are prescribed either at the external surface or in the interior of the soil system. Thicknesses and number of the medium strata are not limited. Employing the Hankel integral transform in cylindrical coordinate, the axisymmetric governing equations in terms of displacements of the multi-layered media are uncoupled. Applying mixed variable formulations, more concise first-order ordinary differential matrix equations from the uncoupled motion equations can be obtained. Solutions of the ordinary differential matrix equations in the transformed domain are acquired by utilizing the approach of PIM. Since PIM is highly accurate to solve the sets of first-order ordinary differential equations, any desired accuracy of the solutions can be achieved. All calculations are based on the corresponding algebraic operations and computational efforts can be reduced to a great extent. Comparisons with the existing numerical solutions are made to confirm the accuracy of the present solutions proposed by this procedure. Several examples are illustrated to explore the influences of the type and degree of material anisotropy, the frequency of excitation and loading positions on the dynamic response of the stratified medium.

Coefficients of Thermal Contraction and Expansion of Asphalt Concrete in the Laboratory

AbstractThe research reported in this paper investigates the coefficient of thermal contraction (CTE) and coefficient of thermal expansion (CTE) of asphalt concrete (AC) under different conditions in the laboratory. As a first step, the CTC and the CTE of AC at different temperatures ranging between −20 and 55°C were measured using field samples to examine the temperature effect. Then, the difference in the CTC and the CTE values in the vertical and horizontal directions (cross anisotropy) were evaluated using field samples. The influences of air void (AV), aggregate type, and aggregate gradation on the CTC and the CTE values were also investigated using laboratory prepared SuperPave gyratory samples. The deformation measuring devices, LVDTs, were calibrated using a zerodur to eliminate the temperature effect on the LVDTs. Results show that the CTC and the CTE values of AC are nonlinear with temperature and vary with aggregate type. However, gradation of aggregate and AV of sample do not affect the CTC an...

Effects of organic matter on stiffness of overconsolidated state and anisotropy of engineered organoclays at small strain

Organic rich soils are frequently encountered beneath infrastructure components that are sensitive to dynamic loading, such as bridges in earthquake prone regions. Because the engineering properties of these soils can be significantly impacted by the presence of organic matter, it is important to characterize their small strain dynamic properties. However, natural organic matter, is heterogeneous and highly variable; consequently, this experimental investigation quantified the dynamic behaviors of six organoclays that were synthesized under controlled laboratory conditions using quaternary ammonium cations as organic carbon in the clay interlayer. The small strain properties of these clays were measured with bender element tests to quantify the effects of organic carbon content on the dynamic properties of the soils, particularly on the overconsolidation and stiffness anisotropy. Experimental results demonstrated that the preloading effect of organoclays decreased with increasing total organic content due to the decrease in permanent fabric change and the release of lateral stress locking. Because of relatively limited rebound of organoclays (Cs/Cc: 0.025–0.07) as compared to inorganic soils (Cs/Cc: 0.1–0.2), the exponent for preloading ratio in the Gmax estimating formula is larger than 0.34, suggesting that tested organoclays showed a significant preloading effect when compared to inorganic soils. Additionally, organoclays tested in this study showed inherent anisotropy (Gmax(HH)/Gmax(VH) when K0=1: 0.93–1.42) and cross anisotropy in HV and VH directions (Gmax(HV)/Gmax(VH): 0.74–1.21), demonstrating behaviors that were comparable to that of inorganic soils.

Efficient Approach to Characterize Strength Anisotropy in Soils

AbstractStrength anisotropy in soils needs to be characterized by proper anisotropic failure criterion. This paper presents a novel yet simple methodology to generalize an isotropic failure criterion to account for strength anisotropy in soils. A salient ingredient of the method involves the introduction of the degree of cross anisotropy and an anisotropic variable, defined by the joint invariant of the deviatoric stress tensor and the deviatoric fabric tensor, into the frictional characteristic of the isotropic criterion. The well-received Lade’s failure criterion is taken as an example to demonstrate the generalization. Predictions using the newly generalized Lade’s criterion for a number of soils, including completely decomposed granite, glass beads (virtual sand), natural clays, sand, as well as silty sand, show good agreement with test data. The proposed approach has proved to be simple and generic, and can be effortlessly applied to many existing isotropic failure criteria to adapt them to account f...

General Strength Criterion for Geomaterials Including Anisotropic Effect

The strengths of geomaterials and their variation under different factors are investigated in this paper. First, a general isotropic variation of a strength criterion is proposed for describing the critical state and peak strengths of geomaterials. Second, the proposed criterion is extended to describe the effect of anisotropy on the peak strength. After an analysis of experimental data, the hypothesis is made that the failure of an element of geomaterial generally occurs in a particular plane when the applied shear stress in that plane reaches the shear resistance of the material. Therefore, the variation of the peak strength of anisotropic materials should be described in terms of the stress tensor applied, a vector parameter defining the position of the potential failure plane of the material, and the material properties. A general failure criterion for geomaterials with cross anisotropy is obtained then from the proposed isotropic strength criterion. The proposed criterion is demonstrated to well represent both the isotropic and anisotropic strengths of various geomaterials. Finally, a general anisotropic criterion is introduced.

Dynamic Analysis of Thin Asphalt Pavements by Using Cross-Anisotropic Stress-Dependent Properties for Granular Layer

A three-dimensional (3-D) finite element (FE) model was developed to investigate the dynamic responses of thin, flexible pavement under impulsive loading similar to a falling weight deflectometer test. The FE model simulated the hot-mix asphalt (HMA) surface layer as a linear viscoelastic material and considered the cross-anisotropic stress dependent modulus for the unbound base layer. Implicit dynamic analysis was used to consider the effect of inertia on pavement structural responses. Using two thin-pavement structures of different HMA layer thicknesses, 76 and 127 mm, the study analyzed the effects of cross-anisotropic stress-dependent aggregate base modulus and dynamic analysis on pavement responses, including surface deflection, tensile strain at the bottom of the HMA layer, deviator stress in the base layer, and compressive strain on top of the subgrade. Results showed that use of the cross-anisotropic stress-dependent modulus for the unbound base layer resulted in greater predicted pavement responses and, hence, less estimated pavement life for rutting and fatigue cracking. It was found that as the thickness of HMA surface layer or the ratio of horizontal modulus to vertical modulus decreases, the effects of stress dependency and cross anisotropy become more significant. Analysis-predicted surface deflections were compared to field-measured values and they were in agreement when the stress dependency and cross anisotropy of the base layer and subgrade were considered.

Micromechanical Modeling for Inherent Anisotropy in Granular Materials

In this paper, a description of inherent anisotropy of soil, based on micromechanics framework, is presented. The problem is formulated by assuming that sliding of two contact particles governed by Coulomb criterion in which the friction angle is a function of the orientation of the interparticle contact. The orientation distribution of these parameters is described by a set of symmetric second-order tensors. The formulation of the problem is illustrated by simulations of Santa Monica Beach Sand under true triaxial tests. In particular, the directional dependence of the strength characteristics is examined for samples with inherent cross anisotropy. The orientations of failure planes between particles are also examined.

Estimating Subgrade Reaction Modulus for Transversely Isotropic Rock Medium

Most of the rock medium possesses intrinsic grain orientation or preferred bedding and joint directions, thus requiring the use of at least transverse isotropy to describe its elastic behavior. This paper presents a series of charts, based on extensive finite element parametric studies along with nonlinear regression analysis of FE simulation results, for estimating the subgrade reaction modulus (or initial tangent to the p-y curve) using five elastic constants of a transversely isotropic rock mass. The proper characterization of subgrade reaction modulus is critical for accurate prediction of the elastic lateral deflection of a rock socketed drilled shaft under the applied lateral loads. The sensitivity of the response of a laterally loaded drilled shaft to the degree of anisotropy and orientation of the plane of anisotropy (bedding plane direction of the rock medium) was demonstrated in this paper for an actual lateral load testing case in Ohio. It is highly recommended to use five elastic constants to estimate subgrade reaction modulus of rock medium exhibiting high degree of cross anisotropy.

Failure Criterion for Cross-Anisotropic Soils

Experimental evidence and analyses of results of three-dimensional (3D) tests show that the shape of the failure surface for soils is influenced by the intermediate principal stress, shear banding, and cross anisotropy. Presented here is a formulation of a general 3D failure criterion for cross-anisotropic soils for both nonrotating and rotating stresses. The formulation relates the loading direction to the principal directions of the cross-anisotropic microstructure of the soil. The criterion is based on a function of stress, previously used as the 3D failure criterion for isotropic frictional materials, which is set equal to a scalar that varies over a sphere. The formulation is specialized for true triaxial tests and torsion shear tests and determination of material parameters is demonstrated. The failure criterion for cross-anisotropic soils is compared with experimental results from the literature to show that it is able to capture the conditions obtained in true triaxial tests without stress rotations as well as the conditions in torsion shear tests performed to study effects of stress rotation. Sets of data from some classic true triaxial tests are reinterpreted to show their true cross-anisotropic behavior.

Modeling Cross Anisotropy in Granular Materials

A constitutive model has been developed to capture the behavior of cross-anisotropic frictional materials. The elastoplastic, single hardening model for isotropic materials serves as the basic framework. Based on the experimental results of cross-anisotropic sands in isotropic compression tests, the principal stress coordinate system is rotated such that the model operates isotropically within the rotated framework. Experimental plastic work contours on the octahedral plane are plotted for a series of true triaxial tests on dense Santa Monica Beach sand to study the effects of cross anisotropy on the evolution of yield surfaces. The amount of rotation of the yield and plastic potential surfaces decreases to zero (isotropic state) with loading. The model is constructed for cases where the principal stress and material symmetry axes are collinear and no significant rotation of principal stresses occur. The model incorporates fourteen parameters that can be determined from simple experiments, such as isotropic compression, drained triaxial compression, and triaxial extension tests. A series of true triaxial and isotropic compression tests on dense Santa Monica Beach sand are used as a basis for verification of the capabilities of the proposed model.

Displacements and Stresses Due to a Uniform Vertical Circular Load in an Inhomogeneous Cross-Anisotropic Half-Space

In this work, we present the solutions for displacements and stresses along the centerline of a uniform vertical circular load in an inhomogeneous cross-anisotropic half-space with its Young's and shear moduli varying exponentially with depth. The planes of cross anisotropy are assumed to be parallel to the horizontal surface. The presented solutions can be directly integrated from the point load solution in a cylindrical coordinate system, which were derived by the writers. However, the resulting integrals of the circular solution for displacements and stresses cannot be given in closed form; hence, numerical integrations are required. For a homogeneous cross- anisotropic half-space, the numerical results agree very well with the exact solutions of Hanson and Puja, published in 1996. Two examples are given to elucidate the effect of inhomogeneity, and the type and degree of soil anisotropy on the vertical displacement and vertical normal stress in the inhomogeneous isotropic/cross-anisotropic soils subjected to a uniform vertical circular load acting on the surface. The proposed solutions can more realistically simulate the actual stratum of loading problem in many areas of engineering practice.

Measurement of Gmax and Estimation of K of Saturated Clay Using Bender Elements in an Oedometer

Abstract Recent developments in bender element technique have made it possible to determine Gmax and estimate K0 of soils under complex loading conditions. By measuring the shear wave velocities in different shear planes, the cross anisotropy in Gmax of soil induced by axial-symmetric loading can also be determined. The shear wave velocities can also be used to estimate the horizontal earth pressure coefficient at rest K0. This paper reports on an experimental setup that uses bender elements installed in an oedometer to measure shear wave velocities in four shear planes of a saturated clay specimen under different consolidation pressures. The data is used to investigate the cross anisotropy of stiffness in clay due to a K0 stress condition. The measured Gmax is compared with the results from a commonly used empirical formula. The measured shear wave velocities on different shear planes are also used to calculate K0 of clay under different consolidation pressures and compared with results from empirical formulae. The applied stress condition includes loading, unloading, and reloading of up to 22 cycles, thus providing information to study the influence of repeated loading on Gmax and K0 of a saturated clay.

Inverse Analysis of Soft Grounds Considering Nonlinearity and Anisotropy

ABSTRACT The inverse analysis method, used to accurately predict the two-dimensional deformation behavior of soft grounds, is discussed in this study. To ensure safety when constructing on a soft ground, in-situ observations are usually made. An inverse analysis is then effective for identifying the in-situ parameters of the ground and for predicting future deformation based on the parameters. The settlement, the lateral displacement, and the pore water pressure are measured during the construction of the structure. It is generally difficult to predict the lateral displacement. In this research, therefore, the cross anisotropy (transverse isotropy) of the ground is introduced to overcome the difficulty of predicting the lateral displacement. Furthermore, a simplified hyperbolic model is introduced to simulate the nonlinear shear behavior. The model is convenient for use with the inverse analysis, since it does not require many parameters. The measured pore water pressure is seldom used in the inverse analysis, because information on the pore water pressure is not required, from a mathematical standpoint, in order to identify the consolidation parameters. The effectiveness of applying the measured pore water pressure for the prediction of future consolidation behavior, is clarified in this study. As a result, the hyperbolic nonlinear model and the assumed anisotropy were found to be useful in predicting the future deformation behavior of clay. Furthermore, the pore water pressure measurement was proved to be effective for the predictions in this study.