Transversely isotropic stiffness parameters and their measurement in Colorado shale

2006 ◽  
Vol 43 (12) ◽  
pp. 1290-1305 ◽  
Author(s):  
Rajeeb Gautam ◽  
Ron CK Wong
Keyword(s):  
Triaxial Test ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Torsion Test ◽  
Stress Path ◽  
Small Strain ◽  
Loading Path ◽  
Triaxial Tests ◽  
Isotropic Elasticity ◽  
Colorado Shale

Drained stress path triaxial tests and confined torsion tests were conducted on Colorado shale core samples to investigate transversely isotropic stiffness parameters at small strain deformation. Nonlinear plastic behaviour occurred along the primary loading path even at strains less than 0.01%. Nonlinear, hysteric behaviour was only observed during the loading–unloading path. However, the shale material displayed transverse isotropy in deformation, and very small or nondetectable Poisson's ratios in vertical and horizontal directions. This special response alludes to the postulate that the Colorado shale could be approximated by a transversely isotropic elasticity model at small strain levels with negligible yielding.Key words: anisotropy, elasticity, stiffness, triaxial test, torsion test, shale.

The strength and dilatancy of sand

1992 ◽  
Vol 29 (3) ◽  
pp. 522-526 ◽  
Author(s):  
Y. P. Vaid ◽  
S. Sasitharan
Keyword(s):  
Relative Density ◽  
Triaxial Test ◽  
Friction Angle ◽  
Stress Path ◽  
Triaxial Tests ◽  
Confining Stress ◽  
Peak Friction Angle ◽  
Loading Direction ◽  
Dilation Rate ◽  
Unique Relationship

The effects of stress path and loading direction in the triaxial test on strength and dilatancy of sand are investigated. It is shown that the unique relationship observed between peak friction angle and dilation rate at peak in conventional triaxial tests is followed regardless of stress path, confining stress at failure, relative density, and the mode of loading (compression or extension). Key words : sand, peak friction angle, dilatancy, stress path, triaxial test.

scholarly journals Wyznaczanie modułu odciążenie – obciążenie powtórne dla gruntów głębokiego podłoża

2018 ◽  
Vol 27 (2) ◽  
pp. 114-122
Author(s):  
Wojciech Tymiński ◽  
Hubert Daniluk ◽  
Tomasz Kiełczewski ◽  
Paweł Stefanek
Keyword(s):  
Triaxial Test ◽  
Small Strain ◽  
Triaxial Tests ◽  
Soil Parameters ◽  
Test Results ◽  
Initial Stiffness ◽  
Test Procedures ◽  
Stiffness Modulus ◽  
Strain Model ◽  
Properties Of Soil

Soil parameters from triaxial tests are required for application of hardening soil small strain model in the geotechnical numerical analyses. In addition to the parameters such as the initial stiffness modulus (E0), stiffness modulus at 50% of the deviatoric stress value (E50), unloading– –reloading modulus (Eur) should be evaluated. The paper presents the test results for soil samples collected from the boreholes approximately 80 m deep. The main focus is put on evaluation of Eur parameter as requiring more advance tests in comparison to E0 and E50 parameters that may be evaluated on the basis of standard triaxial tests with shear wave velocity measurement. Based on the triaxial test results a correlation formula is proposed between Eur modulus and basic physical properties of soil and changes of effective stress values. The triaxial test procedures aimed at evaluation of E0, E50 and Eur are also presented.

Permanent deformation characteristics of saturated sand under cyclic loading

2015 ◽  
Vol 52 (6) ◽  
pp. 795-807 ◽  
Author(s):  
Yuanqiang Cai ◽  
Qi Sun ◽  
Lin Guo ◽  
C. Hsein Juang ◽  
Jun Wang
Keyword(s):  
Shear Stress ◽  
Stress Ratio ◽  
Permanent Deformation ◽  
Confining Pressure ◽  
Stress Path ◽  
Deviatoric Stress ◽  
Loading Path ◽  
Triaxial Tests ◽  
Deformation Characteristics ◽  
Torsional Shear

The loading path involving principal stress rotation (PSR) during shear is an important phenomenon encountered in many field conditions. Typically for traffic loading, both the magnitude and direction of principal stresses may vary with time due to the motion of vehicles, and the stress path can be mimicked by a heart shape in the deviatoric stress space. Conventional triaxial tests are not suitable to recreate this type of stress path in that no torsional shear stress can be applied on the test samples. To overcome this limitation, a series of tests using a hollow cylinder apparatus were conducted on sand to investigate the permanent deformation characteristics under drained conditions with different levels of confining pressure (σc), cyclic vertical stress ratio (CVSR), and cyclic torsional stress ratio (η). The results clearly show an increase in the permanent deformation with η, indicating that the PSR effect on permanent deformation cannot be ignored. Both σc and CVSR were found to also affect permanent deformation, which was more pronounced when PSR was coupled into the test. A five-parameter formulation that accounted for the effect of confining pressure, deviatoric stress, torsional shear stress, and number of loading cycles was subsequently established to analyze the permanent strain. The formulation coefficients were first determined and then used to explain the effects of stress variables on the permanent deformation. Validation studies were performed to address the adequacy of the formulation to predict permanent deformation.

Yield states and stress–strain relationships in a natural plastic clay

1983 ◽  
Vol 20 (3) ◽  
pp. 502-516 ◽  
Author(s):  
J. Graham ◽  
M. L. Noonan ◽  
K. V. Lew
Keyword(s):  
Yield Surface ◽  
Transversely Isotropic ◽  
Stress Path ◽  
Anisotropic Elasticity ◽  
Elastic Behaviour ◽  
Triaxial Tests ◽  
Large Strains ◽  
Plastic Strain Increment ◽  
Geological Processes ◽  
Systematic Effects

Natural clays are commonly anisotropic due to their mode of deposition, and lightly overconsolidated because of a variety of subsequent geological processes. They exhibit marked changes in stiffness when they yield. Yield stresses from individual tests can be generalized into a yield surface for the clay if displacements during loading are taken into account by calculating specific volumes V = (1 + e) throughout the tests.This paper describes tests on 76 mm diameter triaxial samples of natural plastic Lake Agassiz clay from Winnipeg. The samples were carefully trimmed, reconsolidated to approximately their in-situ stresses, and loaded in stress controlled tests along various stress paths in p′,q stress space.The tests produced well-defined yield envelopes in p′,q; p′, V; and q, V plots, and in corresponding plots where the stresses were normalized with respect to the vertical preconsolidation pressure σvc′. Comparison of one-dimensional yielding states with results from K0-triaxial tests that were continued to large strains suggests that the clay is cemented. At stresses inside the yield surface, the clay exhibits substantially linear elastic behaviour which is transversely isotropic. Values of bulk modulus, shear modulus, and a cross modulus which can be used to link mean effective pressures with shear strains, and deviator stresses with volumetric strains, have been evaluated in normalized form using a least-squares solution. The directions of plastic strain increment vectors after yielding have been examined. Consideration of the results suggests that they are not normal to the yield surface, and are influenced by systematic effects. Plastic compliances vary markedly with stress path direction. Keywords: clay, yield, critical state, anisotropic elasticity, associated flow, plasticity.

Effects of Stress Path and Stress History on the Stiffness of Reconstituted London Clay

1986 ◽  
Vol 2 (1) ◽  
pp. 139-144 ◽  
Author(s):  
J. H. Atkinson ◽  
J. S. Evans ◽  
D. Richardson
Keyword(s):  
Stress Path ◽  
Triaxial Tests ◽  
Soil Parameters ◽  
Stress History ◽  
Strain Behaviour ◽  
Reconstituted Soil ◽  
Path Dependent ◽  
London Clay ◽  
Soil Behaviour

AbstractSoil behaviour is stress history dependent and stress path dependent and soil parameters, particularly those for stress-strain behaviour, measured in conventional triaxial tests may not represent the behaviour of soil in many civil engineering works.To obtain more realistic parameters it may be necessary to conduct laboratory tests which more closely represent in situ conditions before and during construction.The paper describes equipment developed at The City University to carry out stress path tests simply and economically. A series of CU triaxial tests and stress path tests on reconstituted soil illustrate the dependence of measured soil parameters on stress history and stress path.

Wrinkling of a Fiber-Reinforced Membrane

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
E. Shmoylova ◽  
A. Dorfmann
Keyword(s):  
Boundary Conditions ◽  
Energy Function ◽  
Mechanical Response ◽  
Transverse Isotropy ◽  
Base Material ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Incompressible Material ◽  
Fiber Reinforced ◽  
Relaxed Energy

In this paper we investigate the response of fiber-reinforced cylindrical membranes subject to axisymmetric deformations. The membrane is considered as an incompressible material, and the phenomenon of wrinkling is taken into account by means of the relaxed energy function. Two cases are considered: transversely isotropic membranes, characterized by one family of fibers oriented in one direction, and orthotropic membranes, characterized by two family of fibers oriented in orthogonal directions. The strain-energy function is considered as the sum of two terms: The first term is associated with the isotropic properties of the base material, and the second term is used to introduce transverse isotropy or orthotropy in the mechanical response. We determine the mechanical response of the membrane as a function of fiber orientations for given boundary conditions. The objective is to find possible fiber orientations that make the membrane as stiff as possible for the given boundary conditions. Specifically, it is shown that for transversely isotropic membranes a unique fiber orientation exists, which does not affect the mechanical response, i.e., the overall behavior is identical to a nonreinforced membrane.

Transverse isotropy of the upper mantle in the vicinity of Pacific fracture zones

1969 ◽  
Vol 59 (1) ◽  
pp. 59-72
Author(s):  
Robert S. Crosson ◽  
Nikolas I. Christensen
Keyword(s):  
Upper Mantle ◽  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Seismic Wave Propagation ◽  
Fracture Zones ◽  
Mantle Material ◽  
Transversely Isotropic Media ◽  
Horizontal Symmetry ◽  
Isotropic Media

Abstract Several recent investigations suggest that portions of the Earth's upper mantle behave anisotropically to seismic wave propagation. Since several types of anisotropy can produce azimuthal variations in Pn velocities, it is of particular geophysical interest to provide a framework for the recognition of the form or forms of anisotropy most likely to be manifest in the upper mantle. In this paper upper mantle material is assumed to possess the elastic properties of transversely isotropic media. Equations are presented which relate azimuthal variations in Pn velocities to the direction and angle of tilt of the symmetry axis of a transversely isotropic upper mantle. It is shown that the velocity data of Raitt and Shor taken near the Mendocino and Molokai fracture zones can be adequately explained by the assumption of transverse isotropy with a nearly horizontal symmetry axis.

Reflection moveout approximations for P-waves in a moderately anisotropic homogeneous tilted transverse isotropy layer

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. C175-C185 ◽  
Author(s):  
Ivan Pšenčík ◽  
Véronique Farra
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
Weak Anisotropy ◽  
P Waves ◽  
3D Space ◽  
Axis Of Symmetry ◽  
Relative Errors ◽  
Symmetry Tests ◽  
Ti Media

We have developed approximate nonhyperbolic P-wave moveout formulas applicable to weakly or moderately anisotropic media of arbitrary anisotropy symmetry and orientation. Instead of the commonly used Taylor expansion of the square of the reflection traveltime in terms of the square of the offset, we expand the square of the reflection traveltime in terms of weak-anisotropy (WA) parameters. No acoustic approximation is used. We specify the formulas designed for anisotropy of arbitrary symmetry for the transversely isotropic (TI) media with the axis of symmetry oriented arbitrarily in the 3D space. Resulting formulas depend on three P-wave WA parameters specifying the TI symmetry and two angles specifying the orientation of the axis of symmetry. Tests of the accuracy of the more accurate of the approximate formulas indicate that maximum relative errors do not exceed 0.3% or 2.5% for weak or moderate P-wave anisotropy, respectively.

Normal moveout from dipping reflectors in anisotropic media

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 268-284 ◽  
Author(s):  
Ilya Tsvankin
Keyword(s):  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Weak Anisotropy ◽  
Anisotropic Models ◽  
Transversely Isotropic Media ◽  
Wide Range ◽  
Isotropic Media ◽  
The Difference

Description of reflection moveout from dipping interfaces is important in developing seismic processing methods for anisotropic media, as well as in the inversion of reflection data. Here, I present a concise analytic expression for normal‐moveout (NMO) velocities valid for a wide range of homogeneous anisotropic models including transverse isotropy with a tilted in‐plane symmetry axis and symmetry planes in orthorhombic media. In transversely isotropic media, NMO velocity for quasi‐P‐waves may deviate substantially from the isotropic cosine‐of‐dip dependence used in conventional constant‐velocity dip‐moveout (DMO) algorithms. However, numerical studies of NMO velocities have revealed no apparent correlation between the conventional measures of anisotropy and errors in the cosine‐of‐dip DMO correction (“DMO errors”). The analytic treatment developed here shows that for transverse isotropy with a vertical symmetry axis, the magnitude of DMO errors is dependent primarily on the difference between Thomsen parameters ε and δ. For the most common case, ε − δ > 0, the cosine‐of‐dip–corrected moveout velocity remains significantly larger than the moveout velocity for a horizontal reflector. DMO errors at a dip of 45 degrees may exceed 20–25 percent, even for weak anisotropy. By comparing analytically derived NMO velocities with moveout velocities calculated on finite spreads, I analyze anisotropy‐induced deviations from hyperbolic moveout for dipping reflectors. For transversely isotropic media with a vertical velocity gradient and typical (positive) values of the difference ε − δ, inhomogeneity tends to reduce (sometimes significantly) the influence of anisotropy on the dip dependence of moveout velocity.

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