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Critical State (critical + state)

Distribution by Scientific Domains
Engineering75%
Earth and Environmental Science16%

Terms modified by Critical State

  • critical state line
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    Selected Abstracts

    Saturation and time dependence of geodynamo models

    GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2010
    M. Schrinner
    SUMMARY In this study we address the question under which conditions a saturated velocity field stemming from geodynamo simulations leads to an exponential growth of the magnetic field in a corresponding kinematic calculation. We perform global self-consistent geodynamo simulations and calculate the evolution of a kinematically advanced tracer field. The self-consistent velocity field enters the induction equation in each time step, but the tracer field does not contribute to the Lorentz force. This experiment has been performed by Cattaneo and Tobias and is closely related to the test field method by Schrinner et al. We find two dynamo regimes in which the tracer field either grows exponentially or approaches a state aligned with the actual self-consistent magnetic field after an initial transition period. Both regimes can be distinguished by the Rossby number and coincide with the dipolar and multipolar dynamo regimes identified by Christensen and Aubert. Dipolar dynamos with low Rossby number are kinematically stable whereas the tracer field grows exponentially in the multipolar dynamo regime. This difference in the saturation process for dynamos in both regimes comes along with differences in their time variability. Within our sample of 20 models, solely kinematically unstable dynamos show dipole reversals and large excursions. The complicated time behaviour of these dynamos presumably relates to the alternating growth of several competing dynamo modes. On the other hand, dynamos in the low Rossby number regime exhibit a rather simple time dependence and their saturation merely results in a fluctuation of the fundamental dynamo mode about its critical state. [source]

    Numerical local analysis of relevant internal variables for constitutive modelling of granular materials

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2010
    Yuhanis Yunus
    Abstract DEM simulations on spherical materials have been performed to study the behaviour of model granular materials not only under monotonous stress path such as triaxial compression or extension, but also under two-way cycling loading paths. Three reference states have been considered to characterize the behaviour of the granular material: the characteristic state, transitory state between volumetric contraction and dilation, the state of maximum resistance and the critical state. These states are regarded with respect to void ratio and anisotropy of fabric which are the two internal variables retained for the description of the internal state of the material. The characteristic state and the state at maximum resistance are clearly dependent on both levels of density and anisotropy at the beginning of a loading path. Bilinear models involving the two internal variables were designed for the characteristic state, the maximum dilatancy and the extent of the dilatancy domain for axisymetric loadings. They show that in each case the effect of density and anisotropy are different in compression and extension. The influence of anisotropy and density seems to be of the same order of magnitude. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    An enhanced constitutive model for crushable granular materials

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2010
    Ali Daouadji
    Abstract Studies in the past have tried to reproduce the mechanical behaviour of granular materials by proposing constitutive relations based on a common assumption that model parameters and parameters describing the properties, including gradation of individual grains are inevitably linked. However successful these models have proved to be, they cannot account for the changes in granular assembly behaviour if the grains start to break during mechanical loading. This paper proposes to analyse the relation between grading change and the mechanical behaviour of granular assembly. A way to model the influence of grain breakage is to use a critical state-based model. The influence of the amount of grain breakage during loading, depending on the individual grain strength and size distribution, can be introduced into constitutive relations by means of a new parameter that controls the evolution of critical state with changes in grain size distribution. Experimental data from a calcareous sand, a quartz sand, and a rockfill material were compared with numerical results and good-quality simulations were obtained. The main consequences of grain breakage are increased compressibility and a gradual dilatancy disappearance in the granular material. The critical state concept is also enriched by considering its overall relation to the evolution of the granular material. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    A unified bounding surface plasticity model for unsaturated soils

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2006
    A.R. Russell
    Abstract A unified constitutive model for unsaturated soils is presented in a critical state framework using the concepts of effective stress and bounding surface plasticity theory. Consideration is given to the effects of unsaturation and particle crushing in the definition of the critical state. A simple isotropic elastic rule is adopted. A loading surface and a bounding surface of the same shape are defined using simple and versatile functions. The bounding surface and elastic rules lead to the existence of a limiting isotropic compression line, towards which the stress trajectories of all isotropic compression load paths approach. A non-associated flow rule of the same general form is assumed for all soil types. Isotropic hardening/softening occurs due to changes in plastic volumetric strains as well as suction for some unsaturated soils, enabling the phenomenon of volumetric collapse upon wetting to be accounted for. The model is used to simulate the stress,strain behaviour observed in unsaturated speswhite kaolin subjected to three triaxial test load paths. The fit between simulation and experiment is improved compared to that of other constitutive models developed using conventional Cam-Clay-based plasticity theory and calibrated using the same set of data. Also, the model is used to simulate to a high degree of accuracy the stress,strain behaviour observed in unsaturated Kurnell sand subjected to two triaxial test load paths and the oedometric compression load path. For oedometric compression theoretical simulations indicate that the suction was not sufficiently large to cause samples to separate from the confining ring. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Experimental study of thermal effects on the mechanical behaviour of a clay

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2004
    Cane Cekerevac
    Abstract The paper presents the results of an experimental study of thermal effects on the mechanical behaviour of a saturated clay. The study was performed on CM clay (Kaolin) using a temperature-controlled triaxial apparatus. Applied temperatures were between 22 and 90°C. A comprehensive experimental program was carried out, including: (i) triaxial shear tests at ambient and high temperatures for different initial overconsolidation ratios; (ii) consolidation tests at ambient and high temperatures; and (iii) drained thermal heating for different initial overconsolidation ratios. The obtained results provide observations concerning a wide scope of the thermo-mechanical behaviour of clays. Test results obtained at 90°C were compared with tests performed at ambient temperature. Based on these comparisons, thermal effects on a variety of features of behaviour are presented and discussed. Focus is made on: (i) induced thermal volume change during drained heating; (ii) experimental evidence of temperature influence on preconsolidation pressure and on compressibility index; (iii) thermal effects on shear strength and critical state; and (iv) thermal effects on elastic modulus. Thermal yielding is discussed and yield limit evolution with temperature is presented. The directions of the induced plastic strains are also discussed. Several remarks on the difference in the mechanical behaviour at ambient and high temperatures conclude the paper. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Influence of particle shape and angularity on the behaviour of granular materials: a numerical analysis

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2003
    C. Nouguier-Lehon
    Abstract This paper analyses the influence of grain shape and angularity on the behaviour of granular materials from a two-dimensional analysis by means of a discrete element method (Contact Dynamics). Different shapes of grains have been studied (circular, isotropic polygonal and elongated polygonal shapes) as well as different initial states (density) and directions of loading with respect to the initial fabric. Simulations of biaxial tests clearly show that the behaviour of samples with isotropic particles can be dissociated from that of samples with anisotropic particles. Indeed, for isotropic particles, angularity just tends to strengthen the behaviour of samples and slow down either local or global phenomena. One of the main results concerns the existence of a critical state for isotropic grains characterized by an angle of friction at the critical state, a critical void ratio and also a critical anisotropy. This critical state seems meaningless for elongated grains and the behaviour of samples generated with such particles is highly dependent on the direction of loading with respect to the initial fabric. The study of local variables related to fabric and particle orientation gives more information. In particular, the coincidence of the principal axes of the fabric tensor with those of the stress tensor is sudden for isotropic particles. On the contrary, this process is gradually initiated for elongated particles. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Theoretical investigation of the cavity expansion problem based on a hypoplasticity model

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2001
    V. A. Osinov
    Abstract The problem of the symmetric quasi-static large-strain expansion of a cavity in an infinite granular body is studied. The body is assumed to be dry or fully drained so that the presence of the pore water can be disregarded. Both spherical and cylindrical cavities are considered. Numerical solutions to the boundary value problem are obtained with the use of the hypoplastic constitutive relation calibrated for a series of granular soils. As the radius of the cavity increases, the stresses and the density on the cavity surface asymptotically approach limit values corresponding to a so-called critical state. For a given soil, the limit values depend on the initial stresses and the initial density. A comparison is made between the solutions for different initial states and different soils. Applications to geotechnical problems such as cone penetration test and pressuremeter test are discussed. Copyright © 2001 John Wiley & Sons, Ltd. [source]

    Strength of two structured soils in triaxial compression

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2001
    Ron C. K. Wong
    Abstract Oil sands are dense granular materials with interlocked structure and clay shales are heavily overconsolidated clays. They are classified as structured soil or weak rock, exhibiting high peak strength with severe softening and dilation, particularly at low confining stress. The triaxial compression test results indicate that both materials yield linear Mohr,Coulomb envelopes with an apparent cohesion for peak and residual strengths. However, the strength components mobilized from these two materials are very different. This paper investigates if these strength parameters are intrinsic properties or responses derived in triaxial compression conditions. Computer tomography scanning technique is used to aid in examining the micro-structural features of the sheared specimens such as shear banding pattern, shear band thickness, spatial porosity distributions inside and outside shear bands. These micro-structural features are used to explain the macro-deformation response observed in the triaxial compression tests. Mobilization of strength components derived from interlocked structure, cementation, dilation, rolling and critical state are analysed for pre-, post-peak softening and residual stages. It is found that the empirical correlation such as Mohr,Coulomb failure criterion based on triaxial compression test results does not necessarily reflect the intrinsic properties of the test materials. Testing conditions are embedded in the empirical correlation. Copyright © 2001 John Wiley & Sons, Ltd. [source]

    Specific and non-specific solvent effects on aromatic nucleophilic substitution.

    JOURNAL OF PHYSICAL ORGANIC CHEMISTRY, Issue 5 2002
    6-dinitrobenzene, Kinetics of the reaction of 1-fluoro-, homopiperidine in binary solvent mixtures
    Abstract This paper presents a comparative study of the solvent effects on the kinetics of the reactions between 1-fluoro-2,6-dinitrobenzene and hexahydro-1H -azepine in ethyl acetate,+,chloroform or acetonitrile and acetonitrile,+,chloroform binary solvent mixtures. The purpose was to asses the contribution of each molecular-microscopic solvent property to the overall solvation effect of the reaction critical state. The influence of the dipolarity/polarizability, hydrogen-bond donor acidity and hydrogen-bond acceptor basicity of the solvent mixtures on the reaction rate was analyzed by the application of the multiparametric approach of Kamlet, Abboud and Taft. The evaluation of the correlation coefficients shows that the solvation effects are dominated by the non-specific interactions. Moreover, the incidence of the hydrogen-bond acceptor solvent ability is more important than that corresponding to the hydrogen-bond donor character, except for the reactions that manifest kinetic retarding effects. The influence of the solvation effects on the base catalysis was analyzed, describing the response patterns of the partial rate coefficients to the mixture composition and also to each solvent property. The application of a preferential solvation model to the kinetic results yields information on the preferential solvation of the reaction critical state by any of the pure solvents, or by the hydrogen-bonded complexed media. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Characterization of photoconductive semiconductor switches under nonlinear mode condition

    MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 1 2009
    Chi Ruan
    Abstract A photoconductive semiconductor switch (PCSS) would work in a nonlinear mode under high biased electrical field. The experimental results of nonlinear critical state have shown that both the biased voltage and the laser energy may have working thresholds to turn on the nonlinear modes. The relation between the biased voltage and the laser energy is inverse ratio, i.e., higher biased field need lower laser energy for nonlinear mode, and vise versa. At the nonlinear critical point, the output of PCSS is unstable, as both the linear and nonlinear pulse may occur. As the laser energy and biased field increase, the PCSS would work in the nonlinear mode steadily. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 56,59, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24001 [source]

    Estimates of effective stress beneath a modern West Antarctic ice stream from till preconsolidation and void ratio

    BOREAS, Issue 2 2001
    SLAWEK TULACZYK
    Preconsolidation stress recorded in subglacial sediments provides important information about subglacial effective stresses. It is commonly used to reconstruct past effective stresses from sediments left after ice retreat. In this article, we use properties of sub-ice-stream till samples to estimate effective stresses beneath a modern West Antarctic ice stream. Two previous estimates of sub-ice-stream effective stress were derived for the Upstream B (UpB) area of Ice Stream B from shear wave velocities (50 ± 40 kPa, Blankenship et al 1987) and borehole water level measurements (63 ± 24 kPa, Engelhardt & Kamb 1997). However, geotechnical tests performed on samples of the UpB till have shown that if subjected to effective stress of 50,63 kPa this till would have significantly lower porosity (,0.32,0.35) and higher strength (,-22,28 kPa) than it apparently has in situ (,0.4 and ,2kPa). We derive new estimates of sub-ice-stream effective stress using: (1) Casagrande's construction applied to the results of six confined uniaxial tests, and (2) a combination of void-ratio data for 51 till samples and 3 experimentally constrained equations describing compressibility of the UpB till under normal consolidation, overconsolidation and in the critical state. Casagrande's method yields an upper bound on effective stress of 25 kPa for four till samples and values of 13, and 4.4kPa for two other samples. The void-ratio approach gives 11.7 ± 2.6 (normal consolidation), 18.3 ± 4.4 (overconsolidation) and 2.0 ± 0.8 kPa (critical state). These new, lower estimates of effective stress are consistent with the low till strength that has been independently measured and inferred from recent theoretical ice-stream models. Our interpretation of data on till void ratio in terms of sub-ice-stream effective stress means that we can qualitatively evaluate the nature of the vertical distribution of this stress in the UpB till layer. We infer that in the sampled top 3 m of till the effective-stress distribution is non-hydrostatic, probably close to lithostatic. The results may be useful in future modeling of ice-stream behavior and may aid efforts to delineate paleo-ice streams based on their geologic record. [source]

    Failure envelopes and plastic potentials for eccentrically loaded surface footings on undrained soil

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2001
    M. Fraser Bransby
    Abstract The failure envelope in V,M space for surface foundations on undrained material under eccentric loading can be determined using an extended version of the scaling (or effective area) concept of Meyerhof. A similar displacement transformation allows production of the plastic potential. The two-dimensional finite element analyses of fully attached foundations subject to combined vertical (V) and moment (M) loading have been used to calculate appropriate scaling points for deduction of the failure envelope and plastic potential. Failure envelopes and plastic potentials are presented for footings on uniform and non-uniform undrained material and it is seen that the equivalent ,critical state' or ,parallel point' lies slightly beneath the peak moment capacity. For accurate prediction of failure envelopes for footings on non-uniform strength soil, consideration must be made of the apparent reduction of the soil heterogeneity as the area of footing in contact with the soil decreases. Copyright © 2001 John Wiley & Sons, Ltd. [source]