Cyclic mobility behaviour of sand by the three‐dimensional strain space multimechanism model

Akiyoshi, T.; Matsumoto, H.; Fuchida, K.; Fang, Huolang

doi:10.1002/nag.1610180604

Cited by 10 publications

(8 citation statements)

References 11 publications

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“…and the vector T is normal to N. With the introduction of scalar variables defined in Equations (41) and (43) for finite strain formulation, the scalar functions defining p ' and q remain the same as those given in Equations (15) through (19) for infinitesimal strain formulation.…”

Section: Integrated Form In Reference Configurationmentioning

confidence: 99%

“…The assumption of hyperbolic function for the backbone curve on the virtual simple shear mechanism defined in Equation (19) gives the virtual simple shear stress, for small strain g/g v ≪ 1, as…”

Section: Parameters and Examplementioning

confidence: 99%

“…By applying the classic postulate of interlocking by Taylor [21] (i.e., portion of shear strain energy is absorbed by dilative component of dilatancy in order to set free the assemblage of particles in granular materials from interlocking) to the backbone curve in Equation (19), dilative component of dilatancy is given by…”

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confidence: 99%

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Finite strain formulation of a strain space multiple mechanism model for granular materials

Iai

Ueda

Tobita

et al. 2012

Num Anal Meth Geomechanics

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SUMMARYThis paper presents the finite strain formulation of a strain space multiple mechanism model for granular materials. Because the strain space multiple mechanism model has an appropriate micromechanical background in which the branch and complementary vectors are defined in the material (or referential) coordinate, the finite strain formulation is carried out by following the change in these vectors, in direction and magnitude, associated with deformation in the material. By applying the methodology for compressible materials established in the finite strain continuum mechanics, decoupled formulation that decomposes the kinematic mechanisms into volumetric and isochoric components is adopted for the strain space multiple mechanism model. Lagrangian (material) description of integrated form is given by a relation between the second Piola-Kirchhoff effective stress tensor and the Green-Lagrange strain tensor; Eulerian (spatial) description by a relation between the Cauchy effective stress tensor and the Euler-Almansi strain tensor. In particular, the volumetric strain is defined as a logarithm of Jacobian determinant. Lagrangian (material) description of incremental form is derived through the material time derivative of the integrated form. The counterpart in the spatial description is derived through the Lie time derivative, given as a relation between the Oldroyd stress rate of Kirchhoff stress and the rate of deformation tensor (sometimes called stretching in the literatures). An example is shown to discuss the applicability of the finite strain formulation.

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Section: Integrated Form In Reference Configurationmentioning

confidence: 99%

Section: Parameters and Examplementioning

confidence: 99%

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Finite strain formulation of a strain space multiple mechanism model for granular materials

Iai

Ueda

Tobita

et al. 2012

Num Anal Meth Geomechanics

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“…According to the approach by Towhata & Ishihara (1985) and Akiyoshi et al (1994), the microscopic shear strength and the microscopic reference shear strain can be defined in terms of the shear strength, ô f , and the shear modulus, G, at a small strain level as…”

Section: Determination Of Parametersmentioning

confidence: 99%

“…Based on similar considerations, many models for the stress-strain of sands have been developed, such as the ones proposed by Chang et al (1992), and Gambarotta & Lagomarsino (1994). Later, Iai (1993) and Akiyoshi et al (1994) extended this type of model from two-dimensional space to three-dimensional space. Later, Iai (1993) and Akiyoshi et al (1994) extended this type of model from two-dimensional space to three-dimensional space.…”

Section: Introductionmentioning

confidence: 99%

A state-dependent multi-mechanism model for sands

Fang¹

2003

Géotechnique

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A state-dependent multi-mechanism model for sands in three-dimensional space is proposed within the framework of critical-state soil mechanics. The mechanical deformation behaviour of sands is characterised with a macroscopic volumetric mechanism and a number of one-dimensional equivalent microscopic shear mechanisms (EMSMs) in various orientations. Each one-dimensional EMSM includes a shear deformation and a volumetric deformation due to dilatancy, which are described by a microscopic shear stress-strain relationship and a microscopic stress-dilatancy relationship respectively. The detailed relationships between the macroscopic and microscopic model parameters are established, and all microscopic model parameters can be defined explicitly or implicitly by soil parameters with a clear and easily understandable physical meaning. Moreover, a state parameter, ł, defined by the difference between the current and critical void ratios at the same confining stress is used, relating the dilatancy and peak stress ratios to the critical stress ratio. Successful simulations of the responses of sands under drained, undrained, monotonic and cyclic loading conditions and during rotation of principal stress direction are obtained.Dans le cadre de la mécanique de sol d'état critique, nous proposons un modèle à mécanismes multiples et dépendant de l'état pour des sables dans un espace tridimensionnel. Le comportement de déformation mécanique des sables est caractérisé avec un mécanisme volumétrique macroscopique et un certain nombre de mécanismes de cisaillements microscopiques équivalents (EMSM) unidimensionnels dans diverses orientations. Chaque EMSM unidimensionnel comprend une déformation de cisaillement et une déformation volumétrique dues à la dilatance, qui sont décrites respectivement par une relation contrainte-déformation de cisaillement microscopique et une relation contrainte-dilatance microscopique. Nous établissons les relations détaillées entre les paramètres de modèle macroscopique et microscopique et nous pouvons définir explicitement ou implicitement tous les paramètres de modèle microscopique par des paramètres de sol avec une signification physique claire et facilement compréhensible. De plus, nous utilisons un paramètre d'état, ł, défini par la différence entre les taux de pore courants et critiques à la même contrainte confinante, paramètre lié aux taux de dilatance et de contrainte de pointe par rapport aux taux de contrainte critique. Nous obtenons de bonnes simulations des réponses de sables sous conditions de charge drainée, non drainée, monotone et cyclique et pendant la rotation de la direction principale de contrainte.

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A Non-Linear Seismic Response Analysis Method for Saturated Soil-Structure System With Absorbing Boundary

Akiyoshi¹,

Fang

Fuchida

et al. 1996

Int. J. Numer. Anal. Methods Geomech.

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A non-linear seismic response analysis method for 2-D saturated soil-structure system with an absorbing boundary is presented. According to the 3-D strain space multimechanism model for the cyclic mobility of sandy soil, a constitutive expression for the plane strain condition is first given. Next, based on Biot's two-phase mixture theory, the finite element equations of motion for a saturated soil-structure system with an absorbing boundary during earthquake loadings are derived. A simulation of the shaking table test is performed by applying the proposed constitutive model. The effectiveness of the absorbing boundary is examined for the 2-D non-linear finite element models subjected to random inputs. Finally, a numerical seismic response analysis for a typical saturated soil-structure system is performed as an application of the proposed method.

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Cyclic mobility behaviour of sand by the three‐dimensional strain space multimechanism model

Cited by 10 publications

References 11 publications

Finite strain formulation of a strain space multiple mechanism model for granular materials

Finite strain formulation of a strain space multiple mechanism model for granular materials

A state-dependent multi-mechanism model for sands

A Non-Linear Seismic Response Analysis Method for Saturated Soil-Structure System With Absorbing Boundary

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