Fusao Oka

FEM-FDM coupled liquefaction analysis of a porous soil using an elasto-plastic model

The phenomenon of liquefaction is one of the most important subjects in Earthquake Engineering and Coastal Engineering. In the present study, the governing equations of such coupling problems as soil skeleton and pore water are obtained through application of the two-phase mixture theory. Using au-p (displacement of the solid phase-pore water pressure) formulation, a simple and practical numerical method for the liquefaction analysis is formulated. The finite difference method (FDM) is used for the spatial discretization of the continuity equation to define the pore water pressure at the center of the element, while the finite element method (FEM) is used for the spatial discretization of the equilibrium equation. FEM-FDM coupled analysis succeeds in reducing the degrees of freedom in the descretized equations. The accuracy of the proposed numerical method is addressed through a comparison of the numerical results and the analytical solutions for the transient response of saturated porous solids. An elasto-plastic constitutive model based on the non-linear kinematic hardening rule is formulated to describe the stress-strain behavior of granular materials under cyclic loading. Finally, the applicability of the proposed numerical method is examined. The following two numerical examples are analyzed in this study: (1) the behavior of seabed deposits under wave action, and (2) a numerical simulation of shaking table test of coal fly ash deposit.

Dispersion and wave propagation in discrete and continuous models for granular materials

Abstract A generalised continuum model for granular media is derived by direct homogenisation of the discrete equations of motion. In contrast to previous works on this topic, continuum concepts such as stress and moment stress are introduced after homogenisation. First, a very simple one-dimensional model is considered and the continuum version for this model is derived by replacing the difference quotients of the discrete model by differential quotients. The dispersion relations of the discrete and the continuous model are derived and compared. Variational boundary conditions for the continuous model are deduced from the stationarity of the corresponding Lagrangian. The three-dimensional case is treated in an essentially similar fashion. The resulting continuum theory is a combination of a Cosserat Continuum and a higher-order deformation gradient continuum. The salient features of the theory are illustrated by means of the dispersion relations for planar wave propagation.

A chemo–thermo–mechanically coupled analysis of ground deformation induced by gas hydrate dissociation

In the present paper, we have numerically analyzed the dissociation process of seabed ground and predicted the deformation of hydrate-bearing sediments. The simulation is conducted using the chemo-thermo-mechanically coupled model that takes into account the phase changes between hydrates and fluids during dissociation, the deformation behavior of the solid skeleton, and heat transfer simultaneously (Kimoto et al. 2007a). In addition, the dependency of the permeability coefficients for water and gas on hydrate saturation is introduced in the present analysis. From the analytical results, it has been found that ground deformation is induced by the dissipation and generation of water and gas and by a reduction of soil strength during the dissociation process.

Effect of dilatancy on the strain localization of water-saturated elasto-viscoplastic soil

Abstract It is well known that geomaterials such as soils exhibit an increase in volume during shearing deformation, referred to as dilatancy. Dilatancy is a typical property of such granular materials as soils and is closely related to changes in the microstructure. Normally consolidated clay exhibits negative dilatancy or contractancy, namely, a decrease in volume during shearing. On the other hand, overconsolidated clay shows positive dilatancy, namely, an increase in volume during shearing. The aim of the present paper is to study the effects of the microstructure, such as dilatancy and permeability, on the strain localization of water-saturated clay using an elasto-viscoplastic constitutive model. Based on the non-linear kinematic hardening theory and a Chaboche type of viscoplasticity model, an elasto-viscoplastic model for both normally consolidated and overconsolidated clays is proposed; the model can address both negative and positive dilatancies. Firstly, the instability of the model under undrained creep conditions is analyzed in terms of the accelerating creep failure. The analysis shows that clay with positive dilatancy is more unstable than clay with negative dilatancy. Secondly, a finite element analysis of the deformation of water-saturated clay is presented with focus on the numerical results under plane strain conditions. From the present numerical analysis, it is found that both dilatancy and permeability prominently affect shear strain localization behavior.

A strain localization analysis using a viscoplastic softening model for clay

Strain localization has become an attractive subject in geomechanics during the past decade. Shear bands are well known to develop in clay specimens during the straining process. Strain localization is closely related to plastic instability. In the present paper, a non-linear instability condition for the viscoplastic strain softening model during the creep process is firstly obtained. It is found that the proposed viscoplastic model is capable of describing plastic instability. Secondly, a two-dimensional linear instability analysis is performed and the preferred orientation for the growth of fluctuation and the instability condition are derived. It is worth noting that the two instability conditions are equivalent. Finally, the behavior of the clay is numerically analyzed in undrained plane-strain compression tests by the finite element method, considering a transport of pore water in the material at a quasi-static strain rate. The numerical results show that the model can predict strain localization phenomena, such as shear banding. From the numerical calculations, the effects of strain rate and permeability are discussed.

Three-dimensional strain localization of water-saturated clay and numerical simulation using an elasto-viscoplastic model

Since strain localization is a precursor of failure, it is an important subject to address in the field of geomechanics. Strain localization has been analysed for geomaterials by several researchers. Many of the studies, however, treated the problems brought about by strain localization as two-dimensional problems, although the phenomena are generally three-dimensional. In the present study, undrained triaxial compression tests using rectangular specimens and their numerical simulation are conducted in order to investigate the strain localization behaviour of geomaterials under three-dimensional conditions. In the experiments, both normally consolidated and over-consolidated clay samples are tested with different strain rates. Using the distribution of shear strain obtained by an image analysis of digital photographs taken during deformation, the effects of the strain rates, the dilation, and the over-consolidation on strain localization are studied in detail. The analysis method used in the numerical simulation is a coupled fluid-structure finite element method. The method is based on the finite deformation theory, in which an elasto-viscoplastic model for water-saturated clay, which can consider structural changes, is adopted. The results of the simulation include not only the distribution of shear strain on the surfaces of the specimens, but also the distributions of strain, stress, and pore water pressure inside the specimens. Through a comparison of the experimental results and the simulation results, the mechanisms of strain localization are studied under three-dimensional conditions.

Instability of gradient-dependent elastoviscoplastic model for clay and strain localization analysis

The instability of the strain gradient-dependent elastoviscoplastic constitutive model for water saturated clay is studied in relation to the strain localization phenomena and pattern formation during deformation. The second-order gradient of volumetric viscoplastic strain is introduced into the constitutive equations to account for the non-local effects associated with the motion of microstructures. Boundary value problems by using finite element are formulated and strain localization analyses are carried out.

Consolidation of Natural Clays and Laboratory Testing

A numerical model has been developed, making use of a strain-rate-dependent compressibility law and a permeability-void ratio law, both experimentally established. The numerical program is used to simulate the behavior ofclay specimens submitted to oedometric tests (MSL, CGT, creep, etc.). The following conclusions are drawn: 1. The effective stress-strain clay behavior depends on the type of test carried out. In particular, the preconsolidation pressure value varies from one test to another. 2. Each element throughout the specimen follows a specific stress-strain relation depending on its strain rate history. Moreover, the oedometric curve, as usually interpreted from a multiple-stage loading (MSL) test, does not agree with any of these relations, not even with the average curve followed by the whole specimen. 3. The pore pressure isochrones maintain the same shape during controlled-gradient (CGT) or creep tests, in particular when the effective stresses correspond to the preconsolidation pressure.

Elasto/viscoplastic constitutive equations with memory and internal variables

Abstract A general elasto/viscoplastic constitutive equation of a material with memory and internal variables is proposed based on the concept of generalized simple body. The proposed theory can describe not only such rate-dependent behaviours as primary and secondary creep, but also accelerating (teritary) creep, in which strain rate increases under constant stress. The application of the proposed theory to elasto/viscoplastic material in uniaxial condition is given and numerically analyzed with respect to strain rate effect.

Instability of gradient dependent elasto-viscoplasticity for clay

A gradient-dependent viscoplastic constitutive model for water saturated clay is proposed to describe the strain localization phenomena and pattern formation during deformation. Second- and fourth-order gradients of volumetric viscoplastic strain are introduced into the constitutive equations to account for the non-local effects due to the motion of microstructures. A linear perturbation analysis is applied to this model. The instability of the government equations (i.e. the constitutive equations and the equations of motion for the clay skeleton and pore water) is discussed for both the one-dimensional and the two-dimensional situations. In addition, issues concerned with the formulation of boundary value problems by finite element analysis in relation to the formulation and the boundary conditions are presented.