By Fusao Oka
"Preface during the last 3 a long time, reviews on constitutive types and numerical research equipment were good constructed. these days, numerical equipment play an important function in geotechnical engineering and in a comparable task known as computational geotechnics. This e-book bargains with the constitutive modeling of multiphase geomaterials and numerical tools for predicting the habit of geomaterials such as soil and rock. The e-book presents primary wisdom of continuum mechanics, constitutive modeling, numerical equipment for multiphase geomaterials, and their purposes. additionally, the monograph comprises contemporary advances during this zone, particularly, the constitutive modeling of soils for rate-dependent habit, pressure localization, the multiphase thought, and their purposes within the context of huge deformations. The presentation is self-contained. a lot realization has been paid to viscoplasticity, water-soil coupling, and pressure localization. bankruptcy 1 provides the basic inspiration and leads to continuum mechanics, similar to movement deformation and rigidity, that are helpful for figuring out the next chapters. This bankruptcy is helping readers make a self-consistent examine of the contents of this publication. bankruptcy 2 offers with the governing equations for multiphase geomaterials according to the idea of porous media, equivalent to water-saturated and air- water-soil multiphase soils together with soil-water attribute curves. This bankruptcy is vital for the research of computational geomechanics. bankruptcy three starts off with the elastic constitutive version and reports the elemental constitutive types together with plasticity and visoplasticity. For the plasticity idea, the steadiness proposal within the experience of Lyapunov is discussed"-- Read more...
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Additional info for Computational Modeling of Multiphase Geomaterials
This u-p formulation can be easily applied to the consolidation problems since the displacement of pore water is explicitly introduced. An infinitesimal strain is used. The relative acceleration of the fluid phase to that of the solid phase is much smaller than the acceleration of the solid phase. The grain particles in the soil are incompressible. The effect of the temperature is disregarded. 1. 2). 1) where superscript a indicates phase a and via is the velocity of the material in phase a, xia is the position of particle of a phase.
13) where K f is the elastic volumetric modulus of the pore fluid. 17) + ρ bi + ρ bi 36 Computational modeling of multiphase geomaterials where bi is the body force vector, and Ri is the term expressing the energy dissipation due to the relative motion between the solid and the fluid phases (Biot 1956). 19) where k is the permeability coefficient(assumed to be scalar because of isotropy), and w i is the relative velocity vector of the fluid phase to the solid phase. γ w = ρf g is the unit weight of the pore water with the gravitational acceleration g.
8 BALANCE OF ANGULAR MOMENTUM AND THE SYMMETRY OF THE STRESS TENSOR From the balance of angular momentum, the sum of the momentum is zero in the case of a zero time rate for the angular momentum. 124) where × denotes the vector product, t(n) is the stress vector, b is the body force vector, a is the inertia force vector, r is the position vector, and M is the couple stress vector. Couple stress is called moment stress and cannot be disregarded for materials with a significant rotation of the particles, such as granular materials.