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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 Read more...

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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.

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