By J. Sulem, I.G. Vardoulakis
This publication examines the experimental and theoretical points of bifurcation research as utilized to geomechanics. assurance contains uncomplicated continuum mechanics for dry and fluid unfiltrated porous media, bifurcation and balance analyses utilized to layered geological media and granular fabrics, and theories for generalized continua as utilized to fabrics with microstructure and relating to pressure localization phenomena.
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Additional info for Bifurcation analysis in geomechanics
56) where ni is the outwards unit normal along the boundary ∂V. e. of a term that is due to changes of its density in V, and a term due to flux υi across the boundary ∂V of V. Making use of the above general material time-differentiation formulae of volume integrals, the expression for conservation of mass, linear, and angular momenta, energy and entropy can be easily derived. 1 Mass balance be the mass of material within the volume dV in C with ρ being the Let mass density. 6) which are the local forms of the mass balance law.
The influence of microstructure of such media, like the existence of a periodic stratification or a double periodic crack array, on the buckling load and the dominant wavelength of the buckling mode is discussed as well. Chapter 5 deals with the continuum mechanics of water-saturated granular materials where a mixture theory approach to modeling is followed. There one can find the derivation of pertinent balance laws, the discussion of Terzaghi’s effective stress principle and its modifications as well as Darcy’s law and its extension to the cases of turbulent and viscous dissipative flows.
In a semi-logarithmic plot, these straight-line fits are characterized by their slopes, the socalled Terzaghi ‘compression’ and ‘swelling’ indices Cc and Cs, respectively. In most cases, straight-line fits are also generated if, instead of the ambiguous logarithmic stress and the inappropriate for large deformations engineering strain, one resorts to conjugate Eulerian measures like the Kirchhoff stress Tij and the logarithmic strain λ. 5 (San Francisco Bay mud: initial voids ratio , initial stress |σ0|=40kPa, primary compression index ; Holtz and Kovacs, 1981).
Bifurcation analysis in geomechanics by J. Sulem, I.G. Vardoulakis