ISSN:
1089-7550
Source:
AIP Digital Archive
Topics:
Physics
Notes:
The evolution of stress and strain during the consolidation of a fluid-saturated porous elastic sphere subjected to a uniform normal surface traction is investigated. The solution of Cryer [Q. J. Mech. Appl. Math. 16, 401 (1963)] for the pore fluid pressure is extended by deriving and fully analyzing new analytical solutions for the strain tensor of the elastic skeleton, the total stress tensor, the trace-free stress deviator tensor, and the effective stress tensor. Asymptotic expansions for small values of time of the stress and strain components, which determine the behavior of these components during the initial stages of the consolidation, are derived. Computer-generated graphs of the exact analytical solutions are presented, which provide insights regarding the redistribution of stress and strain throughout the consolidation. As fluid is expelled from the outermost layers of the sphere, fluid discharge builds up quickly to a peak rate and then subsides slowly as successively deeper layers are drained. During this initial consolidation, the stresses, strains, deviator stresses, and effective stresses within the outermost layers all change very rapidly. The nature of the Mandel–Cryer effect (pore fluid pressure increase within the sphere during initial fluid expulsion) is illuminated. Two other quantities, the transverse component of the total stress tensor and the total mean normal pressure, also show changes of opposite sign in the near surface and deeper regions, respectively: diminution in the outermost layers and simultaneous increase in the deeper portions. All of these effects are derived from Biot's theory of poroelasticity, in which the dilatation satisfies the diffusion equation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.349065
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