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Poroelastic‐plastic consolidation — analytical solution
Author(s) -
Pariseau W. G.
Publication year - 1999
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/(sici)1096-9853(199906)23:7<577::aid-nag984>3.0.co;2-u
Subject(s) - poromechanics , consolidation (business) , mechanics , compressibility , pore water pressure , finite element method , plasticity , materials science , boundary value problem , elasticity (physics) , geotechnical engineering , mathematics , geology , structural engineering , mathematical analysis , engineering , composite material , physics , porous medium , porosity , accounting , business
Consolidation of a poroelastic material that yields according to Drucker–Prager or Mohr–Coulomb criteria leads to a Stefan problem for time‐dependent pore fluid pressure. The solution to the Stefan problem for a column of infinite depth is known and is adapted to poroelastic/plastic consolidation of a weightless material under a uniform surface load applied instantaneously and subsequently maintained constant. In this approach, the plastic potential and yield criterion need not be the same. If yielding occurs concurrently with application of load, then collapse is instantaneous. Otherwise, yielding may occur during the consolidation period. If so, then the elastic–plastic zone first appears at the surface and subsequently moves down the column. Depth to the elastic–plastic boundary is given by the simple expression Z = 2 β √ t where β is a constant determined from continuity conditions at the elastic–plastic boundary. Time‐dependent surface displacement that occurs during consolidation is directly proportional to Z . There is little difference between elastic–plastic and purely elastic results in a numerical example because there is little difference in the respective consolidation coefficients. Elastic–plastic finite element results obtained from a column of finite depth are in close agreement with analytical results as long as the pore pressure at the bottom of the column does not change significantly from the value induced by application of the surface load. The analytical solution provides for: (1) efficient evaluation of material properties effects on consolidation, including strength and fluid compressibility, and (2) an accurate way of validating poroelastic/plastic computer codes that are based on Drucker–Prager and Mohr–Coulomb criteria. Copyright © 1999 John Wiley & Sons, Ltd.