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A mathematical model for voigt poro‐visco‐plastic deformation
Author(s) -
Yang XinShe
Publication year - 2002
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2001gl014014
Subject(s) - constitutive equation , rheology , mechanics , hydrostatic equilibrium , finite element method , nonlinear system , viscoelasticity , porous medium , deformation (meteorology) , hydrostatic pressure , thermal conduction , materials science , porosity , kelvin–voigt material , geotechnical engineering , geology , physics , thermodynamics , composite material , quantum mechanics
A mathematical model for poro‐visco‐plastic compaction and pressure solution in porous sediments has been formulated using the Voigt‐type rheological constitutive relation as derived from experimental data. The governing equations reduce to a nonlinear hyperbolic heat conduction equation in the case of slow deformation where permeability is relatively high and the pore fluid pressure is nearly hydrostatic, while travelling wave exists in the opposite limit where overpressuring occurs and the pore fluid pressure is almost quasi‐lithostatic. Full numerical simulation using a finite element method agree well with the approximate analytical solutions.