Premium
Bifurcation analysis of deep boreholes: I. Surface instabilities
Author(s) -
Vardoulakis I. G.,
Papanastasiou P. C.
Publication year - 1988
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/nag.1610120404
Subject(s) - biot number , hodograph , borehole , bifurcation , instability , finite element method , mechanics , constitutive equation , geology , compressibility , plasticity , stress (linguistics) , surface (topology) , deformation (meteorology) , geotechnical engineering , bifurcation theory , mathematics , geometry , structural engineering , engineering , physics , nonlinear system , thermodynamics , linguistics , philosophy , oceanography , quantum mechanics
In this paper a bifurcation analysis of boreholes in deep rock formations under uniform stress at infinity is presented. Rock is described by the constitutive equations of a deformation theory of plasticity for rigidplastic, incompressible and cohesive‐frictional material. The corresponding bifurcation problem is solved numerically by the finite element method. The evidence gained from the numerical solution is utilized to establish a simplified borehole stability analysis that combines Biot's hodograph method with a surface instability analysis.