Page 360 - Numerical Analysis and Modelling in Geomechanics
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RESERVOIR COMPACTION, SUBSIDENCE AND WELL DAMAGE 341
Figure 11.3 The yield envelope used in the ABAQUS program.
where R is a material parameter that controls the shape of the elliptical cap
surface, p a is an evolution parameter for volumetric plastic, strain-driven
hardening and softening of the cap, and α is numerical parameter used to
construct a smooth transition surface between the shear failure and the cap
plasticity surfaces.
Hardening and softening of the cap surface is governed by the piecewise
linear, functional dependence of the hydrostatic compression yield stress, p , on
b
the volumetric plastic strain, :
(11.38)
where describes the initial state of the material when the analysis is beginning.
Figure 11.4 is an example of a typical relationship between p b and, which
indicates that the plastic volumetric strain increases in compression with
increasing hydrostatic pressure (i.e., the pore volume shrinks). The evolution of
the cap surface is captured by the parameter, p , in Equation (11.37) as:
a
(11.39)
To ensure a smooth, continuous transition from the shear failure surface to the
cap surface, a circular arc transition surface is used, defined by:
