Page 359 - Numerical Analysis and Modelling in Geomechanics
P. 359
340 RESERVOIR COMPACTION, SUBSIDENCE AND WELL DAMAGE
81
DiMaggio and Sandier. This is a multi-surface plasticity model, which includes
a non-associative shear failure surface and an associative cap plasticity surface.
The ABAQUS program, used for the computations presented later in this
chapter, includes a linear Drucker-Prager shear failure surface, combined with a
Cap plasticity surface. 55 This constitutive model is not identical to that
implemented by DiMaggio and Sandler, but is based on the same
phenomenological framework and is similar in many respects. A sketch of the
yield envelope is shown in Figure 11.3. The Drucker-Prager linear failure
surface is given by:
(11.35)
where t is a deviatoric stress measure, p is the mean stress, β is the internal
friction angle, and d is the cohesion. The deviatoric stress measure in Equation
(11.35), which is the ordinate in Figure 11.3, is defined as:
(11.36)
where
The parameter K in Equation (11.36) is a material parameter that controls the
dependence of the yield surface on the value of the intermediate principal stress.
In this model, the surface is constructed so that K is the ratio of the yield stress in
triaxial tension to the yield stress in triaxial compression, so K=1 gives a von
Mises (circular) yield surface plotted in the 0 plane. Convexity of the yield
surface is assured if K≥ 0.778.
The Cap yield surface is given by:
(11.37)
