The results obtained for the specific application considered here,
*i.e.*, pore fluid effects on shear modulus, show that the pore
fluid interaction with overall shear behavior is complicated. The changes
from drained to undrained behavior for shear modulus can
range from being a negligible effect (as it is according to Gassmann's
results for microhomogeneous and isotropic media)
to being a bigger effect than the changes in bulk modulus under some
circumstances (see Figures 5 and 11 showing that the ratio of
compliance differences *R* > 1 in some cases). Influences of pore
geometry can also be studied in this model if desired,
but this complication was avoided here by parameterizing the fluid
effects through the use of Skempton's coefficient *B*.
All the pore microgeometry effects were thereby
hidden in the present analysis, but these could be brought out in future
studies of the same and/or many other related systems.

Another related result of some importance to analysis of partially and patchy saturated systems was obtained in Appendix B. The results are illustrated in Figure 12 and show that deviations from a system satisfying Hill's equation (3) need not be small if the shear modulus heterogeneity is large. The analysis does show, however, that if shear modulus variation is small, then the observed deviations from predictions of Hill's equation should also be correspondingly small.

An implicit assumption made throughout the present paper is that the porosity and -- most importantly -- the fluid permeability of the geomechanical system under consideration is relatively uniform. Then, the pore fluid pressures equilibrate on essentially the same timescale throughout the whole system. If this is not true, as it would not be in a double-porosity dual-permeability system (Berryman and Wang, 1995), then the present analysis needs to be modified to account for the presence of more than one pertinent timescale. One direction for future work along these lines will therefore be focused on this more complex, but nevertheless important, problem commonly encountered in real earth reservoirs. The random polycrystal of porous laminates model is flexible enough to allow this set of problems to be studied within a very similar framework.

5/3/2005