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The dual to the problem just studied replaces compliances everywhere
with stiffnesses, and then proceeds as before. Equations
(15)(18) are replaced by
 
(28) 
(in all cases the * superscripts indicate that the porefluid
effects are included) and the reduced matrix
 
(29) 
where
 

 (30) 
 
It is a straightforward exercise to check that the two reduced
problems are in fact inverses of each other. We will not repeat this
analysis here, as it is wholly repetitive of what has gone before.
The main difference in the details is that the expressions for the
B's in terms of the 's are rather more complicated than those
for the compliance version, which is also why we chose to display
the compliance formulation instead.
Next: Effective and undrained shear G_{eff} G_{u}
Up: Eigenvectors for Transverse Isotropy
Previous: Case III. , .
Stanford Exploration Project
5/23/2004