Our main conclusion is that the two best constants to study for our
present purposes are the ones derived from the Reuss and Voigt bounds,
*G*_{eff}^{(1)} and *G*_{eff}^{(2)}. Furthermore, these estimates are
naturally paired with the Voigt and Reuss bounds on bulk
modulus through the product formulas (see the Appendix for a derivation)

(55) |

Eq.(60) shows explicitly that *G*_{eff}^{(2)} = *m* together
with generally negative corrections whose magnitude depends strongly on
fluctuations in layer shear modulus. The contribution of these
correction terms decreases as Skempton's coefficient *B* increases, so
*G*_{eff}^{(2)} is a monotonically increasing function of *B*.
This is exactly the behavior we were trying to explicate in the
present paper, so (60) is one example of the types of
aid-to-intuition that we were seeking. The leading term in
*G*_{eff}^{(2)} is also easy to understand, as *G*_{eff}^{(2)} was
first obtained here using the Voigt average, which is an upper bound
on the overall behavior; so it is natural that the leading term is
*m*, which is just the Voigt average of the 's in the layers.

7/8/2003