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Bulk modulus K

The bulk modulus K for the layered system is well-defined. Assuming that the external compressional/tensional stresses are hydrostatic so that $\sigma_{11} = \sigma_{22} = \sigma_{33} = \sigma$, and the total volume strain is e = e11 + e22 + e33, we find directly that
   \begin{eqnarray}
e = {{\sigma}\over{K}},
 \end{eqnarray} (16)
where, after some rearrangment of the resulting expressions, we have
   \begin{eqnarray}
K = f + \left({{1}\over{\mu_1^*}} + {{1}\over{2\mu_3^*}}\right)^{-1}.
 \end{eqnarray} (17)
The new terms in (18) are defined by
   \begin{eqnarray}
2\mu_1^* \equiv a + b - 2f\qquad\hbox{and}\qquad
2\mu_3^* \equiv c -f.
 \end{eqnarray} (18)
and are measures of shear behavior in the simple layered system. We can write the formula (18) this way, or in another suggestive form
   \begin{eqnarray}
{{1}\over{K - f}} = {{1}\over{a - m - f}} + {{1}\over{c - f}},
 \end{eqnarray} (19)
in anticipation of results concerning various shear modulus measures that will be discussed at length in the next section.


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Next: Effective bulk modulus estimates Up: BULK MODULUS K AND Keff Previous: BULK MODULUS K AND Keff
Stanford Exploration Project
7/8/2003