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Table 1 presents data for Barre granite and Bedford limestone
taken from laboratory measurements by Coyner [1984].
Coyner's experiments included a series of tests on several types
of laboratory scale rock samples at different confining pressures. The values
quoted for *K* and *K*_{s} are those for a moderate confining pressure of 10 MPa
(values at lower confining pressures were also measured but we avoid using
these values because the rocks generally exhibit nonlinear behavior in that
region of the parameter space), while the values quoted for *K*^{(1)} and
*K*_{s}^{(1)} are at 25 MPa,
which is close to the value beyond which the constants cease
depending on pressure -- and therefore for which we assume all the cracks
were closed.
Thus, based on the idea that the pressure behavior is associated with two
kinds of porosity in the laboratory samples -- a crack porosity, which is
being closed between 10 and 25 MPa, and a residual matrix porosity above
25 MPa, we assume the available data are *K*, *K*_{s}, *K*^{(1)}, *K*_{s}^{(1)},
*K*_{f}, , and *v*^{(2)}. We find that these data are sufficient
to compute all the coefficients. In Table 2,
we find in both types of rock that the coefficient
*a*_{23} is positive and small
-- about an order of magnitude smaller than the other matrix elements.
Another unusual feature of the results computed using these laboratory
data is the occurrence of values larger than unity for *B* and *B*[*u*^{(1)}]
in Barre granite; similar results were observed by Berryman and
Wang [1995] for Chelmsford granite, and in subsequent work for Westerly granite.
Also note that for both rocks is close to
unity for these calculations.
In this example, seven measurements (together with Poisson's ratio) are
sufficient to determine completely the mechanical behavior of the
double-porosity model.
Having a direct measurement of *K* eliminates the necessity of
assuming *a*_{23} = 0, which we have found is sometimes necessary when
dealing with field data [Berryman and Wang, 1995].

T

ABLE 2. Double porosity parameters computed from material
properties in Table 1.

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Stanford Exploration Project

8/21/1998