Crack Models For A Transversely Anisotropic Medium
Name
1992.9 Cheng.pdf
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429.64 KB
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Adobe PDF
Checksum (MD5)
95061a5c81b79f416c9e9aea0ff71135
Author(s)
Cheng, C. H.
Date Issued
1992
Publisher
Massachusetts Institute of Technology. Earth Resources Laboratory
Series/Report no.
Earth Resources Laboratory Industry Consortia Annual Report;1992-09
Abstract
A commonly used model for a transversely anisotropic crack rock is that by Hudson
(1980, 1981). This model is based on a simplified analysis of a thin circular crack, with
displacement and stress conditions specified on the boundary. These papers have a
second order correction in addition to the first order term in porosity/crack density. In
this paper we compare the results of Hudson with those of Anderson et al. (1974) and
Cheng (1978) using the long wavelength static approximation and the ellipsoidal crack
model first proposed by Eshelby (1957). We showed that the Hudson model and those
based on the complete Eshelby theory agree for small aspect ratio cracks and small
crack densities, as expected, provided the weak inclusion version of Hudson's model
(1981) is used. For larger crack densities but small aspect ratios, Hudson's first order
term agrees with the Eshelby solution. The expansion in the second order term in crack
density is an asymptotic series and not a uniformly converging series. Thus there is no
general statement one can make about the accuracy of the second order expansion that
is valid for a variety of situations. A new expansion based on the Pade approximation is
proposed which is identical to Hudson's expansion up to second order in density. This
expansion avoids some of the problems associated with Hudson's second order expansion
such as increasing moduli with crack density at relatively small crack densities.
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