Engineering Rock Mechanics

Questions and answers: anisotropy and inhomogeneity^167

Parallel to

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dipping

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Question 10.6 is included to test your powers of conviction. A tensor
component can only vary according to the transformation equations,
which are in the form a cos2 8 + b sin2 8. Therefore, the maximal and
minimal values, in this case parallel and perpendicular to the bedding,
must have the same form of mathematical variation. The maximum is
not on a cusp, so the minimum cannot be. Therefore, there must be
something about the way the variation is plotted that causes the cusp,
and indeed there is.
In the left-hand diagram below, the variation is shown for the three
cases, R2, &, and &, in which the maximal and minimal components
of the hydraulic conductivity tensor are in the ratios 2 : 1,4 : 1, and 8 : 1,
respectively. It is especially clear in the R2 case that there is no cusp at

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Linear radial scale Logarithmic radial scale