Engineering Rock Mechanics

Questions and answers: anisotropy and inhomogeneity 165

Configuration 1 (inaccurate and precise) Configuration 2 (inaccurate and imprecise)

Load, ZM) '1 ./ , Load, .. ~ '* I ,

N (^150) N 100 /
100
50
0
0 5 10 15 20 0 5 10 15
Strength, MPa Strength, MPa
Configuration 3 (accurate and precise) Configuration 4 (accurate and imprecise)
Load, I/ , Load, Jf ,
N 100 N 100
50
0
0 5 10 15 20 0 10 20 30
Strength, MPa Strength, MPa
be made for the bias. Configuration 2 has hopeless precision and should
be abandoned. Configuration 4 is better, but the imprecision is probably
too large to be worthwhile in comparison to configurations 1 and 3.
470.5 A vertical site investigation borehole intersects a stratum of
sandstone which is dipping at 17O. A length of intact core from
this borehole was taken to the laboratory for hydraulic conduct-
ivity testing, and two small-diameter plugs drilled from it: one
axially and one radially. These plugs were then tested in a per-
meameter, and the values of the hydraulic conductivity were found
to be 1.728 x 1 0-7 m/s and 1.557 x 1 0-6 m/s in the axial and the ra-
dial directions, respectively. Stating any assumptions that you make,
compute estimates of the hydraulic conductivity normal and parallel
to the bedding.
A70.5 We have been given hydraulic conductivity values in specific
directions. Assuming that hydraulic conductivity is a tensor quantity, we
can determine the components in any directions and the principal values
using the transformation equations. We know the dip of the bedding
relative to the tested plug directions and we assume that the anisotropy
in conductivity is structurally related (i.e. the principal directions are
normal and parallel to the bedding).
m/s, and an orientation of
ea = 90 + 17 = 107". For the radial plug, the orientation is 0, = 179 with
k, = 1.557 x m/s. Writing down the transformation equations3 for
these conditions, in terms of the principal values k, (normal to bedding)
For the axial plug we have k, = 1.728 x
Angles: anticlockwise positive,. zero being horizontal to the right.