Questions and answers: anisotropy and inhomogeneity 163erty values depending on where it is located. In any given region, the
property values will also depend on scanline direction because different
amounts of each scanline will occur per metre of an inclined scanline.
Moreover, different types of anisotropy will be experienced at different
locations in the different directions because the strata are inhomogeneous.
410.3 The following data are pairs of point load strength (PL) and
uniaxial compressive strength (UCS) values for a particular rock type.
UCS (MPa) 52.4 60.7 44.6 66.6 47.6 56.3 61.5 48.2 49.6 47.2 56.7 48.4 61.5 52.9
PL (MPa) 2.51 2.87 2.14 3.04 2.31 2.64 2.90 2.21 2.25 2.18 2.55 2.23 2.75 2.55
We wish to correlate these strength values, and can do so either in
the form PL =aut + 6 or in the form u, = cPL + d. On the basis of the
best independent variable, which of these forms is appropriate?
Determine values for the appropriate constants (Le. either u and
b, or c and d).
A70.3 When a straight line of the form y = mx + c (or any other curve)
is fitted to a set of observations, we are assuming that the x-values
represent the independent variable (i.e. are the known controlled vari-
able), and that the y-values represent the dependent variable. In the
case of the two variables, Point Load strength and Uniaxial Compressive
Strength, we know that the PL values - from an index test - exhibit
a wide spread; whereas the UCS values - from a relatively precise
and direct laboratory procedure - have a much reduced spread. As a
result, and for this case, we can take uniaxial compressive strength as the
independent variable and fit the straight line PL = aa, + b to the data.
Fitting a straight line to the data (taking care to make sure that the line
is constrained to pass through the origin), gives a value of a = 0.0465.
We then rearrange the equation to give the relation
(^1) I
a- PL or a, = 21.49 PL.
' - 0.046532
Had we tried to fit an equation of the form a, = cPL + d to the data,
we would have found that c = 21.48. In this case the difference between
the two coefficients is negligible, and not significant for engineering con-
siderations, but the second method is incorrect and in other cases could
introduce a much greater difference having engineering significance. It
is important to carefully assess which of the variables is the independent
variable and use it appropriately.
Q10.4 Imagine that a new index test for determining the tensile
strength of specimens of intact rock is under development in the
Rock Mechanics laboratory at Imperial College. This test involves
bonding a steel rod to the surface of a specimen with high strength
adhesive, and then measuring the tensile load required to pull the
rod together with a small piece of rock away from the main block of
rock. Four test configurations are under consideration, and for each
of these a theoretical relation between rock strength and pull-off
force has been developed. Test results for the four configurations,