52 In situ stressgauge has either 9 or 12 separate strain gauges, in rosettes of three, so there
is some redundancy in the measurements-thus permitting statistical
analysis of the data. Alternatively, if the rock is assumed to be transversely
isotropic rather than completely isotropic, then the extra readings allow the
stress state to be calculated incorporating the rock anisotropy. For a fuller
discussion of anisotropy and the numbers of associated elastic constants,
the reader is referred to Chapters 5 and 10.
One major advantage of this and similar gauges is that the resulting
hollow cylinder is retrieved from the borehole and can be subjected to
laboratory testing under controlled conditions in order to determine both
the functionality of the system (e.g. whether any strain gauges have
debonded, whether the cylinder is composed of intact rock, etc.) and the
necessary elastic constants.
As with all the methods discussed, this technique has its limitations and
disadvantages. One major problem is the environment within the
borehole: prior to gluing the gauge in place, the surface of the wall can
easily become smeared with material deleterious to adhesion; if the drilling
fluid is at a different temperature to the rock, then thermal expansion or
contraction of the hollow cylinder can lead to misleading strains being
induced; and the long-term stability of the glue may not be compatible with
the installed life of the gauge. Against this are the factors that the gauge is
relatively cheap, it contains built-in redundancy (both electrical and
mathematical) and, uniquely of the four methods described here, the
complete state of stress can be established with one installation.
4.4 Statistical analysis of stress state data
With repeated measurements of a variable, it is customary scientific practice
to apply some form of statistical treatment for the purpose of establishing
the accuracy and precision of the measurement system. Thus, when a scalar
quantity is being measured, the mean and standard deviation are
conventionally used as measures of the value and its variability. However,
a scalar is defined by only one value, whereas, in the case of the stress
tensor, there are six independent values. This has crucial ramifications for
averaging a number of stress tensors and for specifying the variability of
the stress state.
We have explained that the stress state is normally specified via the
magnitudes and orientations of the principal stresses. So, if a number of
stress measurements have been made in a particular region, it is very
tempting to estimate the average stress field by averaging the principal
stresses and their orientations separately, as demonstrated in Fig. 4.10@).
This is incorrect: it is wrong to take the average of the major principal stresses
in a number of stress tensors-because they may well all have different
orientations. The correct procedure is to find all the stress components with
reference to a common reference system, average these components, and then
calculate the principal stresses from the six values of averaged components,
as demonstrated in Fig. 4.10@) and the box in the text. Note also that each
of the six independent components of the stress tensor has its own mean
and standard deviation: these will generally be different for each of the six