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METHODS OF IN SITU STRESS DETERMINATION
between the local state of strain in the hole wall and the field stresses as
1 2
Eε A = p ll [(1 − ) − (1 + ) cos 2 ] − (1 − )(1 − cos 2 ) cos 2
2
1 2
+ p mm [(1 − ) − (1 + ) cos 2 ] + (1 − )(1 − cos 2 ) cos 2
2
1
+ p nn [(1 − ) + (1 + ) cos 2 ]
2
2
− p lm 2(1 − )(1 − cos 2 ) sin 2
+ P mn 2(1 + ) sin 2 cos
− p nl 2(1 + ) sin 2 sin
(5.6a)
or
a 1 p ll + a 2 p mm + a 3 p nn + a 4 p lm + a 5 p mn + a 6 p nl = b (5.6b)
Equations 5.6a and 5.6b indicate that the state of strain in the wall of a borehole, at
a defined position and in a particular orientation, specified by the angles
and ,is
determined linearly by the field stress components. In equation 5.6b, the coefficients
a i (i = 1 − 6) can be calculated directly from the position and orientation angles for
the measurement location and Poisson’s ratio for the rock. Thus if six independent
observations are made of the state of strain in six positions/orientations on the hole
wall, six independent simultaneous equations may be established. These may be
written in the form
[A][p] = [b] (5.7)
where [p] represents a column vector formed from the stress components
p ll , p mm , p nn , p lm , p mn , p nl . Provided the positions/orientations of the strain obser-
vations are selected to ensure a well conditioned coefficient matrix [A], equation 5.7
can be solved directly for the field stress components p ll , p lm , etc.. A Gaussian elimi-
nation routine, similar to that given by Fenner (1974), presents a satisfactory method
of solving the set of equations.
The practical design of a triaxial strain cell usually provides more than the minimum
number of six independent strain observations. The redundant observations may be
used to obtain large numbers of equally valid solutions for the field stress tensor
(Brady et al., 1976). These may be used to determine a locally averaged solution
for the ambient state of stress in the zone of influence of the stress determination.
Confidence limits for the various parameters defining the field stress tensor may also
be attached to the measured state of stress.
5.3.3 Flatjack measurements
Stress measurement using strain gauge devices is usually performed in small-diameter
3
holes, such that the volume of rock whose state of stress is sampled is about 10 −3 m .
Larger volumes of rock can be examined if a larger diameter opening is used as the
measurement site. For openings allowing human access, it may be more convenient
to measure directly the state of stress in the excavation wall, rather than the state of
strain. This eliminates the need to determine or estimate a deformation modulus for
the rock mass. The flatjack method presents a particularly attractive procedure for
determination of the boundary stresses in an opening, as it is a null method, i.e. the
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