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(16.9)
where R is the radius of the pilot hole. Coeffi cients A
ri
and A
zi
are functions of the angle
θ
between the x direction and the position of the displacement transducer (Fig. 16.10,
lower) and
ν
:
A
ri
= f
ri
(
θ
,
ν
),
(16.10)
A
zi
= f
zi
(
θ
,
ν
).
(16.11)
Expressions for A
ri
and A
zi
are provided by Panek (1966), Hiramatsu & Oka (1968),
Pariseau (1987) and ISRM (1987a). An explicit solution of Equations (16.8) and (16.9)
for the in-situ stress components is presented by Bonnechere & Cornet (1977).
For transversely isotropic rock mass with elastic constants E
1
, E
2
, G
2
,
ν
2
the
following relations between measured radial and axial displacements and the in-situ
stresses have been found (Amadei 1983):
ν
1
and
(16.12)
(16.13)
with
(16.14)
(16.15)
Expressions for A
ri
and A
zi
that allow least square adjustment are given by Amadei
(1983). An explicit solution of Equation (16.12) for the components of the secondary
principal stresses in the plane normal to the borehole is presented by Rahn (1981).
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