Field Tests - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 458

(15.3)

is the mean volume of the measuring cell. V 0 and V represent the measuring cell's vol-
ume at zero reading and at the loading stage p, respectively, on which the evaluation is
based. Poisson's ratio

must be estimated as in the case of dilatometer tests.
The volume measurement corresponds to a measurement of diameter changes in all di-
rections and subsequent calculation of the mean value. Because of this integrating effect,
in isotropic rock mass the volume measurement may be regarded as more reliable than
the mean obtained from three or four individual measurements of diameter changes
(Wittke 1990).

ν

From the results of a borehole jack test, Young's modulus can be calculated as
follows, when the rock mass is assumed to be homogeneous and its stress-strain
behavior is elastic and isotropic (Goodman et al. 1968, Hustrulid 1976, Swolfs &
Kibler 1982, ISRM 1996):

(15.4)

where d is the borehole diameter and d is the change of the borehole diameter in the

direction of the diametrically arranged steel plates due to the load increment

Δ

Δ p. Also,

γ is denoted as the “ram constant” that depends on the ratio of length l of the loaded

borehole section and the borehole diameter d, and K depends on Poisson's ratio ν of

the rock mass, which has to be estimated, and the half apex angle β of the steel plates

(Fig. 15.4). For the Goodman Jack (see Fig. 15.2, right), = 45° applies,

and K varies between 1.15 and 1.52, depending on the assumed Poisson's ratio (Heuze
& Amadei 1985, ISRM 1996).
The evaluation is normally conducted assuming full contact between the steel plates
and the borehole wall, that is, the contact angle 2

γ = 0.93 and β

β c between the steel plates and the

borehole wall corresponds to the apex angle 2 (Fig. 15.4). However, because the radius

of the borehole is slightly larger than the radius of the steel plates, in hard rock the half
contact angle

β

(Fig. 15.4, left) and also dependent on
the stress level. This can lead to an underestimation of Young's modulus by a factor
of 3 to 4, when calculated according to (15.4) (Hustrulid 1976, Swolfs & Kibler 1982).
Thus, particularly in hard rock,

β c is considerably smaller than β

β c is a very sensitive parameter, which has to be reliably
estimated (Shuri 1981, Swolfs & Kibler 1982). The use of the borehole jack in hard rock
therefore cannot be recommended.
In rock mass with higher deformability the steel plates may adapt to the borehole wall
(Fig. 15.4, right). To investigate weak rock, in Germany borehole jacks such as the
Stuttgarter Borehole Jack and the Ettlinger Borehole Jack were developed which allow
the measurement of diameter changes of the borehole wall up to 40 mm and 50 mm
in boreholes of 101 mm and 146 mm diameter, respectively (Fecker 1997, GIF 2004).
However, a borehole jack, owing to the applied diametrical pressure, induces tangential
tensile stresses into the rock mass (Fig. 15.4, right). In weak rock these tensile stresses