Laboratory Tests - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 414

The elastic constants E 1 and ν 1 are obtained from the results of tests conducted on

specimens with β = 90°:

(14.19)

(14.20)

From the results of tests on specimens with β = 45° G 2 can be calculated as

(14.21)

It is also possible to determine the elastic constants of transversely isotropic intact
rock on specimens with four or more different angles that can be arbitrarily select-

ed (Wittke 1990, Amadei 1996). In this case, however, the elastic constants cannot be
determined independently from each other, since the results of tests carried out with
different angles

β

must be combined.
In Amadei (1983) formulas are provided to determine the nine elastic constants of ortho-
tropic elastic intact rock, defi ned in Section 3.2.1, by uniaxial compression tests.

β

If the stress-strain behavior to a certain extent is nonlinear the elastic constants may be
determined for specifi ed stress intervals.
On the basis of the results of a total of 35,600 uniaxial compression tests on three rock
types, Rodrigues (1974) found that measured strains within a specifi ed stress interval
are normally distributed. Since Young's modulus of intact rock is inversely propor-
tional to the measured strains, the reciprocal of E IR must be normally distributed. As a
consequence, the mean value of E IR from a series of n tests should be calculated as the
harmonic mean (Wittke 1990):

(14.22)

The harmonic mean is generally smaller than the arithmetic mean especially in cases of
large scatter of test results.
Depending on the behavior of the intact rock, brittle or ductile, the axial stress after
failure may drop abruptly or continuously (Fig. 14.6, left).