Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 46

isotropic and transversely isotropic bodies. The following relations are valid for an
isotropic elastic body (Love 1927):

E ≥ 0 (3.13)

and

- 1 ≤ ν ≤ 0.5. (3.14)

The corresponding restrictions for a transversely isotropic elastic body are (Pickering 1970):

E 1 ≥ 0, E 2 ≥ 0, G 2 ≥ 0 (3.15)

and

(3.16)

Relations (3.14) and (3.16) imply that, in principle, negative values of Poisson's ratios
may also be possible. However, with a few exceptions regarding highly anisotropic rocks
only, Poisson's ratios between 0 and 0.5 are reported in the related literature (Vutukuri
et al. 1974, Hatheway & Kiersch 1986, Gercek 2007).
Further restrictions for Poisson's ratios

ν 1 and ν 2 of transversely isotropic rocks were

found by Knops & Payne (1971)

- 1 < ν 1 < 0.5 (3.17)

and Amadei (1996)

(3.18)

Both inequalities were later derived by Exadaktylos (2001) assuming plane strain conditions.
Not all intact rocks can be described by isotropic or transversely isotropic elastic behav-
ior. The general anisotropic body with no symmetry at all, exhibits 21 elastic constants
(Lekhnitskii 1963). However, the effort needed to evaluate more than fi ve elastic con-
stants is unjustifi ably high and therefore carried out only in exceptional cases.

3.2.2 Strength and Failure Criteria

Shear and tensile strength of intact rocks with random grain structure
Experience has shown that intact rocks with random grain structure may be considered
as isotropic with regard to their strength. The shear strength of those rocks can be de-
scribed by an approximation using the Mohr-Coulomb failure criterion: