Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 82

constants can be expressed by the elastic constants (E IR , ν IR , E F , ν F ) and the volumetric

contents α and β = 1 - α of the intact rock and the fi lling, respectively, as follows:

E 1 = α ⋅ E IR , (3.87)

(3.88)

(3.89)

ν 1 =

ν IR , (3.90)

(3.91)

Equations (3.87) to (3.91) were derived assuming and E IR >> E F and account-

ing for shear bond between intact rock and fi lling (Wittke 1990). E oedF in (3.88) and
(3.91) is the oedometric modulus of the discontinuity fi lling defi ned as

α >> β

(3.92)

The example represented in Fig. 3.26 demonstrates the marked infl uence of persistent,
fi lled discontinuities on the elastic deformability of a rock mass even when their volu-
metric content is only 2%.
The elastic constants of a closely spaced alternating sequence of two rock types A and
B were determined by Pinto (1966) assuming shear bond between the individual rock
layers. The elastic behavior can then also be described as transversely isotropic. The
comprehensive formulas for the elastic constants presented by Pinto (1966) can be sim-
plifi ed while retaining suffi cient accuracy as follows (Wittke 1990):

E 1 = α ⋅ E A + β ⋅ E B , (3.93)

(3.94)

(3.95)