Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 72

Replacing κ l by κ p yields:

(3.80)

To describe the peak shear strength of non-persistent discontinuities an equation simi-
lar to (3.80) has been proposed by Robertson (1970) and Jennings (1970):

(3.81)

Relationships (3.80) and (3.81) are identical if c D = 0, as we have presupposed in our
derivation.
According to Wittke (1990), the residual shear strength of a non-persistent disconti-
nuity can be described by the mean value of the residual shear resistances of the rock
bridges and the persistent sections of the discontinuity weighted with the planar degree
of separation

κ p :

(3.82)

Tensile strength of discontinuities
The tensile strength of persistent discontinuities is generally zero. If a non-persistent
discontinuity is loaded by a normal tensile stress and a shear stress, the strength should
conservatively also be considered as negligible. The tensile strength of all types of dis-
continuities can therefore be assumed to be zero.

Summary and conclusion
In Fig. 3.19 the failure criteria for peak shear strength, residual shear strength and ten-
sile strength for discontinuities of different appearance are summarized.
It can be concluded that the strength of discontinuities is signifi cantly smaller than that
of the intact rock. As an example, Fig. 3.20 shows the shear strength of a rock block
that exhibits two mutually perpendicular discontinuity sets D1 and D2 and is loaded
by the principal normal stresses σ 3 , as a function of the direction of loading

with respect to the discontinuities. Of these,

σ 1 and

σ 3 is defi ned by the angles of dip β 1 and

β 2 = 90° - β 1 of D1 and D2, respectively, which are varied between 0° and 90°. The

maximum principal normal stress σ 1 , which leads to a shear failure of the intact rock

and/or on the discontinuities, is obtained as a function of

β 1 , β 2 , the shear parameters

of the intact rock (c IR and φ IR ) and those of the two discontinuity sets (c D1 , φ D1 , c D2

and φ D2 ) from the following equation (Wittke 1990):