Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 67

(3.65)

Equation (3.63) can be rewritten as:

or

(3.66)

Thus, the local stresses σ n,IR (x) in (3.62) can be replaced by the mean

stresses and existing in the intact rock along the discontinuity's plane
between two neighboring cracks.

τ res,IR (x) and

To obtain relationships between the mean stresses and in the intact rock and
the applied mean stresses and we must account for the fact that shear and normal
stresses in the intact rock cannot be transmitted across the open discontinuity sections. It
follows that

(3.67)

(3.68)

Inserting (3.66) and (3.67) into (3.68) yields:

(3.69)

In the case under consideration the linear degree of separation introduced in Section
2.7.2 can be expressed as

(3.70)

and thus

(3.71)

Inserting (3.71) into (3.69) the following peak shear strength criterion for a one-dimen-
sional non-persistent discontinuity formed by regularly ordered Griffi th cracks separat-
ed by rock bridges is obtained:

(3.72)