Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 60

However, natural discontinuities in hard rocks such as granite show nonlinear but elas-
tic stress-displacement behavior under cycling loading (Pyrak-Nolte et al. 1987). This
can be explained by purely elastic closure and opening of asperities resulting from an
increase and decrease of contact areas during cyclic loading (Myer 2000).
The deformability of a filled discontinuity loaded by a normal compressive stress is
determined by the compressibility of the filling material.

3.3.3 Strength and Failure Criteria

Shear strength of discontinuities
The shear strength of persistent, planar discontinuities can be described exclusively by
friction and may be approximated by a linear relationship between τ res and σ n :

τ res = σ n ⋅ tan φ D . (3.48)

The friction angle φ D may be the same or lower than that of the intact rock due to

weathering or greasy films on the discontinuity's surfaces. The residual friction angle
φ D * of persistent, planar and closed discontinuities can be assumed to be equal to

φ D .
On uneven discontinuities two modes of shear failure may occur as illustrated in Fig.
3.12 by the example of a regular sawtoothed discontinuity. At low normal compressive
stress σ ns a sliding on the discontinuity surfaces takes place under the shear loading

τ res (Fig. 3.12, left upper). Consideration of the ultimate state of equilibrium provides
the following peak shear strength:

σ n ≤

τ res = σ n ⋅ tan ( φ D' + i) = σ n ⋅ tan φ D (3.49)

in which i is the sliding-up angle and φ D' is the friction angle of the discontinuity sur-

faces (Fig. 3.12). If the normal stress exceeds a certain value σ ns , instead of a sliding

on the discontinuity surfaces, the failure takes place in the intact rock by shearing off
the sawtoothed asperities (Fig. 3.12, upper right). Both the friction and cohesion of the
intact rock have to be overcome to initiate this shearing process. Thus, the peak shear
strength for

σ n > σ ns is given by

τ res = σ n ⋅ tan φ IR' + c IR', (3.50)

where φ IR and c IR for

the unweathered intact rock. Combination of (3.49) and (3.50) leads to the bilinear fail-
ure criterion for peak shear strength illustrated in Fig. 3.12 (lower) as was first suggested
by Patton (1966).

φ IR' and c IR' , due to weathering, may take on smaller values than