Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 55

the following we will distinguish between peak strength described by the strength param-
eters σ tIR * = 0.

When describing intact rock as an isotropic ideally viscoplastic solid the derivations of
viscoplastic strain components with respect to time t referred to as “strain rates” {

φ IR * , c IR * and φ IR , c IR and σ tIR and residual strength characterized by

}

are defi ned according to Perzyna (1966) as follows:

(3.34)

where

F IR and Q IR are the so-called “yield function” and “plastic potential”, respectively, and
η IR is denoted as the “viscosity”. Equation (3.34) is referred to as the “fl ow rule”. The
yield function F IR is related to the failure criterion. The Mohr-Coulomb failure criteri-
on (3.19), for example, can be formulated by a yield function F IR as follows:

(3.35)

or alternatively

(3.36)

If the peak shear strength is exceeded, the viscoplastic strain rate { } according to

(3.34) is defi ned as:

(3.37)

The yield function F IR * is formulated as a function of the residual strengths parameters
φ IR * , c IR * and σ tIR * , instead of the peak strength parameters c IR , σ tIR . This

means that after exceeding the peak strength (F IR > 0) an instantaneous reduction of
strength down to the residual strength takes place (Fig. 3.9, upper right).

φ IR and

The plastic potential Q IR is defi ned as with the function F IR :

(3.38)

The so-called dilatancy angle ψ IR specifi es the volume increase or loosening of the intact

rock when the peak shear strength is exceeded. When φ IR the plastic potential Q IR

is equal to F IR . Then we are talking about an “associated fl ow rule”. When an associated

ψ IR =