Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 57

If the intact rock's strength is exceeded in the rock matrix as well as on the isotropic
plane the strain rates according to (3.37) and (3.40) have to be superimposed:

(3.44)

To calculate in (3.37), (3.40) and (3.44) Q IR and Q S need to be expressed as func-
tions of the stress components σ x , σ y , σ z , τ xy , τ yz and τ zx of the global coordinate system

(Wittke 1990).

3.2.4 Intact Rocks with Deviations from Elastic-Viscoplastic
Stress-Strain Behavior
The assumption that the stress-strain behavior of intact rock below strength may be
regarded as linear elastic and independent of time of course represents an idealization.
However, a very large number of rock types can be described reasonably well by this
idealization provided that consideration is restricted to the stresses and temperatures
usually arising in rock engineering. Deviation from linear elastic stress-strain behavior
that is not time-dependent may nonetheless occur, particularly in weak or soft rocks
such as argillaceous rocks. Considerable differences between Young's moduli for initial
loading, unloading and reloading may be observed in laboratory tests conducted on
such rock types. Also the strains measured during phases of constant load may indicate
time-dependent behavior prior to failure (Section 14.4).
Intact rocks, even though brittle, tend towards ductile behavior at high confi ning stress.
When ductile behavior becomes dominant, in some cases the strength increases with
increasing strain which is known as “strain hardening” or “work hardening” (Singh
1989). Hardening may also cause an initially isotropic rock to become anisotropic
(Celle & Cheatham 1981). However, as already mentioned in Section 3.2.2 the range of
high confi ning stress is usually not too relevant for rock engineering problems.
Deformability and strength of intact rocks are also dependent on stress history. Cy-
clic loading and unloading often causes intact rock to fail at a stress level lower than
its compressive strength determined in static compression tests (Rao et al. 1985, Ray
et al. 1999). This lower stress level is often denoted as “fatigue stress” or “long-term
strength”. On the other hand, it has been found that Young's modulus and strength of
intact rocks increase considerably with increasing stress rate and strain rate (Cristescu
& Hunsche 1998, Ray et al. 1999, Li & Xia 2000). Also the deformation at failure shows
a marked dependence on stress rate or strain rate (Cristescu & Hunsche 1998). In ad-
dition, it has been observed that intact rock behaves more brittly at higher strain rates
(Ray et al. 1999). However, under quasi-static loading conditions these effects in most
cases are negligible.
In certain rock types under constant stress levels below strength time-dependent
deformation takes place which is referred to as “creep” (Chapter 5). Another feature of
time-dependent behavior is a change of stress state under constant deformation referred
to as “relaxation”.