Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 53

rocks (Donath 1964, McLamore & Gray 1967, Nova 1980, Niandou et al. 1997, Du-
veau et al. 1998, Tien & Tsao 2000, Tien et al. 2006). To obtain a better fi t of the test
results the original single plane of weakness theory was modifi ed (McLamore & Gray
1967, Nova 1980, Duveau & Shao 1998, Tien & Kuo 2001). Recently also the nonlinear
Hoek-Brown criterion was modifi ed to apply to anisotropic intact rocks (Saroglou &
Tsiambaos 2008). However, the benefi t of such refi nements is questionable because of
the inhomogeneity of test specimens with respect to mineralogical composition, which
usually leads to a large scatter of test results.
The tensile strength of intact rock with planar grain structure can be described cor-
respondingly to (3.29) with the aid of Equations (3.23) and (3.26) when setting σ n ( β )

= - σ tS in (3.26) and solving for σ 3 :

(3.32)

Alternative formulations for the tensile strength of anisotropic intact rocks are given,
for example, by Barron (1971), Nova & Zaninetti (1990) and Liao et al. (1997).

3.2.3 Post-Failure Behavior

Intact rocks with random grain structure
In Fig. 3.9 (upper left) a realistic stress-strain curve for uniaxial compressive loading
also referred to as “complete stress-strain curve” is represented. Strength after failure
(residual strength) is usually lower than strength at failure (peak strength). If strength
after failure drops to very low values or to zero we are talking about brittle behavior.
Otherwise we are talking about ductile behavior. Ductile behavior is typical, for exam-
ple, for argillaceous rocks and salt rocks. Most intact rocks, however, exhibit brittle
behavior at low confi ning stress with a gradual transition to ductile behavior at high
confi ning stresses that virtually eliminates microfracturing.
The stress-strain curve in the model used within this topic is idealized by an elas-
tic-viscoplastic stress-strain curve illustrated in Fig. 3.9 (upper right). Stresses

σ

below the unconfi ned compressive strength of intact rock σ cIR only lead to elastic

el that are independent of time and proportional to the stresses (green line
in Fig. 3.9). If

strains ε

σ cIR is reached, the stress in case of brittle behavior instantaneous-
ly drops to low values or to zero (dashed red line in Fig. 3.9). In case of ductile
behavior the stress either maintains its level or drops down to a lower stress level
(continuous and dashed-dotted red lines in Fig. 3.9). In the post-failure domain,
inelastic irreversible strains

vp occur that increase with time (blue line in Fig. 3.9,
lower left) and are referred to as “viscoplastic strains”.

ε