Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 84

Extended approaches according to the homogeneous model describing the elastic be-
havior of alternating sequences that are composed of isotropic and anisotropic rocks
can be found in Salamon (1968), Wardle & Gerrard (1972) and Gerrard (1982a).

Strength and failure criteria
According to the homogeneous model, the strength of jointed rock can be described by
the superposition of the intact rock's strength and the strengths of the different disconti-
nuity sets as illustrated by the example represented in Fig. 3.20 and expressed by Equation
(3.83). The validity of this superposition principle was checked by John (1969), Brown
(1970), Yang et al. (1998) and Prudencio & Van Sint Jan (2007) by means of compression
tests on regularly jointed artifi cial model materials. In these tests, dependent on the direc-
tion of loading, different failure modes were observed, including failure of intact rock,
sliding on discontinuities and mixed failure modes. The last may be due to complex fail-
ure mechanisms particularly of non-persistent discontinuities explained in Section 3.3.3.
However, the results of these tests confi rmed to a large extent the superposition principle,
so that from a practical point of view this principle is applicable with suffi cient accuracy.
Strength criteria for rock masses based on the Hoek-Brown criterion (Hoek 1983, Hoek
et al. 1992, Hoek 1994, Hoek et al. 1995, Hoek & Brown 1997, Hoek et al. 2002, Benz
et al. 2008) are generally not suitable to be applied to jointed rock because anisotropy
is not accounted for, which is a decisive characteristic of jointed rock. To overcome this
shortcoming, recently an approach was made to modify the Hoek-Brown criterion for the
prediction of strength of transversely isotropic rock masses (Lee & Pietruszczak 2008).

Post-failure behavior
According to the homogeneous model, the normal strain ε n and the shear strain γ res of a

rock mass with one discontinuity set D being subjected to a normal stress σ n perpendic-

ular to the discontinuities and a shear stress τ res parallel to the discontinuities according

to (3.84) and (3.85) is obtained by a superposition of the strains of the intact rock and
the discontinuities. The latter can be resolved into elastic and viscoplastic parts:

(3.98)

(3.99)

δ s,D el are the elastic displace-
ments which take place before the peak shear strength is reached. Subsequently irrevers-
ible, viscoplastic displacements

δ n,D el and

where s is the mean spacing of discontinuities.

δ s,D vp occur.
According to the homogeneous model, the stress-displacement behavior of discontinu-
ities can be idealized as shown in Fig. 3.27. The elastic displacements for two normal
stress levels

δ n,D vp and

σ n1 and σ n2 are represented by green lines in the τ res - δ s,D and δ n,D - δ s,D dia-

grams in Fig. 3.27 (upper). After the peak shear strength τ res is exceeded, a sudden drop