Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 56

fl ow rule is applied, the viscoplastic volumetric strain is often overestimated. Therefore
the dilatancy angle is usually chosen to be smaller than φ IR . Then we are talking about a

“non-associated fl ow rule”. If ψ IR = 0 no volume increase of the intact rock occurs after

peak shear strength is exceeded. Thus, the dilatancy angle has a marked infl uence on the
viscoplastic strains and also on the stresses if volumetric strain is confi ned.
The dilatancy angle, among others, is dependent on the stress level and the viscoplas-
tic shear strain (Detournay 1986, Lai (2002), Yuan & Harrison 2004, Alejano & Alonso
2005, Chen et al. 2007). At large shear deformation and high confi ning stress therefore,
as a rule, volumetric viscoplastic strain will be overestimated when using a constant dila-
tancy angle which is not equal to zero. However, for reasons already discussed in Section
3.2.2 the range of high confi ning stress is not very relevant for civil engineering structures
in rock, and large deformations are usually not admitted in rock engineering. However,
if in the surrounding of a tunnel or underground opening the strength of the intact rock
is exceeded in a large area, major viscoplastic deformations may occur. In such a case it
may be useful to assume zero dilatancy angle after a certain viscoplastic volumetric strain
has occurred. Such conditions are referred to as “squeezing rock conditions” (Chapter 4).

If in squeezing rock the rock mass pressure cannot be carried by an immediate installa-
tion of the support a yielding support is required (Section 4.3). In such cases large time
dependent displacements are allowed to occur and the viscosity η IR of the intact rock is

of importance for evaluation of the time dependency of the stresses and strains.
Tensile failure in isotropic intact rock is described by an associated fl ow rule:

(3.39)

Intact rocks with planar grain structure
If in case of an intact rock with planar grain structure the peak strength is exceeded on
the isotropic plane the viscoplastic strain rate is calculated as

(3.40)

with

(3.41)

and

(3.42)

in the case of a shear failure and

(3.43)

in the case of a tensile failure.