Rock Salt - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 122

(5.23)

with

(5.24)

In the σ m - σ eff plane, Ff fi = 0 defi nes the peak strength of rock salt (Fig. 5.2), σ c is the uncon-

fi ned compressive strength and φ the friction angle. According to (5.24), the magnitude of

ε v t and by the magnitude of the failure mod- the compressive strength σ c is controlled by

ulus N. The upper limit of σ c is the compressive strength of the undisturbed rock salt σ c0 .

Thus, σ c is dependent on the rate of loading as is observed in uniaxial compression tests

(Döring & Kiehl 1996).

σ fi is assumed to be the lower limit of σ c because, at stresses smaller

than σ fi , no failure occurs. On the other hand, large tertiary volumetric strains lead to a

reduction of

σ c down to σ fi = 0. Therefore the dilatancy boundary and the peak strength at

σ c = σ fi = 0 are often referred to as the “long-term strength” of rock salt, which is im-

portant for the long-term stability of large openings in rock salt such as storage caverns.
In (5.21)

η fi is the viscosity of rock salt with regard to the post-failure behavior. After fail-
ure, an instantaneous drop from the peak strength (Ff fi = 0) down to the residual strength
(F fi * = 0) is assumed. The yield function Ff* fi * is expressed in terms of the residual friction
angle

* and the residual unconfi ned compressive strength

σ c * .

φ

The plastic potential Qf fi in (5.21) is defi ned as

(5.25)

Q fi corresponds to Q t but the dilatancy angle is set equal to zero. Therefore viscoplastic
strains due to shear failure do not lead to further volumetric strains. The usefulness of
such a dilatancy control was pointed out in Section 3.2.3.
The yield functions Ff t , F fi and F fi * have the form of the Drucker-Prager yield criteria
(Drucker & Prager 1952). This is because the shear strength of rock salt is dependent
on the intermediate principal normal stress and not independent of this fi gure, as can
normally be assumed for isotropic intact rocks (Section 3.2.2). Otherwise it would not
be possible to represent the dilatancy boundary and the peak shear strength in a

σ m
diagram (Fig. 5.2). The dependency of the shear strength on the intermediate principal
normal stress was confi rmed by the results of some 250 uniaxial, biaxial and true tri-
axial compression tests carried out on cubical-shaped specimens of rock salt. Triaxial
compression tests with

σ eff -

σ 1 > σ 2 = σ 3 resulted in up to 30% higher shear strengths than

triaxial extension tests with σ 1 = σ 2 > σ 3 (Hunsche & Albrecht 1990, Hunsche 1992a,

Hunsche 1994).
Although the relationship between σ m , for both the dilatancy boundary and

the peak strength, are nonlinear (Fig. 5.2) these curves in (5.18) and (5.22) are approx-
imated by straight lines. As will be shown below, however, this approximation leads to
reasonable agreement with the results of creep tests and fi eld measurements.

σ eff and