Civil Engineering Reference
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while at high strain rates and stress rates brittle failure is observed (Döring & Kiehl
1996). Thus, after failure, the strength depending on the loading rate reduces until the
residual strength, also referred to as “long-term strength”, is reached.
In the case of unloading, the so-called “healing boundary”, which is not represented in
Fig. 5.2, forms the upper limit of the compaction zone. Between the dilatancy boundary
and the healing boundary neither healing nor further damage occurs during unloading.
In this zone strains due to unloading are associated with constant volume deformations.
Below the healing boundary the rock salt is compacted not only due to elastic strains
but also due to the closing of microcracks, which may lead to a healing of damage (Hou
1997, Hou 2003, Hou & Lux 2002).
The
σ
eff
plane can be divided by the uniaxial stress path (Fig. 5.2). To the left of
this line at least one principal stress is a tensile stress while to the right of this line all
principal stresses are compressive stresses. The intersection points of the uniaxial stress
line with the dilatancy boundary and the peak strength specify the uniaxial yield stress
σ
f
and the uniaxial compressive strength
σ
m
-
σ
c
, respectively (Fig. 5.2).
WBI has undertaken an engineering approach to describe the complex constitutive be-
havior of rock salt including primary, secondary and tertiary creep as well as failure
and post-failure behavior (Kiehl et al. 1998, Kiehl & Reim 1999, Wittke 2000b, Kiehl &
Erichsen 2002, Erichsen 2006). Since this model was established for isothermal condi-
tions the temperature dependence of creep is not accounted for.
The structure of this stress-strain law in its one-dimensional form can be described with
the aid of the rheological model represented in Fig. 5.3. This consists of a series of fi ve
different rheological bodies each of them corresponding to one strain component:
-
el
to describe the elastic behavior
a linear elastic strain component (spring)
ε
-
a viscoplastic strain component (strain hardening sliding element with a dashpot in
parallel)
p
to describe primary creep
ε
s
to describe secondary creep
-
a viscose strain component (dashpot)
ε
-
a viscoplastic strain component (strain softening sliding element with a dashpot in
parallel)
t
to describe tertiary creep
ε
-
a viscoplastic strain component (a further strain softening sliding element with a
dashpot in parallel)
vp
to describe post-failure behavior.
All strain components except the elastic component
ε
el
are irreversible. According to
experience, elastic deformation, tertiary creep and deformations that occur after failure
can produce volumetric strain
ε
ε
V
while primary and secondary creep do not lead to
volume changes (Fig. 5.3). The constitutive equations are formulated as rate equations
because of the time dependency of the stress-strain behavior.
According to Hooke's law, the elastic strain rate
is proportional to the stress rate
(5.7)
In (5.7) isotropic elastic behavior described by the elastic constants E and
ν
is assumed.
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