Salt Disposal of Heat-Generating Nuclear Waste

terms of principal stresses. Stress states that led to dilation were defined in terms
of the first invariant of the traditional Cauchy stress tensor, I 1 , and the second
invariant of the deviatoric stress tensor, J 2 . These invariants are related to mean
(or confining) stress and deviatoric stress, respectively, and are defined as
follows:
I
1
= 3σ m
= σ
1
+ σ
2
+ σ
3
J
1/ 2
2
2
2
2
[( σ −σ
) + ( σ −σ
) + ( σ − ) ]
⎧1
= ⎨ 1 2 2 3 3
σ
1
⎩6
⎫
⎬
⎭
1/ 2
where σ m is the mean stress and σ 1 , σ 2 , and σ 3 are the three principal stress
components for a particular type of test. Using these definitions, Van Sambeek,
Ratigan, and Hansen (1993) demonstrated that a clear delineation in the I 1 – J 2
stress space exists between conditions that cause dilation and those that do not,
regardless of the type of salt or type of test considered. They suggested an
empirical relationship to divide dilating stress states from nondilating stress states
and expressed this relationship as follows:
J
2
= 0.
27I
This relationship is called the stress-invariant model and has been used for several
applications in analyses for of drift geotechnical barriers and shaft seal systems.
The investigations of damage evolution have benefited from collaborations with
international researchers. SNL has a long-standing collaboration with peers in
European salt programs, most notably with the Bundesanstalt für
Geowissenschaften und Rohstoffe (BGR). Salt researchers at the BGR have led
development of a constitutive relationship between dilatancy and permeability
(e.g., Cristescu and Hunsche 1998, Hunsche and Schulze 2000, Schulze 2007).
Their experiments and theory show that dilatancy (also called volume change or
damage) is linearly increasing with creep deformation under dilatant conditions
and decreasing or healing with time in the compressive domain.
The stress-invariant dilatancy model has been used in structural calculations for
approximately 10 years and remains a viable tool for engineering purposes and
can be coupled with numerical analyses to predict disturbed or damaged zones
around a typical waste disposal room. The stress-invariant model quantifies
neither the level of damage nor the increase in permeability associated with the
DRZ. These and other questions remain with respect to DRZ healing and affect
the uncertainty of repository performance analyses, particularly with HLW.
2.4.1.5 Laboratory Healing Studies
In laboratory tests Costin and Wawersik (1980), Brodsky (1990), and Pfeifle and
Hurtado (1998) demonstrated that the damage evolution process in salt is
1
30