SALT Workshop

1. 1
Importance of Small Deviatoric Stresses on the Creep of Rock Salt
Leo L. Van Sambeek
RESPEC
Rapid City, South Dakota
Creep is recognized as rock salt’s primary deformation mechanism based on many years’ of
underground observations in salt and potash mines and laboratory testing. A common aspect of
these observations, however, is that the measured creep deformations (rates) typically resulted
from relative large rock stresses – whether in underground or in the laboratory. Because the
preponderance of data are creep rates at these large stresses, the creep laws developed from the
data are representative for large stresses, but the creep laws might not be suitable for small
stresses. In general this was not considered a problem until well-controlled field studies of
structures in rock salt with pre-test and post-test numerical modeling of those field studies
consistently under-predicted the measured behavior. A culprit in producing the too-small
calculated response is that the commonly-used creep laws fail to predict the significant creep at
small deviatoric stresses. Consequently, too-small structural responses are calculated. The
prevailing argument has been that most of the creep deformation in a structure surely results
because of the faster creep in the high-stress regions, and that ignoring or under-predicting slow
creep in the lower-stress regions is inconsequential. That prevailing argument is wrong for one
simple reason: on a volume basis, the vast majority of most salt structures has small stresses,
and the cumulative effect of this large volume dominates or at least influences the structural
response.
Since the stress distribution around the structure depends on the active creep mechanisms, a
complex multi-mechanism creep can be simplified by using a piece-wise linear (or multilinear
segmented) representation. A general solution was developed for
multilinear creep law with three or more power-law segments, which
allows easy estimation of the influence for particular combinations of
different stress exponents. For example, creep strain rates as a
function of a low-, multiple intermediate-, and a high-stress regime
are hypothetically illustrated in figure. Using an analytical solution
for stress distributions around a circular opening (open wellbore or
cavern) for a multilinear segmented creep law reveals a factor of 10
increase in volumetric closure rate when including four creep-law
segments with progressively smaller stress exponents but larger
coefficients compared to a single segment with the same largest stress exponent and a smallest
coefficient. In retrospect, such a result is mandatory even in a qualitative sense. The principle of
strain compatibility requires that as an element of salt creeps “toward” the opening, another
element of salt must creep into the formerly occupied location. In other words, the deformation
caused by creep cannot create any voids or change in the volume of salt. Nearest the opening, the
effective stresses are greatest; farther from the opening, the effective stress is smaller; however,
the volume of salt with smaller effective stresses is vastly greater than the volume of salt with
larger effective stresses. In an axisymmetric situation, the “radius-squared deformation
dependency” must be the same for each area. If not, either a void in the salt would develop or the
volume of salt would need to change, and neither is permissible in pure creep.