Importance of Small Deviatoric Stresses on the Creep of Rock Salt

Leo L. Van SambeekRESPEC

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.

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