53rd U.S. Rock Mechanics/Geomechanics Symposium,
New York City, New York
2019. American Rock Mechanics Association
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ABSTRACT: Steady state creep rate of rock salt often is described through the Norton-Hoff (NH) law. Recent experimental results suggest that this law must be modified in the low deviatoric stress range. It is suggested to adopt, instead of a linear law, a step-wise linear law in the (Equation) plot, (Bilinear law, or BL). Predictions of NH and BL laws are compared in the case of an elongated cylindrical cavern submitted to a varying internal pressure when Poisson's ratio is v = 0.5. These constitutive laws do not include transient creep behavior; however, in a cavern, transient creep closure is observed; it is much longer when NH law is adopted (rather than BL law). When cavern pressure is increased abruptly after a long idle period, effective tensile stresses appear at cavern wall; they are larger and remain tensile longer when the NH model is selected. When cavern pressure is cycled, the average creep closure rate is much faster than when cavern pressure is kept constant; this is all the more true when the BL model is selected.
A uniaxial formulation of salt behavior can be written: (Equation) (contractions and compressions are positive in this Section) where (Equation) is the strain rate, (Equation) the strain rate, E is the Young's modulus, (Equation) the thermal expansion coefficient, (Equation) the temperature rate, (Equation) the transient strain rate and (Equation) the steady state creep rate. In the following, the transient strain rate is disregarded,(Equation). It is often accepted that in a (Equation) plot, steady-state behavior can be represented by straight lines, each of which corresponds to a given temperature or: (Equation) (“power law”, or Norton-Hoff (NH)- law), where, in principle, A and n are two constants (when temperature is fixed) and n is in the 3-5 range, Bérest (2013).
However, this assertion is based on creep tests performed in the 5 MPa < σ < 20 MPa stress range whose results are extrapolated to smaller stresses, σ < 5 MPa. In fact, recent tests (Bérest et al., 2005 and Bérest et al., 2019) performed under small deviatoric stresses (0.1 MPa < σ 3 Mpa) confirm a prediction made by Spiers et al. (1990) and Urai et al. (2007): in this low stress domain, pressure solution is the main deformation mechanism (rather than dislocation creep); strain rate is strongly influenced by grain size and brine amount in the sample; the exponent of the power law is p = 1, as suggested by a paper published by Herchen et al., 2018 (Figure 1). In this context, the NH-law must be modified. Such a modification was suggested by several authors, for instance Marketos et al. (2016) or Cornet et al. (2017) and Cornet et al. (2018). In this paper it is suggested to adopt a simple “bilinear” law as represented in a (Equation) plot by Fig. 2 (temperature is constant):
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