Abstract
Actual problems in geotechnical design, e.g., of underground openings for radioactive waste repositories or high-pressure gas storages, require sophisticated constitutive models and consistent parameters for rock salt that facilitate reliable prognosis of stress-dependent deformation and associated damage. Predictions have to comprise the active mining phase with open excavations as well as the long-term development of the backfilled mine or repository. While convergence-induced damage occurs mostly in the vicinity of openings, the long-term behaviour of the backfilled system is dominated by the damage-free steady-state creep. However, because in experiments the time necessary to reach truly stationary creep rates can range from few days to years, depending mainly on temperature and stress, an innovative but simple creep testing approach is suggested to obtain more reliable results: A series of multi-step tests with loading and unloading cycles allows a more reliable estimate of stationary creep rate in a reasonable time. For modelling, we use the advanced strain-hardening approach of Günther–Salzer, which comprehensively describes all relevant deformation properties of rock salt such as creep and damage-induced rock failure within the scope of an unified creep ansatz. The capability of the combination of improved creep testing procedures and accompanied modelling is demonstrated by recalculating multi-step creep tests at different loading and temperature conditions. Thus reliable extrapolations relevant to in-situ creep rates (\(10^{-9}\) to \(10^{-13}\) s\(^{-1}\)) become possible.
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Notes
The effective stress is the norm of the stress deviator, \(\sigma _{\rm eff}=\sqrt{\frac{3}{2}{{\mathrm{tr}}}\,\sigma ^d \sigma ^d}\).
Abbreviations
- \(\epsilon _{\rm cr}\) :
-
Total creep deformation
- \(\epsilon _{\rm cr}^{\rm V}\) :
-
Hardening component of creep deformation
- \(\epsilon _{\rm cr}^{\rm E}\) :
-
Recovery component of creep deformation
- \(\epsilon _{\rm cr}^{\rm S}\) :
-
Damage-induced component of creep deformation
- \(\epsilon _0^{\rm V}\) :
-
Initial hardening
- \(A^{(p)}\), \(\beta\), \(\mu\) :
-
Primary creep parameters
- \(A^{(s)}_{1,2}\), \(Q_{1,2}\), \(n_{1,2}\) :
-
Secondary creep parameters (two-component power law)
- \(A_0\), \(h_0\) :
-
Initial sample cross section and height
- \(\Delta h\) :
-
Reduction in sample height
- \(\epsilon _{\rm ax}=\Delta h/h_0\) :
-
Axial strain
- \(\sigma _{\rm eff}\) :
-
Effective stress, \(\sigma _{\rm eff}=\sqrt{\frac{3}{2}{{\mathrm{tr}}}\,\sigma ^d \sigma ^d}\) with deviatoric stress \(\sigma ^d\)
- \(\sigma _1\), \(\sigma _3\) :
-
Major and minor principal stress
- \(\sigma _{\rm diff}\) :
-
Differential stress, \(\sigma _{\rm diff}=\sigma _1-\sigma _3\)
- T :
-
Temperature
- R :
-
Gas constant, \(R=0.00831\;{\rm kJ}/({\rm mol}\cdot{\rm K})\)
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Acknowledgments
Financial support by the Federal Ministry of Education and Research (BMBF, projects I and II) and the Federal Ministry of Economics and Technology (BMWi, project III), and advisory support by the Project Management Agency Karlsruhe (PTKA-WTE) are gratefully acknowledged. We thank the partners in the “Comparison of Constitutive Models” for the joint projects “Thermo–Mechanical Behaviour of Rock Salt” for the long-lasting and fruitful cooperation.
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Günther, RM., Salzer, K., Popp, T. et al. Steady-State Creep of Rock Salt: Improved Approaches for Lab Determination and Modelling. Rock Mech Rock Eng 48, 2603–2613 (2015). https://doi.org/10.1007/s00603-015-0839-2
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DOI: https://doi.org/10.1007/s00603-015-0839-2