International Journal of Civil Engineering

, Volume 17, Issue 1, pp 131–143 | Cite as

On the Global Sensitivity Analysis Methods in Geotechnical Engineering: A Comparative Study on a Rock Salt Energy Storage

  • Elham MahmoudiEmail author
  • Raoul Hölter
  • Rayna Georgieva
  • Markus König
  • Tom Schanz
Research Paper


The large number of input factors involved in a sophisticated geotechnical computational model is a challenge in the concept of probabilistic analysis. In the context of model calibration and validation, conducting a sensitivity analysis is substantial as a first step. Sensitivity analysis techniques can determine the key factors which govern the system responses. In this paper, three commonly used sensitivity analysis methods are implemented on a sophisticated geotechnical problem. The computational model of a compressed air energy storage, mined in a rock salt formation, includes many input parameters, each with large amount of uncertainties. Sensitivity measures of different variables involved in the mechanical response of the cavern are computed by different global sensitivity methods, namely, Sobol/Saltelli, Random Balance Design, and Elementary Effect method. Since performing sensitivity analysis requires a large number of model evaluations, the concept of surrogate modelling is utilised to decrease the computational burden. In the following, the accuracy levels of various surrogate techniques are compared. In addition, a comparative study on the applied sensitivity analysis methods shows that the applied sensitivity analysis techniques provide identical parameter importance rankings, although some may also give more information about the system behaviour.


Sensitivity analysis Geotechnical engineering Variance-based methods Elementary Effect Sobol’ indices RBD 



The Authors would like to gratefully acknowledge the support of the German Research Foundation (DFG) through the Collaborative Research Center SFB 837 (subproject C2).


German Research Foundation (DFG)-The Collaborative Research Center SFB 837 “Interaction models for mechanized tunneling”.


  1. 1.
    Khaledi K, Mahmoudi E, Datcheva M, Schanz T (2016) Stability and serviceability of underground energy storage caverns in rock salt subjected to mechanical cyclic loading. Int J Rock Mech Min Sci 86:115–131Google Scholar
  2. 2.
    Sternik K (2017) Elasto-plastic constitutive model for overconsolidated clays. Int J Civ Eng 15:431–440Google Scholar
  3. 3.
    Cacuci DG (2003) Sensitivity and uncertainty analysis, volume 1: theory. CRC Press, Boca RatonzbMATHGoogle Scholar
  4. 4.
    Schanz T, Zimmerer MM, Datcheva M, Meier J (2006) Identification of constitutive parameters for numerical models via inverse approach. Felsbau 24(2):11–21Google Scholar
  5. 5.
    Hamm N, Hall J, Anderson M (2006) Variance-based sensitivity analysis of the probability of hydrologically induced slope instability. Comput Geosci 32(6):803–817Google Scholar
  6. 6.
    Mollon G, Dias D, Soubra A-H (2013) Range of the safe retaining pressures of a pressurized tunnel face by a probabilistic approach. J Geotech Geoenviron Eng 139:1954–1967Google Scholar
  7. 7.
    Miro S, Hartmann D, Schanz T (2014) Global sensitivity analysis for subsoil parameter estimation in mechanized tunneling. Comput Geotech 56:80–88Google Scholar
  8. 8.
    Bérest P, Brouard B (2003) Safety of salt caverns used for underground storage. Oil Gas Sci Technol 58:361–384Google Scholar
  9. 9.
    Mahmoudi E, Khaledi K, von Blumenthal A, König D, Schanz T (2016) Concept for an integral approach to explore the behavior of rock salt caverns under thermo-mechanical cyclic loading in energy storage systems. Environ Earth Sci 75:1069Google Scholar
  10. 10.
    Ratigan WR, Hannum WD (1980) Mechanical behavior of new mexico rock salt in triaxial compression up to 200 c. J Geophys Res 85:891–900Google Scholar
  11. 11.
    Sane S, Desai C, Jenson J, Contractor D, Carlson A, Clark P (2008) Disturbed state constitutive modeling of two pleistocene tills. Quatern Sci Rev 27:267–283Google Scholar
  12. 12.
    Ma L-J, Liu X-Y, Wang M-Y, Xu H-F, Hua R-P, Fan P-X, Jiang S-R, Wang G-A, Yi Q-K (2013) Experimental investigation of the mechanical properties of rock salt under triaxial cyclic loading. Int J Rock Mech Min Sci 62:34–41Google Scholar
  13. 13.
    Hölter R, Mahmoudi E, Schanz T (2015) Optimal sensor location for parameter identification in soft clay. AIP conference proceedings, vol 1684Google Scholar
  14. 14.
    Hölter R, Zhao C, Mahmoudi E, Lavasan AA, Datcheva M, König M, Schanz T (2018) Optimal measurement design for parameter identification in mechanized tunneling. Undergr Space. ISSN 2467-9674.
  15. 15.
    Rocquigny E, Devictor N, Tarantola S (2008) Uncertainty in industrial practice: a guide to quantitative uncertainty management. Wiley, OxfordzbMATHGoogle Scholar
  16. 16.
    Saltelli A, Chan K, Scott EM (2000) Sensitivity analysis, vol 134. Wiley, New YorkzbMATHGoogle Scholar
  17. 17.
    Cukier RI, Fortuin CM, Schuler KE, Petschek AG, Schaibly JH (1973) Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients, I theory. J Chem Phys 59(8):3873–3878Google Scholar
  18. 18.
    Sobol’ IM (1993) Sensitivity estimates for nonlinear mathematical models. Math Modell Comput Exp 1:407–414 (English translation of russian original paper Sobol’ (1990))MathSciNetzbMATHGoogle Scholar
  19. 19.
    Chan K, Saltelli A, Tarantola S (1997) Sensitivity analysis of model output: variance-based methods make the difference. In: Proceedings of the 29th conference on Winter simulation, IEEE Computer Society, pp 261–268Google Scholar
  20. 20.
    Tarantola S, Gatelli D, Mara T (2006) Random balance designs for the estimation of first order global sensitivity indices. Reliab Eng Syst Saf 91(6):717–727Google Scholar
  21. 21.
    Saltelli A, Tarantola S, Chan KPS (1999) A quantitative model-independent method for global sensitivity analysis of model output. Technometrics 41(1):39–56Google Scholar
  22. 22.
    McKay MD (1997) Nonparametric variance-based methods of assessing uncertainty importance. Reliab Eng Syst Saf 57(3):267–279Google Scholar
  23. 23.
    Saltelli A (2002) Making best use of model evaluations to compute sensitivity indices. Comput Phys Commun 145(2):280–297MathSciNetzbMATHGoogle Scholar
  24. 24.
    Saltelli A, Andres T, Ratto M (2008) Global sensitivity analysis. The primer. Wiley, OxfordzbMATHGoogle Scholar
  25. 25.
    Marzban S, Lahmer T (2016) Conceptual implementation of the variance-based sensitivity analysis for the calculation of the first-order effects. J Stat Theory Pract 10(4):589–611MathSciNetGoogle Scholar
  26. 26.
    Dimov I, Georgieva R (2010) Monte carlo algorithms for evaluating Sobol’ sensitivity indices. Math Comput Simul 81:506–514MathSciNetzbMATHGoogle Scholar
  27. 27.
    Koda M, Mcrae GJ, Seinfeld JH (1979) Automatic sensitivity analysis of kinetic mechanisms. Int J Chem Kinet 11(4):427–444Google Scholar
  28. 28.
    Iman RL, Hora SC (1990) A robust measure of uncertainty importance for use in fault tree system analysis. Risk Anal 10(3):401–406Google Scholar
  29. 29.
    Mara TA (2009) Extension of the rbd-fast method to the computation of global sensitivity indices. Reliab Eng Syst Saf 94(8):1274–1281Google Scholar
  30. 30.
    Satterthwaite FE (1959) Random balance experimentation. Technometrics 1(2):111–137MathSciNetGoogle Scholar
  31. 31.
    Nguyen-Tuan L, Lahmer T, Datcheva M, Schanz T (2017) Global and local sensitivity analyses for coupled thermo-hydro-mechanical problems. Int J Numer Anal Meth Geomech 41(5):707–720Google Scholar
  32. 32.
    Saltelli A, Andres T, Homma T (1993) Sensitivity analysis of model output. Comput Stat Data Anal 15(2):211–238zbMATHGoogle Scholar
  33. 33.
    Homma T, Saltelli A (1996) Importance measure in global sensitivity analysis of nonlinear models. Reliab Eng Syst Saf 52(12):1–17Google Scholar
  34. 34.
    Khaledi K, Mahmoudi E, Datcheva M, König D, Schanz T (2016) Sensitivity analysis and parameter identification of a time dependent constitutive model for rock salt. J Comput Appl Math 293:128–138MathSciNetzbMATHGoogle Scholar
  35. 35.
    Hamby DM (1994) A review of techniques for parameter sensitivity analysis of environmental models. Environ Monit Assess 32(2):135–154Google Scholar
  36. 36.
    Morris MD (1991) Technometrics, factorial sampling plans for preliminary computational experiments. Taylor & Francis Ltd., RoutledgeGoogle Scholar
  37. 37.
    Campolongo F, Cariboni J, Saltelli A (2007) An effective screening design for sensitivity analysis of large models. Modelling, computer-assisted simulations, and mapping of dangerous phenomena for hazard assessment. Environ Modell Softw 22(10):1509–1518Google Scholar
  38. 38.
    Hunsche U, Hampel A (1999) Rock salt—the mechanical properties of the host rock material for radio active waste repository. Eng Geol 52:271–291Google Scholar
  39. 39.
    Mahmoudi E, Khaledi K, Miro S, König D, Schanz T (2017) Probabilistic analysis of a rock salt cavern with application to energy storage systems. Rock Mech Rock Eng 50(1):139–157Google Scholar
  40. 40.
    Desai C, Zhang D (1987) Viscoplastic model for geologic material with generalized flow rule. Int J Numer Anal Meth Geomech 11:603–627zbMATHGoogle Scholar
  41. 41.
    Lancaster P, Salkauskas K (1981) Surfaces generated by moving least squares methods. Math Comput 37(155):141–158MathSciNetzbMATHGoogle Scholar
  42. 42.
    Hardy RL (1971) Multiquadric equations of topography and other irregular surfaces. J Geophys Res 76(8):1905–1915Google Scholar
  43. 43.
    Buljak V (2010) Proper orthogonal decomposition and radial basis functions algorithm for diagnostic procedure based on inverse analysis. FME Trans 38:129–136Google Scholar
  44. 44.
    Buljak V (2012) Inverse analysis with model reduction: proper orthogonal decomposition in structural mechanics. Springer, BerlinzbMATHGoogle Scholar
  45. 45.
    Khaledi K, Miro S, König M, Schanz T (2014) Robust and reliable metamodels for mechanized tunnel simulations. Comput Geotech 61:1–12Google Scholar
  46. 46.
    Mullur AA, Messac A (2006) Metamodeling using extended radial basis functions: a comparative approach. Eng Comput 21(3):203–217Google Scholar
  47. 47.
    McKay M, Beckman R (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21:235–239MathSciNetzbMATHGoogle Scholar
  48. 48.
    Sobol’ IM, Myshetskaya EE (2007) On sensitivity estimation for nonlinear mathematical models. Monte Carlo Methods Appl 13(5–6):455–465MathSciNetzbMATHGoogle Scholar

Copyright information

© Iran University of Science and Technology 2018

Authors and Affiliations

  • Elham Mahmoudi
    • 1
    Email author
  • Raoul Hölter
    • 1
  • Rayna Georgieva
    • 2
  • Markus König
    • 1
  • Tom Schanz
    • 1
  1. 1.Department of Civil and Environmental EngineeringRuhr-Universität BochumBochumGermany
  2. 2.Department of Parallel AlgorithmsBulgarian Academy of SciencesSofiaBulgaria

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