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Simulation of random fields of soil properties by the local average subdivision method and engineering applications

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Abstract

The seismic performance of oil and natural gas pipelines founded or embedded in earth slopes encompasses great uncertainty related both to the earthquake shaking characteristics and to the natural heterogeneity of geomaterials. Regarding the latter, the parameters of shear strength, stiffness, density, etc., may vary indeed from point to point even within the same soil layer as a result of the natural formation process. Apart from their cross-correlation, such random variables exhibit autocorrelation, in which the soil properties at a given point appear to be spatially correlated with the properties of neighbouring points. Therefore, there is a need to use stochastic methods in the safety evaluation of such systems. Aiming at the reliability assessment of such soil-pipeline systems under seismic shaking, this paper introduces an automated methodology for generating random fields using the Local Average Subdivision (LAS) method by Fenton and Vanmarcke (J Eng Mech 116(8):1733–1749, 1990). Subsequently, it performs rigorous nonlinear dynamic analysis of a given slope using the finite difference method. The automated procedure is used in a Monte-Carlo simulation scheme for computing the probability of exceeding different levels of anticipated permanent slope movement for different levels of shaking intensity. The results demonstrate that the effect of the spatial variability of the soil properties on the permanent displacements of natural slopes is important, leading to a range of variation of about ± 60%.

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References

  1. Fenton, A.G., Vanmarcke, E.H.: Simulation of random fields via local average subdivision. J. Eng. Mech. 116(8), 1733–1749 (1990)

    Article  Google Scholar 

  2. Vazouras, P., Dakoulas, P., Karamanos, S.A.: Soil–structure interaction effects of steel pipelines crossing active seismic faults. J. Soil Dyn. Earthq. Eng. 72, 45–65 (2015)

    Article  Google Scholar 

  3. Sarvanis, G., Karamanos, S.A., Vazouras, P., Mecozzi, E., Lucci, A., Dakoulas, P.: Permanent ground-induced actions in buried pipelines: numerical modeling and experimental verification. J. Earthq. Eng. Struct. Dyn. 47(4), 966–987 (2017)

    Article  Google Scholar 

  4. Fenton, A.G., Griffiths, D.V.: Risk Assessment in Geotechnical Engineering. Wiley, Hoboken (2008)

    Book  Google Scholar 

  5. Griffiths, D.V., Fenton, G.A.: Probabilistic Methods in Geotechnical Engineering. International Centre for Mechanical Sciences. Springer Wien, New York (2007)

    Book  Google Scholar 

  6. Alamanis, N.O.: Effect of the spatial variability of soil properties on the permanent seismic displacements of road slopes. Ph.D. thesis, University of Thessaly, Department of Civil Engineering, Volos, Greece (2017)

  7. Wolfram Research, Inc.: Mathematica, version 11. Champaign, IL (2018). www.wolfram.com

  8. Itasca Consulting Group: Fast Langrangian Analysis of Continua, FLAC v.7. User Manual, Minneapolis, MN (2011)

  9. Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19(90), 297–301 (1965)

    Article  MathSciNet  Google Scholar 

  10. Matheron, G.: The intrinsic random functions and their applications. Adv. Appl. Probab. 5, 439–468 (1973)

    Article  MathSciNet  Google Scholar 

  11. Mantoglou, A., Wilson, J.L.: Simulation of Random Fields with the Turning Bands Method. Massachusetts Institute of Technology, Cambridge (1981). (Report 264)

    Google Scholar 

  12. Griffiths, D.V., Fenton, G.A.: Probabilistic slope stability analysis by finite elements. J. Geotech. Geoenviron. Eng. 130(5), 507–518 (2004)

    Article  Google Scholar 

  13. Fenton, G.A., Griffiths, D.V., Urquhart, A.: A slope stability model for spatially random soils. In: Kiureghian, A., et al. (eds.) Proc. 9th Int. Conf. Applications of Statistics and Probability in Civil Engineering (ICASP9), pp. 1263–1269. Millpress, San Francisco, CA (2003)

  14. Griffiths, D.V., Huang, J., Fenton, G.A.: Influence of spatial variability on slope reliability using 2-D random fields. J. Geotech. Geoenviron. Eng. 135, 1367–1375 (2009)

    Article  Google Scholar 

  15. Griffiths, D.V., Huang, J., Fenton, G.A.: Probabilistic infinite slope analysis. Comput. Geotech. 38, 577–584 (2011)

    Article  Google Scholar 

  16. Fortsakis, P., Stylianidi, E., Kavadas, M.: Slope Stability Analysis using stochastic methods. In: 6th Panhellenic Conference of Geotechnical and Geoenvironmental Engineering, TEE, pp. 1–8. (2010)

  17. Vanmarcke, E.H.: Probabilistic modeling of soil profiles. J. Geotech. Eng. 103(11), 1227–1246 (1977)

    Google Scholar 

  18. Smith, I.M., Griffiths, D.V.: Programming the Finite Element Method, 4th edn. Wiley, New York (2004)

    MATH  Google Scholar 

  19. Gentle, J.E.: Cholesky Factorization. Numerical Linear Algebra for Applications in Statistics, pp. 93–95. Springer, Berlin (1998)

    Book  Google Scholar 

  20. Babu, S.G.L., Mukesh, M.O.: Effect of soil variability on reliability of soil slopes. Geotechnique 54(5), 335–337 (2004)

    Article  Google Scholar 

  21. Cho, S.E.: Effects of spatial variability of soil properties on slope stability. Eng. Geol. 92, 97–109 (2007)

    Article  Google Scholar 

  22. Cheng, Y.M., Lau, C.K.: Slope Stability Analysis and Stabilization, pp. 138–151. Routledge, New York (2008)

    Book  Google Scholar 

  23. Low, B.K., Lacasse, S., Nadim, F.: Slope reliability analysis accounting for spatial variation. Georisk Assess. Manag. Risk Eng. Syst. Geohazards 1(4), 177–189 (2007)

    Article  Google Scholar 

  24. Wolff, T.F.: Probabilistic slope stability in theory and practice. In: Shackelford, C.D., et al. (eds.) Uncertainty in the Geological Environment: From Theory to Practice. Geotechnical Special Publication No. 58, pp. 419–433. ASCE, New York (1996)

    Google Scholar 

  25. Wu, X.Z.: Trivariate analysis of soil ranking correlated characteristics and its application to probabilistic stability assessments in geotechnical engineering problems. Soils Found. 53(4), 540–556 (2013)

    Article  Google Scholar 

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Authors and Affiliations

  1. General Department, University of Thessaly, Vólos, Greece

    Nikolaos Alamanis

  2. Department of Civil Engineering, University of Thessaly, Vólos, Greece

    Panos Dakoulas

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  1. Nikolaos Alamanis
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  2. Panos Dakoulas
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Correspondence to Nikolaos Alamanis.

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Alamanis, N., Dakoulas, P. Simulation of random fields of soil properties by the local average subdivision method and engineering applications. Energy Syst 12, 841–861 (2021). https://doi.org/10.1007/s12667-019-00362-y

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