Skip to main content
Springer Nature Link
Log in

Probabilistic risk assessment of earth dams with spatially variable soil properties using random adaptive finite element limit analysis

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

Risk assessment of earth dams is concerned not only with the probability of failure but also with the corresponding consequence, which can be more difficult to quantify when the spatial variability of soil properties is involved. This study presents a risk assessment for an earth dam in spatially variable soils using the random adaptive finite element limit analysis. The random field theory, adaptive finite element limit analysis, and Monte Carlo simulation are employed to implement the entire process. Among these methods, the random field theory is first introduced to describe the soil spatial variability. Then the adaptive finite element limit analysis is adopted to obtain the bound solution and consequence. Finally, the failure probability and risk assessment are counted via the Monte Carlo simulation. In contrary to the deterministic analysis that only a factor of safety is given, the stochastic analysis considering the spatial variability can provide statistical characteristics of the stability and assess the risk of the earth dam failure comprehensively, which can be further used for guiding decision-making and mitigation. Besides, the effects of the correlation structure of strength parameters on the stochastic response and risk assessment of the earth dam are investigated through parametric analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Zhang L, Peng M, Chang D, Xu Y (2016) Dam failure mechanisms and risk assessment. John Wiley & Sons, Singapore

    Book  Google Scholar 

  2. Guo X, Dias D, Carvajal C, Peyras L, Breul P (2021) Modelling and comparison of different types of random fields: case of a real earth dam. Eng Comput. https://doi.org/10.1007/s00366-021-01495-4

    Article  Google Scholar 

  3. Liu X, Wang Y, Li DQ (2019) Investigation of slope failure mode evolution during large deformation in spatially variable soils by random limit equilibrium and material point methods. Comput Geotech 111:301–312. https://doi.org/10.1016/j.compgeo.2019.03.022

    Article  Google Scholar 

  4. Huang J, Lyamin AV, Griffiths DV, Krabbenhoft K, Sloan SW (2013) Quantitative risk assessment of landslide by limit analysis and random fields. Comput Geotech 53:60–67. https://doi.org/10.1016/j.compgeo.2013.04.009

    Article  Google Scholar 

  5. Jiang SH, Huang JS, Griffiths DV, Deng ZP (2022) Advances in reliability and risk analyses of slopes in spatially variable soils: a state-of-the-art review. Comput Geotech 141:104498. https://doi.org/10.1016/j.compgeo.2021.104498

    Article  Google Scholar 

  6. Cheng H, Chen J, Chen R, Chen G, Zhong Y (2018) Risk assessment of slope failure considering the variability in soil properties. Comput Geotech 103:61–72. https://doi.org/10.1016/j.compgeo.2018.07.006

    Article  Google Scholar 

  7. Vanmarcke EH (2010) Random fields: analysis and synthesis. World Scientific Publishing Co Pte Ltd, Singapore

    Book  MATH  Google Scholar 

  8. Griffiths DV, Fenton GA (2004) Probabilistic slope stability analysis by finite elements. J Geotech Geoenviron Eng 130(5):507–518. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(507)

    Article  Google Scholar 

  9. Griffiths DV, Huang J, Fenton GA (2009) Influence of spatial variability on slope reliability using 2-D random fields. J Geotech Geoenviron Eng 135(10):1367–1378. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000099

    Article  Google Scholar 

  10. Hicks MA, Nuttall JD, Chen J (2014) Influence of heterogeneity on 3D slope reliability and failure consequence. Comput Geotech 61:198–208. https://doi.org/10.1016/j.compgeo.2014.05.004

    Article  Google Scholar 

  11. Gholampour A, Johari A (2019) Reliability-based analysis of braced excavation in unsaturated soils considering conditional spatial variability. Comput Geotech 115:103163. https://doi.org/10.1016/j.compgeo.2019.103163

    Article  Google Scholar 

  12. Jiang SH, Liu X, Huang J (2020) Non-intrusive reliability analysis of unsaturated embankment slopes accounting for spatial variabilities of soil hydraulic and shear strength parameters. Eng Comput. https://doi.org/10.1007/s00366-020-01108-6

    Article  Google Scholar 

  13. Xue Y, Miao F, Wu Y, Li L, Meng J (2021) Application of uncertain models of sliding zone on stability analysis for reservoir landslide considering the uncertainty of shear strength parameters. Eng Comput. https://doi.org/10.1007/s00366-021-01446-z

    Article  Google Scholar 

  14. Tabarroki M, Ching J (2019) Discretization error in the random finite element method for spatially variable undrained shear strength. Comput Geotech 105:183–194. https://doi.org/10.1016/j.compgeo.2018.10.001

    Article  Google Scholar 

  15. Chwała M (2021) Upper-bound approach based on failure mechanisms in slope stability analysis of spatially variable c-φ soils. Comput Geotech 135:104170. https://doi.org/10.1016/j.compgeo.2021.104170

    Article  Google Scholar 

  16. Sloan SW (2013) Geotechnical stability analysis. Geotechnique 63(7):531–572. https://doi.org/10.1680/geot.12.RL.001

    Article  Google Scholar 

  17. Ali A, Lyamin AV, Huang J, Sloan SW, Cassidy MJ (2017) Undrained stability of a single circular tunnel in spatially variable soil subjected to surcharge loading. Comput Geotech 84:16–27. https://doi.org/10.1016/j.compgeo.2016.11.013

    Article  Google Scholar 

  18. Zhou H, Liu H, Yin F, Chu J (2018) Upper and lower bound solutions for pressure-controlled cylindrical and spherical cavity expansion in semi-infinite soil. Comput Geotech 103:93–102. https://doi.org/10.1016/j.compgeo.2018.07.011

    Article  Google Scholar 

  19. Tang C, Phoon K (2019) Prediction of bearing capacity of ring foundation on dense sand with regard to stress level effect. Int J Geomech 18(11):04018154. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001312

    Article  Google Scholar 

  20. Wu G, Zhao H, Zhao M, Zhu Z (2021) Stochastic analysis of dual tunnels in spatially random soil. Comput Geotech 129:103861. https://doi.org/10.1016/j.compgeo.2020.103861

    Article  Google Scholar 

  21. Lyamin AV, Sloan SW (2003) Mesh generation for lower bound limit analysis. Adv Eng Softw 34(6):321–338. https://doi.org/10.1016/S0965-9978(03)00032-2

    Article  MATH  Google Scholar 

  22. Lyamin AV, Sloan SW, Krabbenhøft K, Hjiaj M (2005) Lower bound limit analysis with adaptive remeshing. Int J Numer Meth Eng 63(14):1961–1974. https://doi.org/10.1002/nme.1352

    Article  MATH  Google Scholar 

  23. Krabbenhoft K, Lyamin AV, Hjiaj M, Sloan SW (2005) A new discontinuous upper bound limit analysis formulation. Int J Numer Methods Eng 63:1069–1088. https://doi.org/10.1002/nme.1314

    Article  MATH  Google Scholar 

  24. Krabbenhoft K, Lyamin AV (2015) Strength reduction finite-element limit analysis. Geotech Lett 5(4):250–253. https://doi.org/10.1680/jgele.15.00110

    Article  Google Scholar 

  25. Li L, Wang Y (2020) Identification of failure slip surfaces for landslide risk assessment using smoothed particle hydrodynamics. Georisk 14(2):91–111. https://doi.org/10.1080/17499518.2019.1602877

    Article  MathSciNet  Google Scholar 

  26. Borges L, Zouain N, Costa C, Feijóo R (2001) An adaptive approach to limit analysis. Int J Solids Struct 38:1707–1720. https://doi.org/10.1016/S0020-7683(00)00131-1

    Article  MATH  Google Scholar 

  27. Ciria H, Peraire J, Bonet J (2008) Mesh adaptive computation of upper and lower bounds in limit analysis. Int J Numer Methods Eng 75:899–944. https://doi.org/10.1002/nme.2275

    Article  MathSciNet  MATH  Google Scholar 

  28. Cho SE (2014) Probabilistic stability analysis of rainfall-induced landslides considering spatial variability of permeability. Eng Geol 171:11–20. https://doi.org/10.1016/j.enggeo.2013.12.015

    Article  Google Scholar 

  29. Zhang D, Lu Z (2004) An efficient, high-order perturbation approach for flow in random porous media via Karhunen-Loève and polynomial expansions. J Comput Phys 194(2):773–794. https://doi.org/10.1016/j.jcp.2003.09.015

    Article  MATH  Google Scholar 

  30. Yang HQ, Zhang L, Xue J, Zhang J, Li X (2019) Unsaturated soil slope characterization with Karhunen-Loève and polynomial chaos via Bayesian approach. Eng Comput 35(1):337–350. https://doi.org/10.1007/s00366-018-0610-x

    Article  Google Scholar 

  31. Jiang SH, Li DQ, Zhang LM, Zhou CB (2014) Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method. Eng Geol 168:120–128. https://doi.org/10.1016/j.enggeo.2013.11.006

    Article  Google Scholar 

  32. Jiang SH, Li DQ, Cao ZJ, Zhou CB, Phoon KK (2015) Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo simulation. J Geotech Geoenviron Eng 141(2):04014096. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001227

    Article  Google Scholar 

  33. Ghanem R, Spanos PD (1991) Stochastic finite element: a spectral approach. Springer-Verlag, New York

    Book  MATH  Google Scholar 

  34. Phoon KK, Huang SP, Quek ST (2002) Implementation of Karhunen-Loeve expansion for simulation using a wavelet-Galerkin scheme. Probab Eng Mech 17(3):293–303. https://doi.org/10.1016/S0266-8920(02)00013-9

    Article  Google Scholar 

  35. Bozorgpour MH, Binesh SM, Rahmani R (2021) Probabilistic stability analysis of geo-structures in anisotropic clayey soils with spatial variability. Comput Geotech 133:104044. https://doi.org/10.1016/j.compgeo.2021.104044

    Article  Google Scholar 

  36. Li DQ, Jiang SH, Cao ZJ, Zhou W, Zhou CB, Zhang LM (2015) A multiple response surface method for slope reliability analysis considering spatial variability of soil properties. Eng Geol 187:60–72. https://doi.org/10.1016/j.enggeo.2014.12.003

    Article  Google Scholar 

  37. Liao K, Wu YP, Miao FS, Li LW, Xue Y (2021) Time-varying reliability analysis of Majiagou landslide based on weakening of hydro-fluctuation belt under wetting-drying cycles. Landslides 18(1):267–280. https://doi.org/10.1007/s10346-020-01496-2

    Article  Google Scholar 

  38. Jiang SH, Huang J, Yao C, Yang J (2017) Quantitative risk assessment of slope failure in 2-D spatially variable soils by limit equilibrium method. Appl Math Model 47:710–725. https://doi.org/10.1016/j.apm.2017.03.048

    Article  MathSciNet  MATH  Google Scholar 

  39. Bishop CM (2006) Pattern recognition and machine learning. Springer, Berlin

    MATH  Google Scholar 

  40. Wang ZZ, Xiao C, Goh SH, Deng MX (2021) Metamodel-based reliability analysis in spatially variable soils using convolutional neural networks. J Geotech Geoenviron Eng 147(3):04021003. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002486

    Article  Google Scholar 

  41. van Genuchten MT (1980) A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44(5):892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x

    Article  Google Scholar 

  42. Krahn J (2004) Seepage modeling with SEEP/W: an engineering methodology. GEO-SLOPE International Ltd, Calgary, Alberta, Canada

    Google Scholar 

  43. El-Ramly H, Morgenstern NR, Cruden DM (2003) Probabilistic stability analysis of a tailings dyke on presheared clay-shale. Can Geotech J 40:192–208. https://doi.org/10.1139/t02-095

    Article  Google Scholar 

  44. Phoon KK, Kulhawy FH (1999) Characterization of geotechnical variability. Can Geotech J 36(4):612–624. https://doi.org/10.1139/t99-038

    Article  Google Scholar 

Download references

Acknowledgements

This research is supported by the National Natural Science Foundation of China (No. 41977244 and No. 42007267). The first author is supported by China Scholarship Council (CSC) as a visiting scholar at the Leibniz University Hannover, under grant No. 202006410089. All support are gratefully acknowledged.

Author information

Authors and Affiliations

  1. Faculty of Engineering, China University of Geosciences, Wuhan, 430074, China

    Kang Liao, Yiping Wu & Fasheng Miao

  2. Institute for Risk and Reliability, Leibniz University Hannover, 30167, Hannover, Germany

    Kang Liao & Michael Beer

  3. Department of Civil and Environmental Engineering, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Yutao Pan

Authors
  1. Kang Liao
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Yiping Wu
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Fasheng Miao
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Yutao Pan
    View author publications

    You can also search for this author inPubMed Google Scholar

  5. Michael Beer
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Yiping Wu.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liao, K., Wu, Y., Miao, F. et al. Probabilistic risk assessment of earth dams with spatially variable soil properties using random adaptive finite element limit analysis. Engineering with Computers 39, 3313–3326 (2023). https://doi.org/10.1007/s00366-022-01752-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-022-01752-0

Keywords