Finite element-based probabilistic stability analysis of rock-fill tailing dam considering regional seismicity

  • A. HegdeEmail author
  • Tanmoy Das
Technical Note


The recent tailing dam failure in Brazil has again emphasized the need of performing robust stability analysis prior to construction. This paper demonstrates the probabilistic dynamic stability analysis of tailing dams considering an existing rock-fill tailing dam in India. The stability analysis was performed using 2D finite element-based package RS2. In the probabilistic analysis, the strength parameters such as cohesion (c) and the friction angle (φ) were considered as random variables. In total, 3000 numbers of samples were generated assuming a normal distribution. Monte Carlo simulation was used to evaluate the probability of failure (PoF) and reliability index. Strength reduction method was used for the finite element analyses. A pseudo-static seismic loading was incorporated in the strength reduction analysis to check the seismic stability of the dam. A factor of safety (FoS) of 1.15 was observed from the deterministic analysis for downstream slope. For the same case, the probabilistic analysis provided a mean FoS of 1.19 with 5.46% probability of failure. The FoS values and the locations of the critical failure surface obtained by the limit equilibrium method and finite element method were compared. The observed FoS values were found to be higher than the values specified in the IS 7894-1975 (reaffirmed in 1997) and ANCOLD (1999). In the case of pseudo-static approach, the maximum displacement of 0.53 m was observed in the slope. Furthermore, nonlinear dynamic stability analysis was performed to simulate a true earthquake event. The permanent deformation of the slope after the earthquake was found to be 0.40 m. The zone of failure observed in both pseudo-static and nonlinear dynamic stability analyses was found to be the same. Overall, the results revealed that the spatial variability of the soil significantly influences the FoS values.


Tailing dam Random variable Monte Carlo simulation Strength reduction method Spatial variability 

List of symbols


Cohesion (KPA)


Factored cohesion (kPa)


Coefficient of variation in normal random variables (dimensionless)


Standard normal deviate (dimensionless)


Young’s modulus (MPa)


Spatial element size (m)


Maximum frequency (Hz)


Probability density function of normal random variables (dimensionless)


Shear modulus of soil (GPa)


Number of random variables (dimensionless)


Number of sample having critical SRF less than or equal to 1 (dimensionless)


Total number of sample (dimensionless)


Probability of failure (%)


Minimum number of realization (dimensionless)


Reliability index (dimensionless)


Normal random variable (dimensionless)


Strength reduction factor (dimensionless)


Shear wave speed (m/s)

\( \alpha_{M} \)

Rayleigh alpha constant (s − 1)

\( \beta_{K} \)

Rayleigh beta constant (s)

\( \gamma \)

Unit weight of soil (kN/m3)

\( \varepsilon \)

Relative percentage error in estimating probability of failure (%)

\( \zeta_{i} \)

Damping ratio for mode i (%)

\( \lambda \)

Wave length associated with the highest frequency component (m)

\( \mu_{s} \)

Mean of normal random variables (dimensionless)

\( \mu_{{{\text{SRF}} }} \)

Mean of critical SRF values (dimensionless)

\( \nu \)

Poisson’s ratio (dimensionless)

\( \rho \)

Bulk unit weight of soil (kN/m3)

\( \sigma_{n} \)

Normal stress in soil (kN/m2)

\( \sigma_{s} \)

Standard deviation of normal random variables (dimensionless)

\( \sigma_{\text{SRF}} \)

Standard deviation of critical SRF values (dimensionless)

\( \tau_{f} \)

Shear stress in soil on the sliding surface (kN/m2)

\( \varphi \)

Friction angle (°)

\( \varphi_{f} \)

Factored friction angle (°)

\( \omega_{i} \)

Natural frequency of mode i (rad/s)


  1. 1.
    ICOLD (2001) Tailings dams: risk of dangerous occurrences: lessons learnt from practical experiences. Bulletin (International Commission on Large Dams) p 121Google Scholar
  2. 2.
    UNEP (1996) Environmental and safety incidents concerning tailings dams at mines: results of a survey for 1980–1996. Mining Journal Research Services & United Nations Environment Programme & United Nations. Department of Humanitarian Affairs, ParisGoogle Scholar
  3. 3.
    Rico M, Benito G, Salgueiro AR, Díez-Herrero A, Pereira HG (2008) Reported tailings dam failures. J Hazard Mater 152:846–852CrossRefGoogle Scholar
  4. 4.
    USCOLD Committee on Tailings Dams (1994) Tailings dam incidents. U.S. Committee on Large Dams, DenverGoogle Scholar
  5. 5.
    El-Ramly H, Morgenstern NR, Cruden DM (2002) Probabilistic slope stability analysis for practice. Can Geotech J 39:665–683CrossRefGoogle Scholar
  6. 6.
    Christian JT, Ladd CC, Baecher GB (1994) Reliability applied to slope stability analysis. J Geotech Eng 120(12):2180–2207CrossRefGoogle Scholar
  7. 7.
    Chowdhury RN, Xu DW (1995) Geotechnical system reliability of slopes. Reliability Engineering & System Safety 47(1995):141–151CrossRefGoogle Scholar
  8. 8.
    Malkawi AIH, Hassan WF, Abdulla FA (2000) Uncertainty and reliability analysis applied to slope stability. Struct Saf 22(2000):161–187CrossRefGoogle Scholar
  9. 9.
    Luzi L, Pergalani F, Terlien MTJ (2000) Slope vulnerability to earthquakes at subregional scale, using probabilistic techniques and geographic information systems. Eng Geol 58(2000):313–336CrossRefGoogle Scholar
  10. 10.
    Bhattacharya G, Jana D, Ojha S, Chakraborty S (2003) Direct search for minimum reliability index of earth slopes. Comput Geotech 30(2003):455–462CrossRefGoogle Scholar
  11. 11.
    Zhao HB (2008) Slope reliability analysis using a support vector machine. Comput Geotech 35(2008):459–467CrossRefGoogle Scholar
  12. 12.
    Kavvadas M, Karlaftis M, Fortsakis P, Stylianidi E (2009) Probabilistic analysis in slope stability. In Proceedings of the 17th international conference on soil mechanics and geotechnical engineering, pp 1650–1653Google Scholar
  13. 13.
    Queiroz IM (2016) Comparison between deterministic and probabilistic stability analysis, featuring consequent risk assessment. International Journal of Geotechnical and Geological Engineering 10(6):636–643Google Scholar
  14. 14.
    Sitharam TG, Hegde A (2017b) Probabilistic seismic slope stability analyses of rock fill tailing dams: a case study. In Proceedings of the 19th international conference on soil mechanics and geotechnical engineering, technical committee, vol 210, pp 2439–2442Google Scholar
  15. 15.
    Sitharam TG, Hegde A (2019) A case study of probabilistic seismic slope stability analysis of rock fill tailing dam. Int J Geotech Earthq Eng 10(2):43–60CrossRefGoogle Scholar
  16. 16.
    Zou JZ, Williams DJ, Xiong WL (1995) Search for critical slip surfaces based on finite element method. Can Geotech J 32(2):233–246CrossRefGoogle Scholar
  17. 17.
    Griffiths DV, Lane PA (1999) Slope stability analysis by finite elements. Geotechnique 48(3):387–403CrossRefGoogle Scholar
  18. 18.
    Zheng YR, Zhao SY, Kong WX, Deng CJ (2005) Geotechnical engineering limit analysis using finite element method. Rock Soil Mech 26(1):163–168Google Scholar
  19. 19.
    Griffiths DV, Marquez RM (2007) Three-dimensional slope stability analysis by elasto-plastic finite elements. Ge ´otechnique 57(6):537–546Google Scholar
  20. 20.
    Baba K, Bahi L, Ouadif L, Akhssas A (2012) Slope stability evaluations by limit equilibrium and finite element methods applied to a railway in the moroccan rif. Open J Civil Eng 2:27–32CrossRefGoogle Scholar
  21. 21.
    Sharma LK, Umrao RK, Singh R, Ahmad M, Singh TN (2017) Stability investigation of hill cut soil slopes along national highway 222 at malshej ghat, maharashtra. J Geol Soc India 89:165–174CrossRefGoogle Scholar
  22. 22.
    Zienkiewicz OC, Humpheson C, Lewis RW (1975) Associated and nonassociated visco-plasticity and plasticity in soil mechanics. Geotechnique 25(4):671–689CrossRefGoogle Scholar
  23. 23.
    Xu B, Low BK (2006) Probabilistic stability analyses of embankments based on finite-element method. J Geotech Geoenviron Eng 132(11):1444–1454CrossRefGoogle Scholar
  24. 24.
    Cheng YM, Lansivaara T, Wei WB (2007) Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods. Comput Geotech 34(2007):137–150CrossRefGoogle Scholar
  25. 25.
    Maji VB (2017) An insight into slope stability using strength reduction technique. J Geol Soc India 89:77–81CrossRefGoogle Scholar
  26. 26.
    Sitharam TG, Hegde A (2017) Stability analysis of rock-fill tailing dam: an Indian case study. Int J Geotech Eng 11(4):332–342CrossRefGoogle Scholar
  27. 27.
    Duncan JM (1996) State of the art: limit equilibrium and finite-element analysis of slopes. J Geotech Eng 122(7):577–596CrossRefGoogle Scholar
  28. 28.
    IS 1893(I) (1984) Criteria for earthquake resistant design of the structures. Indian Standard, New DelhiGoogle Scholar
  29. 29.
    Lumb P (1966) The variability of natural soils. Can Geotech J 3:74–97CrossRefGoogle Scholar
  30. 30.
    Lee IK, White W, Ingles OG (1983) Geotechnical engineering. Pitman, LondonGoogle Scholar
  31. 31.
    Hahn GJ, Shapiro SS (1967) Statistical model in engineering. Wiley, New YorkGoogle Scholar
  32. 32.
    Chok YH (2008) Modelling the effects of soil variability and vegetation on the stability of natural slopes. Doctoral thesis, The University of Adelaide, AustraliaGoogle Scholar
  33. 33.
    IS 7894 (1975) Code of practice for the stability analysis of the earth dams. Indian Standard, New DelhiGoogle Scholar
  34. 34.
    ANCOLD (1999) Guidelines on tailings dam design, construction and operation. Australian National Committee on Large DamGoogle Scholar
  35. 35.
    Dell’Avanzi E, Sayão A (1998) Avaliação da probailidade de rupture de taludes”. Congresso Brasileiro de Mecânica dos Solos e Engenharia Geotécnica 11(2):1289–1295Google Scholar
  36. 36.
    Seed HB (1979) Considerations in the earthquake-resistant design of earth and rockfill dams. In Nineteenth rankine lecture, Geotechnique, vol 29(3), pp 215–263Google Scholar
  37. 37.
    Griffrin MEH, Franklin AG (1984) Rationalizing the seismic coefficient method. Final Report, Miscellaneous Paper GL-84-13. Waterways Experiment Station, U.S. Army Corps of Engineers, VicksburgGoogle Scholar
  38. 38.
    Kavazanjian EJ, Matasovic N, Hamou TH, Sabatini PJ (1997) Geotechnical engineering circular #3, Design guidance: geotechnical earthquake engineering for highways, vol 1, design principles. Federal Highway Administration, U.S. Department of Transportation, WashingtonGoogle Scholar
  39. 39.
    Ang AHS, Tang WH (2007) Probability concepts in engineering. Wiley, New JerseyGoogle Scholar
  40. 40.
    Arya VK, Holden HD (1978) Deconvolution of seismic data—an overview. IEEE Trans Geosci Electron 16(2):95–98CrossRefGoogle Scholar
  41. 41.
    Kuhlemeyer RL, Lysmer J (1973) Finite element method accuracy for wave propagation problems. J Soil Mech Found Div 99(5):421–427Google Scholar
  42. 42.
    Nielsen AH (2006) Absorbing boundary conditions for seismic analysis in ABAQUS. ABAQUS Users’ ConferenceGoogle Scholar
  43. 43.
    Çetin M, Mengi Y (2003) Transmitting boundary conditions suitable for analysis of dam reservoir interaction and wave load problems. Appl Math Model 27(2003):451–470CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringIndian Institute of Technology PatnaPatnaIndia

Personalised recommendations