Skip to main content
SpringerLink
Log in

Seismic Stability of Non-homogenous Cohesive Soil by Using Calculus of Variation

  • Conference paper
  • First Online:
Local Site Effects and Ground Failures

Part of the book series: Lecture Notes in Civil Engineering ((LNCE,volume 117))

Abstract

In this article, the factor of safety of a cohesive soil slope subjected to seismic load is determined by employing the variational method and pseudostatic analysis. Unlike the conventional limit equilibrium method, there is no requirement to consider any kinematical or static assumption in the variational method. The factor of safety (F) is defined as a functional which is minimized by using the Euler–Lagrangian equation. The (i) transversality and boundary conditions are imposed at the intersection of slip surface, and the slope surface, and (ii) continuity and natural boundary states are forced at the intermediate point of the slip surface. The soil is considered to be completely saturated and loaded under undrained conditions. The cohesion of the soil is assumed to increase linearly with depth. The critical slip surface and consequently critical factor of safety, Fs is being obtained by varying the slope geometry, soil properties, and seismic loadings. The available solutions compare quite well with the convenient solution for the pseudostatic slope stability analysis. The proposed design charts will be quite useful to practicing engineers.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Baker R (2003) Sufficient conditions for existence of physically significant solutions in limiting equilibrium slope stability analysis. Int J Solids Struct 40:3717–3735

    Article  Google Scholar 

  2. Baker R, Garber M (1978) Theoretical analysis of the stability of slopes. Geotechnique 28(4):395–411

    Article  Google Scholar 

  3. Baker R, Shukha R, Operstein V, Frydman S (2006) Stability charts for pseudostatic slope stability analysis. Soil Dyn Earthq Eng 26(9):813–823

    Article  Google Scholar 

  4. Bishop AW (1955) The use of the slip circle in the stability analysis of slopes. Geotechnique 5(1):7–17

    Article  Google Scholar 

  5. Booker JR, Davis EH (1972) A note on a plasticity solution to the stability of slopes in inhomogenous clays. Géotechnique 22(3):509–513

    Article  Google Scholar 

  6. Chai J, Carter JP (2009) Simulation of the progressive failure of an embankment on soft soil. Comput Geotech 36(6):1024–1038

    Article  Google Scholar 

  7. Chen J, Yang Z, Hu R, Zhang H (2016) Study on the seismic active earth pressure by variational limit equilibrium method. Hindawi Publishing Corporation Shock and Vibration, pp 1–11

    Google Scholar 

  8. Chen WF, Snitbhan N, Fang HY (1975) Stability of slopes in anisotropic, non-homogeneous soils. Can Geotech J 12(1):146–152

    Article  Google Scholar 

  9. Chen ZY, Morgenstern NR (1983) Extensions to the generalized method of slices for stability analysis. Can Geotech J 20(1):104–119

    Article  Google Scholar 

  10. Duncan JM (1996) State of the art: limit equilibrium and finite-element analysis of slopes. J Geotech Eng 122(7):577–596

    Article  Google Scholar 

  11. Fellenius W (1936) Calculation of stability of earth dam. In: Transactions 2nd congress large dams, Washington, DC, vol 4, pp 445–462

    Google Scholar 

  12. Gens A, Hutchinson JN, Cavounidis S (1988) Three-dimensional analysis of slides in cohesive soils. Geotechnique 38(1):1–23

    Article  Google Scholar 

  13. Gibson RE, Morgenstern N (1962) A note on the stability of cuttings in normally consolidated clays. Geotechnique 12(3):212–216

    Article  Google Scholar 

  14. Griffiths DV, Yu X (2015) Another look at the stability of slopes with linearly increasing undrained strength. Géotechnique 65(10):824–830

    Article  Google Scholar 

  15. Hossley A, Leshchinsky B (2019) Stability and failure geometry of slopes with spatially varying undrained shear strength. J Geotech Geoenviron Eng 145(5):06019002

    Article  Google Scholar 

  16. Hunter JH, Schuster RL (1968) Stability of simple cuttings in normally consolidated clays. Geotechnique 18(3):372–378

    Article  Google Scholar 

  17. Janbu N (1954) Application of composite slip surface for stability analysis. Proc Eur Conf Stab Earth Slopes, Sweden 3:43–49

    Google Scholar 

  18. Kim J, Salgado R, Yu HS (1999) Limit analysis of soil slopes subjected to pore-water pressures. J Geotech Geoenviron Eng 125(1):49–58

    Article  Google Scholar 

  19. Kopacsy J (1961) Distribution des contraintes a la rupture forme de la surface de glissement et hauteur theorique des talus. In: Proceedings of the 5th international conference on soil mechanics and foundation engineering paris, France, pp 641–650

    Google Scholar 

  20. Koppula SD (1984) On stability of slopes in clays with linearly increasing strength. Can Geotech J 21(3):577–581

    Article  Google Scholar 

  21. Koppula SD (1984) Pseudo-static analysis of clay slopes subjected to earthquakes. Geotechnique 34(1):71–79

    Article  Google Scholar 

  22. Krahn J (2003) The 2001 RM hardy lecture: the limits of limit equilibrium analyses. Can Geotech J 40(3):643–660 (2003)

    Google Scholar 

  23. Lane PA, Griffiths DV (2000) Assessment of stability of slopes under drawdown conditions. J Geotech Geoenviron Eng 126(5):443–450

    Google Scholar 

  24. Leshchinsky D, Smith DS (1989) Deep-seated failure of a granular embankment over clay. Stability analysis. Soils Found 29(3):105–114

    Google Scholar 

  25. Li B, Zhang F, Wang D (2018) Impact of crack on stability of slope with linearly increasing undrained strength. Math Prob Eng 1–11. https://doi.org/10.1155/2018/1096513

  26. Low BK (1989) Stability analysis of embankments on soft ground. J Geotech Eng 115(2):211–227 (1989)

    Google Scholar 

  27. Michalowski RL (2002) Stability charts for uniform slopes. J Geotech Geoenviron Eng 128(4):351–355

    Google Scholar 

  28. Morgenstern NU, Price VE (1965) The analysis of the stability of general slip surfaces. Geotechnique 15(1):79–93

    Google Scholar 

  29. Nakase A (1970) Stability of low embankment on cohesive soil stratum. Soils Found 10(4):39–64

    Google Scholar 

  30. Narayan CGP (1975) Variational methods in stability analysis of slopes. PhD dissertation submitted to Indian Institute of Technology, Delhi, India

    Google Scholar 

  31. Revilla J, Castillo E (1977) The calculus of variations applied to stability of slopes. Geotechnique 27(1):1–11

    Google Scholar 

  32. Sarkar S, Chakraborty M (2019) Pseudostatic slope stability analysis in two-layered soil by using variational method. In: Earthquake geotechnical engineering for protection and development of environment and constructions (7th ICEGE, Rome), pp 4857–4864

    Google Scholar 

  33. Sarkar S, Chakraborty M (2020) Pseudo-static slope stability analysis for cohesive-frictional soil by using variational method. In: Advances in computer methods and geomechanics. Springer, Singapore , pp 159–171

    Google Scholar 

  34. Sarma SK (1973) Stability analysis of embankments and slopes Geotechnique 23(3):423–433

    Google Scholar 

  35. Spencer E (1967) A method of analysis of the stability of embankments assuming parallel inter-slice forces. Geotechnique 17(1):11–26

    Google Scholar 

  36. Taylor DW (1937) Stability of earth slopes. J Boston Soc. Civ Eng 24(3):197–247

    Google Scholar 

  37. Yu HS, Salgado R, Sloan SW, Kim JM (1998) Limit analysis versus limit equilibrium for slope stability. J Geotech Geoenviron Eng 124(1):1–11

    Google Scholar 

  38. Zaki A (1999) Slope stability analysis overview. University of Toronto (1999)

    Google Scholar 

Download references

Acknowledgements

The corresponding author acknowledges the support of the “Department of Science and Technology (DST), Government of India” under grant number DST/INSPIRE/04/2016/001692.

Author information

Authors and Affiliations

  1. Indian Institute of Technology (BHU), Varanasi, 221005, India

    Sourav Sarkar & Manash Chakraborty

Authors
  1. Sourav Sarkar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manash Chakraborty
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manash Chakraborty .

Editor information

Editors and Affiliations

  1. Indian Institute of Technology Guwahati, Guwahati, Assam, India

    T. G. Sitharam

  2. Department of Earthquake Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Ravi Jakka

  3. Department of Civil Engineering, Bangalore University, Bengaluru, Karnataka, India

    L. Govindaraju

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Sarkar, S., Chakraborty, M. (2021). Seismic Stability of Non-homogenous Cohesive Soil by Using Calculus of Variation. In: Sitharam, T.G., Jakka, R., Govindaraju, L. (eds) Local Site Effects and Ground Failures. Lecture Notes in Civil Engineering, vol 117. Springer, Singapore. https://doi.org/10.1007/978-981-15-9984-2_20

Download citation

  • DOI: https://doi.org/10.1007/978-981-15-9984-2_20

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-9983-5

  • Online ISBN: 978-981-15-9984-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation