Skip to main content
SpringerLink
Log in

Improved slope safety analysis by new Druker-Prager type criterion

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

Based on Mohr-Coulomb (M-C) criterion, the parameters of Druker-Prager (D-P) criterion for geomaterial were determined under non-associated flow rule, and thus a new D-P type criterion was presented. Two assumptions were employed during the derivation: 1) principal strains by M-C model and D-P model are equal, and 2) the material is under plane strain condition. Based on the analysis of the surface on π plane, it is found that the proposed D-P type criterion is better than the D-P criterion with M-C circumscribed circle or M-C inscribed circle, and is applicable for stress Lode angle less than zero. By comparing the predicted results with the test data of sand under plane strain condition and other D-P criteria, the proposed criterion is verified and agrees well with the test data, which is further proved to be better than other D-P type criteria in certain range of Lode angle. The criterion was compiled into a finite difference package FLAC3D by user-subroutine, and was used to analyze the stability of a slope by strength reduction method. The predicted slope safety factor from the proposed criterion agrees well with that by Spencer method, and it is more accurate than that from classic D-P criteria.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. KOITER W T. Stress-strain relations, uniqueness and variational theorems for elasto-plastic materials with a singular yield surface [J]. Quarterly of Applied Mathematics, 1953, 11(3): 350–354.

    MathSciNet  MATH  Google Scholar 

  2. CHEN W F. Limit analysis and soil plasticity [M]. Amsterdam: Elsevier Scientific Press, 1975: 637–639.

    Google Scholar 

  3. LADE P V, NELSON R B. Incrementalization procedure for elasto-plastic constitutive model with multiple, intersecting yield surfaces [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1984, 8(4): 311–323.

    Article  MATH  Google Scholar 

  4. GUDEHUS G A comprehensive constitutive equation for granular materials [J]. Soils and Foundations, 1996, 36(1): 1–12.

    Article  Google Scholar 

  5. MATSUOKA H, SAKAKIBARA K A. A constitutive model for sands and clays evaluating principal stress rotation [J]. Soils and Foundation, 1987, 27(4): 73–88.

    Article  Google Scholar 

  6. FAKHARIAN K, EVGIN E. Elasto-plastic modeling of stress-path-dependent behavior of interface [J]. Int J Number Analyt Method Geomech, 2000, 24(2): 183–199.

    Article  MATH  Google Scholar 

  7. DOVE J E, JARRETT B. Behavior of dilative sand interface in a geotribology framework [J]. Journal of Geotech and Geoeviron Eng, 2002, 125(7): 545–555.

    Google Scholar 

  8. DEJONG J T, WESTGATE Z J. Role of overconsolidation on sand-geomembrane interface response and material damage evolution [J]. Geotxtilesand and Geomembranes, 2005, 23(6): 486–512.

    Article  Google Scholar 

  9. SAID I, DEGENNARO V, FRANK R. Axisymmetric finite element analysis of pile loading test [J]. Computers and Geotechnics, 2009, 36(1/2): 6–19.

    Article  Google Scholar 

  10. DRUNKER D C, PRAGER W. Soil mechanics and plastic analysis in limit design [J]. Quarterly of Applied Mathematics, 1952, 10(2): 157–165.

    MathSciNet  Google Scholar 

  11. WANG Fu-shou, CHEN Ching-ben, HWANG J H, CHANG Pai-chi, CHEN Wei-fang. Models for evaluating the revolving cutter profile of circular-arc end mills [J]. Int J Adv Manuf Technol, 2006, 28(3/4): 228–235.

    Article  Google Scholar 

  12. XU Gan-cheng, ZHENG Ying-ren. Study on application of yield criterions in geotechnical engineering [J]. Chinese journal of Geotechnical Engineering, 1990, 12(2): 93–99. (in Chinese)

    MathSciNet  Google Scholar 

  13. RAMEZANI S, NAGHDABADI R, SOHRABPOUR S. An additive theory for finite elastic-plastic deformations of the micropolar continuous media [J]. Acta Mechanica, 2009, 206()1/2: 81–93.

    Article  MATH  Google Scholar 

  14. ARSLAN H, STURE S. Finite element analysis of localization and micro-macro structure relation in granular materials [J]. Acta Mechanica, 2008, 197(3/4): 153–171.

    Article  MATH  Google Scholar 

  15. LAMBRECHT M, MIEHE C, STUTTGART, GERMANY. Two non-associated istotropic elastoplastic hardening models for frictional materials [J]. Acta Mechanica, 1999, 135(1/2): 73–90.

    Article  MathSciNet  MATH  Google Scholar 

  16. PALLARÉS F J, AGÜERO A, IVORRA S. A comparison of different failure criteria in a numerical seismic assessment of an industrial brickwork chimney [J]. Materials and Structures, 2009, 42(2): 213–226.

    Article  Google Scholar 

  17. GONG Xiao-nan. Geotechnical computer analysis [M]. Beijing: Building Industry Press, 2000: 222–226. (in Chinese)

    Google Scholar 

  18. LIU Yuan-xue. Study of several basic problems in constitutive theory of geomaterials [J]. Chinese Journal of Geotechnical Engineering, 2001, 23(1): 45–48. (in Chinese)

    Google Scholar 

  19. YANG Xiao-li, HUANG Fu. Slope stability analysis considering joined influences of nonlinearity and dilation [J]. Journal of Central South University of Technology, 2009, 16(2): 292–296.

    Article  Google Scholar 

  20. GANJIAN N, ASKARI F, FARZANEH O. Influences of non-associated flow rules on three-dimensional seismic stability of loaded slopes [J]. Journal of Central South University of Technology, 2010, 17(3): 603–611.

    Article  Google Scholar 

  21. LAVASAN A A, GHAZAVI M. Influence of interference on failure mechanism of closely constructed circular footings on reinforced sand [C]// Proceedings of the 4th Aasia Regional Conference on Geosynthetics. Shanghai: Zhejiang University Press, 2008: 311–317.

    Google Scholar 

  22. ZHANG Lu-yu, SHI Wei-min, ZHENG Ying-ren. The slope stability analysis by FEM under the plane strain condition [J]. Chinese Journal of Geotechnical Engineering, 2002, 24(4): 487–490. (in Chinese)

    Google Scholar 

  23. ZHENG Ying-ren, WANG Jing-lin, ZHU Xiao-kang. Discussion on velocity of slip line theory for geotechnical materials [J]. Journal of Hydraulic Engineering, 2001, 32(6): 1–7. (in Chinese)

    Google Scholar 

  24. LI Guang-xin, HUANG Yong-nan, ZHANG Qi-guan. The principal stress of soil in the direction of plane strain [J]. Chinese Journal of Geotechnical Engineering, 2001, 23(3): 358–361. (in Chinese)

    Google Scholar 

  25. KHALID A, HEATH S W. A true triaxial apparatus for soil testing with mixed boundary conditions [J]. Geotechnical Testing Journal, 2005, 28(6): 534–543.

    Google Scholar 

  26. LADE P V, DUNCAN J M. Cubical triaxial tests on cohesionless soil [J]. Journal of the Soil Mechanics and Foundations Division, 1973, 99(SM10): 793–812.

    Google Scholar 

  27. LI Guang-xin, ZHANG Qi-guan, HUANG Yong-nan. Study on transforming of principal stresses in constant stress ratio plane strain tests [J]. Rock and Soil Mechanics, 2006, 27(11): 1867–1872. (in Chinese)

    Google Scholar 

  28. HUANG Mao-song, JIA Cang-qin. Strength reduction FEM in stability analysis of soil slopes subjected to transient unsaturated seepage [J]. Computers and Geotechnics, 2009, 36(1): 93–101.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Geo-mechanics and Embankment Engineering of Ministry of Education, Hohai University, Nanjing, 210098, China

    Jun-gao Zhu  (朱俊高), Kai Peng  (彭凯) & Han-long Liu  (刘汉龙)

  2. Geotechnical Research Institute, Hohai University, Nanjing, 210098, China

    Jun-gao Zhu  (朱俊高), Kai Peng  (彭凯) & Han-long Liu  (刘汉龙)

  3. Laboratoire de Mécanique de Lille, UMR CNRS 8107, Equipe Mécanique des Géomatériaux Cohérents, Polytech’Lille, Cité Scientifique, 59655, Villeneuve d’Ascq, France

    J. F. Shao

Authors
  1. Jun-gao Zhu  (朱俊高)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kai Peng  (彭凯)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. F. Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Han-long Liu  (刘汉龙)
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Foundation item: Project(2010B14814) supported by the Fundamental Research Funds for the Central Universities of China; Project(200801133) supported by the Ministry of Water Resources of China for Public Welfare Profession; Project(50809023) supported by the National Natural Science Foundation of China

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhu, Jg., Peng, K., Shao, J.F. et al. Improved slope safety analysis by new Druker-Prager type criterion. J. Cent. South Univ. Technol. 19, 1132–1137 (2012). https://doi.org/10.1007/s11771-012-1119-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-012-1119-x

Key words

Search

Navigation