Skip to main content
SpringerLink
Log in

Assessment on strength reduction schemes for geotechnical stability analysis involving the Drucker-Prager criterion

基于Drucker-Prager准则的岩土体稳定性强度折减方案评价

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

Abstract

For geotechnical stability analysis involving the Drucker-Prager (DP) criterion, both the c-φ reduction scheme and the M-K reduction scheme can be utilized. With the aid of the second-order cone programming optimized finite element method (FEM-SOCP), a comparison of the two strength reduction schemes for the stability analysis of a homogeneous slope and a multilayered slope is carried out. Numerical investigations disclose that the FoS results calculated by the c-φ reduction scheme agree well with those calculated by the classical Morgenstern-Price solutions. However, the FoS results attained by the M-K reduction scheme may lead to conservative estimation of the geotechnical safety, particularly for the cases with large internal friction angles. In view of the possible big difference in stability analysis results caused by the M-K reduction scheme, the c-φ reduction scheme is recommended for the geotechnical stability analyses involving the DP criterion.

摘要

对于涉及Drucker-Prager准则的岩土体稳定性分析, 可以使用c-φ折减方案和M-K折减方案. 基 于二阶锥规划有限元法, 对均质土边坡和多层土边坡稳定性分析中的两种强度折减方案进行了对比. 研究表明, 基于c-φ 折减方案得到的安全系数与Morgenstern-Price 法计算获得的结果吻合较好. 然而, 基于M-K折减方案得到的安全系数结果可能导致对岩土体安全性的保守估计, 特别是对于大内摩擦角 的情况. 考虑到M-K折减方案在稳定性分析结果上可能会造成较大差异, 对于涉及Drucker-Prager 准 则的岩土体稳定性分析建议采用c-φ 折减方案.

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. ZIENKIEWICZ O C, HUMPHESON C, LEWIS R W. Associated and non-associated visco-plasticity and plasticity in soil mechanics [J]. Géotechnique, 1975, 25(4): 671–689. DOI:https://doi.org/10.1680/geot.1975.25.4.671.

    Article  Google Scholar 

  2. GRIFFITHS D V, LANE P A. Slope stability analysis by finite elements [J]. Géotechnique, 1999, 49(3): 387–403. DOI:https://doi.org/10.1680/geot.1999.49.3.387.

    Article  Google Scholar 

  3. GUROCAK Z, ALEMDAG S, ZAMAN M M. Rock slope stability and excavatability assessment of rocks at the Kapikaya dam site, Turkey [J]. Engineering Geology, 2008, 96(1, 2): 17–27. DOI:https://doi.org/10.1016/j.enggeo.2007.08.005.

    Article  Google Scholar 

  4. HUANG Fu, ZHANG Dao-bing, SUN Zhi-bin, JIN Qi-yun. Upper bound solutions of stability factor of shallow tunnels in saturated soil based on strength reduction technique [J]. Journal of Central South University, 2012, 19(7): 2008–2015. DOI:https://doi.org/10.1007/s11771-012-1238-4.

    Article  Google Scholar 

  5. SLOAN S W. Geotechnical stability analysis [J]. Géotechnique, 2013, 63(7): 531–571. DOI:https://doi.org/10.1680/geot.12.RL.001.

    Article  Google Scholar 

  6. YUAN Wei, BAI Bing, LI Xiao-chun, WANG Hai-bin. A strength reduction method based on double reduction parameters and its application [J]. Journal of Central South University, 2013, 20(9): 2555–2562. DOI:https://doi.org/10.1007/s11771-013-1768-4.

    Article  Google Scholar 

  7. KAYA A, ALEMDAĞ S, DAĞ S, GÜROCAK Z. Stability assessment of high-steep cut slope debris on a landslide (Gumushane, NE Turkey) [J]. Bulletin of Engineering Geology and the Environment, 2016, 75(1): 89–99. DOI:https://doi.org/10.1007/s10064-015-0753-6.

    Article  Google Scholar 

  8. GUO Shuang-feng, LI Ning, LIU Chun, LIU Nai-fei. Unraveling the progressive failure behaviors and mechanisms of the slope with a local dynamic method based on the double strength reduction [J]. International Journal of Geomechanics, 2020, 20(6): 04020069. DOI:https://doi.org/10.1061/(ASCE)GM.1943-5622.0001693.

    Article  Google Scholar 

  9. SUN Chao-wei, CHAI Jun-rui, LUO Tao, XU Zeng-guang. Nonlinear shear-strength reduction technique for stability analysis of uniform cohesive slopes with a general nonlinear failure criterion [J]. International Journal of Geomechanics, 2021, 21(1): 06020033. DOI:https://doi.org/10.1061/(ASCE)GM.1943-5622.0001885.

    Article  Google Scholar 

  10. CHEN Xi, WU Yong-kang, YU Yu-zhen, LIU Jian-kun, XU X F, REN Jun. A two-grid search scheme for large-scale 3-D finite element analyses of slope stability [J]. Computers and Geotechnics, 2014, 62: 203–215. DOI:https://doi.org/10.1016/j.compgeo.2014.07.010.

    Article  Google Scholar 

  11. ALEMDAĞ S, KAYA A, KARADAĞ M, GÜROCAK Z, BULUT F. Utilization of the limit equilibrium and finite element methods for the stability analysis of the slope debris: an example of the Kalebasi district (NE Turkey) [J]. Journal of African Earth Sciences, 2015, 106: 134–146. DOI:https://doi.org/10.1016/j.jafrearsci.2015.03.010.

    Article  Google Scholar 

  12. ZHANG Xue, SHENG Dai-chao, SLOAN S W, BLEYER J. Lagrangian modelling of large deformation induced by progressive failure of sensitive clays with elastoviscoplasticity [J]. International Journal for Numerical Methods in Engineering, 2017, 112(8): 963–989. DOI:https://doi.org/10.1002/nme.5539.

    Article  MathSciNet  Google Scholar 

  13. MENG Jing-jing, ZHANG Xue, HUANG Jin-song, TANG Hong-xiang, MATTSSON H, LAUE J. A smoothed finite element method using second-order cone programming [J]. Computers and Geotechnics, 2020, 123: 103547. DOI:https://doi.org/10.1016/j.compgeo.2020.103547.

    Article  Google Scholar 

  14. CHEN Xi, WANG Dong-yong, TANG Jian-bin, MA Wen-chen, LIU Yong. Geotechnical stability analysis considering strain softening using micro-polar continuum finite element method [J]. Journal of Central South University, 2021, 28(1): 297–310. DOI:https://doi.org/10.1007/s11771-021-4603-3.

    Article  Google Scholar 

  15. ABBO A J, SLOAN S W. A smooth hyperbolic approximation to the Mohr-Coulomb yield criterion [J]. Computers and Structures, 1995, 54(3): 427–441. DOI:https://doi.org/10.1016/0045-7949(94)00339-5.

    Article  Google Scholar 

  16. CHEN Xi, WANG Dong-yong, YU Yu-zhen, LV Yan-nan. A modified Davis approach for geotechnical stability analysis involving non-associated soil plasticity [J]. Géotechnique, 2020, 70(12): 1109–1119. DOI:https://doi.org/10.1680/jgeot.18.p.158.

    Article  Google Scholar 

  17. CAMARGO J, VELLOSO R Q, VARGAS E A. Numerical limit analysis of three-dimensional slope stability problems in catchment areas [J]. Acta Geotechnica, 2016, 11(6): 1369–1383. DOI:https://doi.org/10.1007/s11440-016-0459-3.

    Article  Google Scholar 

  18. KRABBENHØFT K. OptumG2: materials. Optum computational engineering [OB/OL]. [2020-12-01] http://www.optumce.com.

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

    Article  MathSciNet  Google Scholar 

  20. ALEJANO L R, BOBET A. Drucker — Prager criterion [J]. Rock Mechanics and Rock Engineering, 2012, 45: 995–999. DOI:https://doi.org/10.1007/s00603-012-0278-2.

    Article  Google Scholar 

  21. KRABBENHØFT K, KARIM M R, LYAMIN A V, SLOAN S W. Associated computational plasticity schemes for nonassociated frictional materials [J]. International Journal for Numerical Methods in Engineering, 2012, 90(9): 1089–1117. DOI:https://doi.org/10.1002/nme.3358.

    Article  MathSciNet  Google Scholar 

  22. VERMEER P A, DE BORST R. Non-associated plasticity for soils, concrete and rock [J]. Heron, 1984, 29 (3): 1–64.

    Google Scholar 

  23. WANG Dong-yong, CHEN Xi, YU Yu-zhen, JIE Yu-xin, LV Yan-nan. Stability and deformation analysis for geotechnical problems with nonassociated plasticity based on second-order cone programming [J]. International Journal of Geomechanics, 2019, 19(2): 04018190. DOI:https://doi.org/10.1061/(ASCE)GM.1943-5622.0001339.

    Article  Google Scholar 

  24. CHENG Y M, LANSIVAARA T, WEI W B. Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods [J]. Computers and Geotechnics, 2007, 34(3): 137–150. DOI:https://doi.org/10.1016/j.compgeo.2006.10.011.

    Article  Google Scholar 

  25. DONALD I B, GIAM P. The ACADS slope stability programs review [C]// Landslides: Proceedings of the 6th International Aymposium, 1992, 3: 1665–1670.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing, 100044, China

    Dong-yong Wang  (王冬勇), Ji-lin Qi  (齐吉琳) & Li-yun Peng  (彭丽云)

  2. Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing, 100044, China

    Xi Chen  (陈曦)

Authors
  1. Dong-yong Wang  (王冬勇)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xi Chen  (陈曦)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ji-lin Qi  (齐吉琳)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Li-yun Peng  (彭丽云)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xi Chen  (陈曦).

Additional information

Foundation item

Projects(42002277, 41972279, 41772291) supported by the National Natural Science Foundation of China; Projects (2020M680321, 2021T140046) supported by the China Postdoctoral Science Foundation; Projects(2020-zz-081, 2021-PC-003) supported by the Beijing Postdoctoral Research Foundation, China; Project(X21074) supported by the Fundamental Research Funds for Beijing University of Civil Engineering and Architecture, China

Contributors

WANG Dong-yong performed some analyses and wrote the first draft; CHEN Xi provided the concept and edited the manuscript; QI Ji-lin gave some revision suggestions on the first draft; PENG Li-yun edited the final revised draft.

Conflict of interest

WANG Dong-yong, CHEN Xi, QI Ji-lin and Peng Li-yun declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Dy., Chen, X., Qi, Jl. et al. Assessment on strength reduction schemes for geotechnical stability analysis involving the Drucker-Prager criterion. J. Cent. South Univ. 28, 3238–3245 (2021). https://doi.org/10.1007/s11771-021-4828-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-021-4828-1

Key words

关键词

Search

Navigation