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Stability and reinforcement analysis of rock slope based on elasto-plastic finite element method

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Abstract

The rigid body limit equilibrium method (RBLEM) and finite element method (FEM) are two widely used approaches for rock slope’s stability analysis currently. RBLEM introduced plethoric assumptions; while traditional FEM relied on artificial factors when determining factor of safety (FOS) and sliding surfaces. Based on the definition of structure instability that an elasto-plastic structure is not stable if it is unable to satisfy simultaneously equilibrium condition, kinematical admissibility and constitutive equations under given external loads, deformation reinforcement theory (DRT) is developed. With this theory, plastic complementary energy (PCE) can be used to evaluate the overall stability of rock slope, and the unbalanced force beyond the yield surface could be the identification of local failure. Compared with traditional slope stability analysis approaches, the PCE norm curve to strength reduced factor is introduced and the unbalanced force is applied to the determination of key sliding surfaces and required reinforcement. Typical and important issues in rock slope stability are tested in TFINE(a three-dimensional nonlinear finite element program), which is further applied to several representatives of high rock slope’s stability evaluation and reinforcement engineering practice in southwest of China.

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References

  1. BISHOP A W. The use of the slip circle in the stability analysis of slopes [J]. Geotechnique, 1955, 5(1): 7–17.

    Article  Google Scholar 

  2. DUNCAN J M. State of the art: Limit equilibrium and finite-element analysis of slopes [J]. Journal of Geotechnical Engineering-ASCE, 1996, 122(7): 577–596.

    Article  Google Scholar 

  3. ZHU Jian-feng, CHEN Chang-fu. Search for circular and noncircular critical slip surfaces in slope stability analysis by hybrid genetic algorithm [J]. Journal of Central South University, 2014, 21(1): 387–397.

    Article  Google Scholar 

  4. CHEN Zu-yu, WANG Xiao-gang, YANG Jian, JIA Zhi-xin, WANG Ye-jie. Rock slope stability analysis: Theory methods and programs [M]. Beijing: China Water Power Press, 2005: 519–522. (in Chinese)

    Google Scholar 

  5. LAOUAFA F, DARVE F. Modelling of slope failure by a material instability mechanism [J]. Computers and Geotechnics, 2002, 29(4): 301–325.

    Article  Google Scholar 

  6. GRIFFITHS D V, LANE P A. Slope stability analysis by finite elements [J]. Geotechnique, 1999, 49(3): 387–403.

    Article  Google Scholar 

  7. CUNDALL P A, STRACK O D L. A discrete numerical model for granular assemblies [J]. Geotechnique, 1979, 29(1): 47–65.

    Article  Google Scholar 

  8. ZHANG Chu-han, PEKAU O A, JIN Feng, WANG Guang-lun. Application of distinct element method in dynamic analysis of high rock slopes and blocky structures [J]. Soil Dynamics and Earthquake Engineering, 1997, 16(6): 385–394.

    Article  Google Scholar 

  9. KAWAI T. New discrete models and their application to seismic response analysis of structure [J]. Nuclear Engineering and Design, 1978, 48: 207–229.

    Article  Google Scholar 

  10. ZHANG Jian-hai, HE Jiang-da, FAN Jing-wei. Static and dynamic stability assessment of slopes or dam foundations using a rigid body-spring element method [J]. International Journal of Rock Mechanics & Mining Sciences, 2001, 38(8): 1081–1090.

    Article  Google Scholar 

  11. SHI Gen-hua, GOODMAN R E. Generalization of two-dimensional dis-continuous deformation analysis for forward modeling [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1989, 13(4): 359–380.

    Article  MATH  Google Scholar 

  12. SHI Gen-hua, GOODMAN R E. Two dimensional discontinuous deformation analysis [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1985, 9(6): 541–556.

    Article  MATH  Google Scholar 

  13. LIU Jian-guo, SUN Qi-cheng, JIN Feng, LIU Qing-kai. Studies on structural and mechanical properties under isostatic compression with large-scale discrete element simulations [J]. Acta Mechanica Solida Sinica, 2014, 27(2): 129–136.

    Article  Google Scholar 

  14. YANG Qiang, LENG Kuang-dai, CHANG Qiang, LIU Yao-ru. Failure mechanism and control of geotechnical structures [C]// Constitutive Modeling of Geomaterials. Berlin, Heidelberg: Springer, 2013: 63–87.

    Chapter  Google Scholar 

  15. ZHENG Hong, THAM L G, LIU De-fu. On two definitions of the factor of safety commonly used in finite element slope stability analysis [J]. Computers and Geotechnics, 2006, 33(3): 188–195.

    Article  Google Scholar 

  16. LIU Yao-ru, HE Zhu, LENG Kuang-dai, HUANG Yue-qun, YANG Qiang. Dynamic limit equilibrium analysis of sliding block for rock slope based on nonlinear FEM [J]. Journal of Central South University, 2013, 20(8): 2263–2274.

    Article  Google Scholar 

  17. MATSUI T, SAN K C. Finite element slope stability analysis by shear strength reduction technique [J]. Soils and Foundations, 1992, 32(1): 59–70.

    Article  Google Scholar 

  18. ZHAO Sang-yi, ZHENG Ying-ren, SHI Wei-min, WANG Jian-lin. Analysis on safety factor of slope by strength reduction FEM [J]. Chinese Journal of Rock Mechanics and Engineering, 2002, 24(3): 343–346. (in Chinese).

    Google Scholar 

  19. DAWSON E M, ROTH W H, DRESCHER A. Slope stability analysis by strength reduction [J]. Geotechnique, 1999, 49(6): 835–840.

    Article  Google Scholar 

  20. LUBLINER J. Plasticity theory [M]. New York: Macmillan Publishing Company, 1990: 169–170.

    Google Scholar 

  21. LUAN Mao-tian, WU Ya-jun, NIAN Ting-kai. A criterion for evaluating slope stability based on development of plastic zone by shear strength reduction FEM [J]. Journal of Disaster Prevention and Mitigation Engineering, 2003, 23(3): 1–8. (in Chinese)

    Google Scholar 

  22. GRIFFITHS D V, KIDGER D J. Enhanced visualization of failure mechanism in finite elements [J]. Computers & Structures, 1995, 55(2): 265–268.

    Article  MATH  Google Scholar 

  23. YANG Qiang, LIU Yao-ru, CHEN Ying-ru, ZHOU Wei-yuan. Deformation reinforcement theory and its application to high arch dams [J]. Science in China, Series E: Technological Science, 2008, 51(Supp 2): 32–47.

    Article  MATH  Google Scholar 

  24. CHEN Zu-yu. On Pan’s principles of soil and rock stability analysis [J]. Journal of Tsinghua University: Science and Technology, 1998, 38(1): 1–4. (in Chinese)

    MATH  Google Scholar 

  25. RICE J R. Inelastic constitutive relations for solids: an integral variable theory and its application to metal plasticity [J]. Journal of the Mechanics and Physics of Solids, 1971, 19(1): 433–455

    Article  MATH  Google Scholar 

  26. YANG Qiang, CHEN Xin, ZHOU Wei-yuan. Thermodynamic relationship between creep crack growth and creep deformation [J]. Journal of Non-equilibrium Thermodynamics, 2005, 30(1): 81–94.

    Article  MathSciNet  MATH  Google Scholar 

  27. ZHUO Jia-shou, SHAO Guo-jian, CHEN Zhen-lei. Disturbing energy method for determining the slipping face and direction and the safety coefficient of engineering stability [J]. Journal of Hydraulic Engineering, 1997 (8): 79, 80–84. (in Chinese)

    Google Scholar 

  28. YIN You-quan. Non-linear finite element basis [M]. Beijing: Peking University Press, 2007: 177–184. (in Chinese)

    Google Scholar 

  29. CHEN Wai-fah. Limit analysis and soil plasticity [M]. Amsterdam, Netherlands: Elsevier Science Publishers, 1975: 40–46

    Google Scholar 

  30. YANG Qiang, CHEN Xin, ZHOU Wei-yuan. A practical 3D elastic-plastic incremental method in FEM based on D-P yield criteria [J]. Chinese Journal of Geotechnical Engineering, 2002, 24(1): 16–20. (in Chinese)

    MATH  Google Scholar 

  31. SCHREYER H L, KULAK R F, KRAMER J M. Accurate numerical solutions for elastoplastic models [J]. J Journals of Pressure Vessel Technology, 1979, 101(2): 226–23

    Article  Google Scholar 

  32. ORTIZ M, POPOV E P. Accuracy and stability of integration algorithms for elastoplastic constitutive relations [J]. International Journal for Numerical Methods in Engineering, 1985, 21(9): 1561–1576.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Hydroscience and Hydraulic Engineering (Tsinghua University), Beijing, 100084, China

    Yao-ru Liu  (刘耀儒), Zhe-shu Wu  (武哲书), Qiang Chang  (常强) & Qiang Yang  (杨强)

  2. Changjiang Institute of Survey, Planning, Design and Research, Wuhan, 430010, China

    Bo Li  (李波)

Authors
  1. Yao-ru Liu  (刘耀儒)
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  2. Zhe-shu Wu  (武哲书)
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  3. Qiang Chang  (常强)
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  4. Bo Li  (李波)
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  5. Qiang Yang  (杨强)
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Corresponding author

Correspondence to Yao-ru Liu  (刘耀儒).

Additional information

Foundation item: Project(51479097) supported by the National Natural Science Foundation of China; Project(2013-KY-2) supported by State Key Laboratory of Hydroscience and Hydraulic Engineering, China

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Liu, Yr., Wu, Zs., Chang, Q. et al. Stability and reinforcement analysis of rock slope based on elasto-plastic finite element method. J. Cent. South Univ. 22, 2739–2751 (2015). https://doi.org/10.1007/s11771-015-2804-3

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  • DOI: https://doi.org/10.1007/s11771-015-2804-3

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