Seismic and Static 3D Stability of Two-stage Slope Considering Joined Influences of Nonlinearity and Dilatancy

  • Jing-shu Xu
  • Yong-xin Li
  • Xiao-li Yang
Geotechnical Engineering


Soil strength nonlinearity and dilatancy have significant impacts on the stability of a slope. In the present analysis, a seismic stability analysis of a three-dimensional two-stage slope considering the joined influences of soil strength nonlinearity and dilatancy is conducted. Based on the limit analysis method, the external work rates by soil weight and the seismic forces as well as the internal energy dissipations are calculated and thereafter the critical height of the slope is derived. In virtue of the nonlinear optimization procedure, the stability factor of a 3D slope subjected to seismic forces is captured. The effects of slope geometry, seismic forces, soil strength nonlinearity and dilatancy on the slope stability are investigated by parameter analysis. It is found from the results that, the depth coefficient α1 and dilative parameter n have positive effects on the stability of a two-stage slope while the other factors such as the seismic coefficient kh and the nonlinear coefficient m have negative effects on it. In addition, the effect of soil nonlinearity on slope stability aggravates when the seismic force coefficient kh and the dilative parameter n increase.


three-dimensional two-stage slope nonlinear failure criterion non-associated flow rule soil dilatancy 


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  1. Areias, P., Msekh, M. A., and Rabczuk, T. (2016a). “Damage and fracture algorithm using the screened Poisson equation and local remeshing.” Engineering Fracture Mechanics, Vol. 158, pp. 116–143, DOI: 10.1016/j.engfracmech.2015.10.042.CrossRefGoogle Scholar
  2. Areias, P. and Rabczuk, T. (2017). “Steiner-point free edge cutting of tetrahedral meshes with applications in fracture.” Finite Elements in Analysis and Design, Vol. 132, pp. 27–41, DOI: 10.1016/j.finel.2017.05.001.CrossRefGoogle Scholar
  3. Areias, P., Rabczuk, T., and Sá, J. C. D. (2016b). “A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement.” Computational Mechanics, Vol. 58, pp. 1003–1018, DOI: 10.1007/s00466-016-1328-5.MathSciNetCrossRefzbMATHGoogle Scholar
  4. Baker, R. (2004). “Stability charts for zero tensile strength Hoek-Brown materials: the variational solution and its engineering implications.” Journal of the Japanese Geotechnical Society Soils and Foundation, Vol. 44, No. 3, pp. 125–132, DOI: 10.3208/sandf.44.3_125.CrossRefGoogle Scholar
  5. Drescher, A. and Detournay, C. (1993). “Limit load in translational failure mechanisms for associative and non-associative materials.” Géotechnique, Vol. 43, No. 3, pp. 443–456, DOI: 10.1680/geot.1993.43.3.443.CrossRefGoogle Scholar
  6. Frydman, S. and Burd, H. J. (1997). “Numerical studies of bearingcapacity factor N?.” Journal of Geotechnical and Geoenvironmental Engineering, Vol. 123, No. 1, pp. 20–29, DOI: 10.1061/(ASCE) 1090-0241(1997)123:1(20).CrossRefGoogle Scholar
  7. Jiang, J. C., Baker, R., and Yamagami, T. (2003). “The effect of strength envelope nonlinearity on slope stability computations.” Canadian Geotechnical Journal, Vol. 40, No. 2, pp. 308–325, DOI: 10.1139/t02-111.CrossRefGoogle Scholar
  8. Kelesoglu, M. K. (2015). “The evaluation of three-dimensional effects on slope stability by the strength reduction method.” KSCE Journal of Civil Engineering, Vol. 20, No. 1, pp. 229–242, DOI: 10.1007/s12205-015-0686-4.CrossRefGoogle Scholar
  9. Kim, J., Salgado, R., and Lee, J. (2002). “Stability analysis of complex soil slopes using limit analysis.” Journal of Geotechnical and Geoenvironmental Engineering, Vol. 128, No. 7, pp. 546–557, DOI: 10.1061/(ASCE)1090-0241(2002)128:7(546).CrossRefGoogle Scholar
  10. Lewin, P., Bishop, A., and Webb, D. (1965). “Undisturbed samples of London clay from the ashford common shaft: Strength-effective stress relationships.” Géotechnique, Vol. 15, No. 1, pp. 1–31, DOI: 10.1680/geot.1965.15.1.1.CrossRefGoogle Scholar
  11. Li, X. J., Ji, Z., Zhu, H. H., and Gu, C. (2012). “A feasibility study of the measuring accuracy and capability of wireless sensor networks in tunnel monitoring.” Frontiers of Structural and Civil Engineering, Vol. 6, No. 2, pp. 111–120, DOI: 10.1007/s11709-012-0150-1.Google Scholar
  12. Liu, G. Y., Zhuang, X. Y., and Cui, Z. Q. (2017). “Three-dimensional slope stability analysis using independent cover based numerical manifold and vector method.” Engineering Geology, Vol. 225, pp. 83–95, DOI: 10.1016/j.enggeo.2017.02.022.CrossRefGoogle Scholar
  13. Michalowski, R. L. (2002). “Stability charts for uniform slopes.” Journal of Geotechnical and Geoenvironmental Engineering, Vol. 128, No. 4, pp. 351–355, DOI: 10.1061/(ASCE)1090-0241(2002)128:4(351).CrossRefGoogle Scholar
  14. Michalowski, R. and Shi, L. (1996). “Closure of “bearing capacity of footings over two-layer foundation soils”.” Journal of Geotechnical Engineering, Vol. 122, No. 8, pp. 701–702, DOI: 10.1061/(ASCE) 0733-9410(1996)122:8(701).CrossRefGoogle Scholar
  15. Michalowski, R. L. and Drescher, A. (2009). “Three dimensional stability of slopes and excavations.” Géotechnique, Vol. 59, No. 10, pp. 839–850, DOI: 10.1680/geot.8.P.136.CrossRefGoogle Scholar
  16. Pan, Q. J. and Dias, D. (2017). “Upper-bound analysis on the face stability of a non-circular tunnel.” Tunnelling and Underground Space Technology, Vol. 62, pp. 96–102, DOI: 10.1016/j.tust.2016.11.010.CrossRefGoogle Scholar
  17. Pan, Q. J. and Dias, D. (2018). “Three dimensional face stability of a tunnel in weak rock masses subjected to seepage forces.” Tunnelling and Underground Space Technology, Vol. 71, pp. 555–566, DOI: 10.1016/j.tust.2017.11.003.CrossRefGoogle Scholar
  18. Pan, Q. J., Xu, J. S., and Dias, D. (2017). “Three-dimensional stability of a slope subjected to seepage forces.” International Journal of Geomechanics, Vol. 17, No. 8, 04017035, DOI: 10.1061/(ASCE) GM.1943-5622.0000913.CrossRefGoogle Scholar
  19. Rabczuk, T. and Areias, P. M. A. (2010). “A new approach for modelling slip lines in geological materials with cohesive models.” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 30, pp. 1159–1172, DOI: 10.1002/nag.522.CrossRefzbMATHGoogle Scholar
  20. Rabczuk, T. and Belytschko, T. (2004). “Cracking particles: A simplified meshfree method for arbitrary evolving cracks.” International Journal for Numerical Methods in Engineering, Vol. 61, pp. 2316–2343, DOI: 10.1002/nme.1151.CrossRefzbMATHGoogle Scholar
  21. Regmi, R. K. and Jung, K. (2016). “Application of dynamic programming to locate the critical failure surface in a rainfall induced slope failure problem.” KSCE Journal of Civil Engineering, Vol. 20, No. 1, pp. 452–462, DOI: 10.1007/s12205-015-0183-9.CrossRefGoogle Scholar
  22. Simoni, A. and Houlsby, G. (2006). “The direct shear strength and dilatancy of sand-gravel mixtures.” Geotechnical and Geological Engineering, Vol. 24, No. 3, pp. 523–549, DOI: 10.1007/s10706-004-5832-6.CrossRefGoogle Scholar
  23. Wang, Y. Z., Liu, X. F., Zhang, Z. K., and Yang, P. (2015). “Analysis on slope stability considering seepage effect on effective stress.” KSCE Journal of Civil Engineering, Vol. 20, No. 6, pp. 2235–2242, DOI: 10.1007/s12205-015-0646-z.CrossRefGoogle Scholar
  24. Xu, J. S., Pan, Q. J., Yang, X. L., and Li, W. T. (2018). “Stability charts for rock slopes subjected to water drawdown based on the modified nonlinear Hoek-Brown failure criterion.” International Journal of Geomechanics, Vol. 18, No. 1, 04017133, DOI: 10.1061/(ASCE) GM.1943-5622.0001039.CrossRefGoogle Scholar
  25. Xu, J. S. and Yang, X. L. (2017). “Effects of seismic force and pore water pressure on three dimensional slope stability in nonhomogeneous and anisotropic soil.” KSCE Journal of Civil Engineering, DOI: 10.1007/s12205-017-1958-y.Google Scholar
  26. Yang, X. L. and Long, Z. X. (2016). “Seismic and static 3D stability of two-stage rock slope based on Hoek-Brown failure criterion.” Canadian Geotechnical Journal, Vol. 53, pp. 551–558, DOI: Scholar
  27. Yang, X. L. and Zhang, R. (2017). “Collapse analysis of shallow tunnel subjected to seepage in layered soils considering joined effects of settlement and dilation.” Geomechanics and Engineering, Vol. 13, No. 2, pp. 217–235, DOI: 10.12989/gae.2017.13.2.217.Google Scholar
  28. Yang, X. L. (2017). “Effect of pore-water pressure on 3D stability of rock slope.” International Journal of Geomechanics, Vol. 17, No. 9, 06017015, DOI: 10.1061/(ASCE)GM.1943-5622.0000969.CrossRefGoogle Scholar
  29. Zhang, X. J. and Chen, W. F. (1987). “Stability analysis of slopes with general nonlinear failure criterion.” International Journal for Numerical and Analytical Methods in Geotechnique, Vol. 11, No. 1, pp. 33–50, DOI: 10.1002/nag.1610110104.CrossRefzbMATHGoogle Scholar
  30. Zheng, W. B., Zhuang, X. Y., Tannant, D. D., Cai, Y. C., and Nunoo, S. (2014). “Unified continuum/discontinuum modeling framework for slope stability assessment.” Engineering Geology, Vol. 179, pp. 90–101, DOI: 10.1016/j.enggeo.2014.06.014.CrossRefGoogle Scholar
  31. Zhuang, X., Augarde, C. E., and Mathisen, K. M. (2012). “Fracture modeling using meshless methods and level sets in 3D: Framework and modeling.” International Journal for Numerical Methods in Engineering, Vol. 92, pp. 969–998, DOI: 10.1002/nme.4365.MathSciNetCrossRefzbMATHGoogle Scholar
  32. Zou, J. F., Xia, Z. Q., and Dan, H. C. (2016). “Theoretical solutions for displacement and stress of a circular opening reinforced by grouted rock bolt.” Geomechanics and Engineering, Vol. 11, No. 3, pp. 439–455, DOI: 10.12989/gae.2016.11.3.439.CrossRefGoogle Scholar
  33. Zou, J. F. and Xia, M. Y. (2017). “A new approach for the cylindrical cavity expansion problem incorporating deformation dependent of intermediate principal stress.” Geomechanics and Engineering, Vol. 12, No. 3, pp. 347–360, DOI: 10.12989/gae.2017.12.3.347.CrossRefGoogle Scholar

Copyright information

© Korean Society of Civil Engineers 2018

Authors and Affiliations

  1. 1.School of Civil EngineeringCentral South UniversityHunanChina

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