Advertisement

Failure Mechanisms of Toppling Rock Slopes Using a Three-Dimensional Discontinuous Deformation Analysis Method

  • Guoyang LiuEmail author
  • Junjie Li
  • Fei Kang
Original Paper
  • 161 Downloads

Abstract

Toppling is a representative failure mode of discontinuity-controlled rock slopes. As a discrete numerical method, discontinuous deformation analysis (DDA) is well-suited for simulating the movement process, contact transformation, and large displacement and deformation of rock block systems, which are formed in jointed rock masses. In the present study, a three-dimensional (3D) DDA method was conducted to study the toppling failure mechanisms of rock slopes by introducing the global contact theory. Considering dynamic equilibrium conditions, the analyses of toppling slopes were performed and the corresponding formulations were derived. The algebraic and mechanical computation of the global contact theory was illustrated and implemented into the 3D DDA method. An experimental apparatus for studying the toppling process of blocks was developed and a series of laboratory experiments were carried out for different block distributions under different conditions. By comparing with the results of the analytical methods and laboratory experiments, the accuracy of the 3D DDA method was verified. Numerical examples, including a classical toppling slope, an ideal mountain slope, and a real toppling case were analyzed to further research the toppling failure mechanisms. The results revealed that the 3D DDA method can effectively predict slope instability and simulate the failure process of toppling slopes. The results of the dynamics-based formulations, experiments and 3D DDA enrich the instability conditions of slope-toppling. Moreover, the general phenomena and laws of the toppling failure were presented.

Keywords

Toppling slope Failure mechanism 3D DDA Contact theory Laboratory experiment 

Notes

Acknowledgements

This research was supported by the National Key Research and Development Program of China under Grant Nos. 2016YFC0401600 and 2017YFC0404906, the National Natural Science Foundation of China under Grant Nos. 51769033 and 51779035, and the Fundamental Research Funds for the Central Universities under Grant No. DUT17ZD205.

References

  1. Aydan Ö, Shimizu Y, Ichikawa Y (1989) The effective failure modes and stability of slopes in rock mass with two discontinuity sets. Rock Mech Rock Eng 22(3):163–188CrossRefGoogle Scholar
  2. Bakun-Mazor D, Hatzor YH, Glaser SD (2012) Dynamic sliding of tetrahedral wedge: the role of interface friction. Int J Nume Anal Meth Geomech 36(3):327–343CrossRefGoogle Scholar
  3. Bao HR, Zhao ZY (2012) The vertex-to-vertex contact analysis in the two-dimensional discontinuous deformation analysis. Adv Eng Softw 45(1):1–10CrossRefGoogle Scholar
  4. Beyabanaki SAR, Mikola RG, Biabanaki SOR, Mohammadi S (2009) New point-to-face contact algorithm for 3-D contact problems using the augmented Lagrangian method in 3-D DDA. Geomech Geoeng Int J 4(3):221–236CrossRefGoogle Scholar
  5. Bray JW, Goodman RE (1981) The theory of base friction models. Int J Rock Mech Min Sci 18(6):453–468CrossRefGoogle Scholar
  6. Chen GQ, Ohnishi Y, Ito T (1998) Development of high-order manifold method. Int J Numer Methods Eng 43(4):685–712CrossRefGoogle Scholar
  7. Chen GQ, Zheng L, Zhang YB, Wu J (2013) Numerical simulation in rockfall analysis: a close comparison of 2-D and 3-D DDA. Rock Mech Rock Eng 46(3):527–541CrossRefGoogle Scholar
  8. Chen ZY, Gong WJ, Ma GW, Wang J, He L, Xing YC, Xing JY (2015) Comparisons between centrifuge and numerical modeling results for slope toppling failure. Sci China Technol Sci 58(9):1497–1508CrossRefGoogle Scholar
  9. Cundall PA (1971) A computer model for simulating progressive, large scale movements in blocky rock systems. Proc Int Symp Rock Fract Nancy, France, pp 129–136Google Scholar
  10. Doolin DM, Sitar N (2004) Time integration in discontinuous deformation analysis. J Eng Mech 130(3):249–258CrossRefGoogle Scholar
  11. Goodman RE, Bray JW (1976) Toppling of rock slopes. In: Proceedings of the specialty conference on rock engineering for foundations and slopes. American Society of Civil Engineers, Boulder, pp 201–234Google Scholar
  12. Goodman RE, Shi GH (1985) Block theory and its application to rock engineering. Prentice-Hall Inc, New JerseyGoogle Scholar
  13. Grayeli R, Mortazavi A (2006) Discontinuous deformation analysis with second-order finite element meshed block. Int J Numer Anal Meth Geomech 30(15):1545–1561CrossRefGoogle Scholar
  14. Hatzor YH, Arzi AA, Zaslavsky Y, Shapira A (2004) Dynamic stability analysis of jointed rock slopes using the DDA method: King Herod’s Palace, Masada, Israel. Int J Rock Mech Min Sci 41(5):813–832CrossRefGoogle Scholar
  15. Hoek E, Bray JW (1977) Rock slope engineering, 1st edn. The Institution of Mining and Metallurgy, LondonGoogle Scholar
  16. Hu YD (2015) The toppling deformation rock characteristics and reinforcement measures of research in the front of the dam of Miaowei hydropower station. Dissertation, Chengdu University of TechnologyGoogle Scholar
  17. Jiang QH, Yeung MR (2004) A model of point-to-face contact for three-dimensional discontinuous deformation analysis. Rock Mech Rock Eng 37(2):95–116CrossRefGoogle Scholar
  18. Keneti AR, Jafari A, Wu JH (2008) A new algorithm to identify contact patterns between convex blocks for three-dimensional discontinuous deformation analysis. Comput Geotech 35(5):746–759CrossRefGoogle Scholar
  19. Liu J, Kong X, Lin G (2004) Formulation of the three-dimensional discontinuous deformation analysis method. Acta Mech Sin 20(3):270–282CrossRefGoogle Scholar
  20. Liu CH, Jaksa MB, Meyers AG (2009) A transfer coefficient method for rock slope toppling. Can Geotech J 46(1):1–9CrossRefGoogle Scholar
  21. Ning Y, Zhao Z (2013) A detailed investigation of block dynamic sliding by the discontinuous deformation analysis. Int J Numer Anal Meth Geomech 37(15):2373–2393CrossRefGoogle Scholar
  22. Pritchard MA, Savigny KW (1990) Numerical modeling of toppling. Can Geotech J 27:823–834CrossRefGoogle Scholar
  23. Sagaseta C (1986) On the modes of instability of a rigid block. Rock Mech Rock Eng 19(4):261–266CrossRefGoogle Scholar
  24. Shi GH (1988) Discontinuous deformation analysis: a new numerical model for the statics and dynamics of block systems. Dissertation, University of California, BerkeleyGoogle Scholar
  25. Shi GH (2001) Three-dimensional discontinuous deformation analysis. In: Proceedings of the 4th international conference on analysis of discontinuous deformation. Scotland, pp 1–21Google Scholar
  26. Shi GH (2015) Contact theory. Sci China Technol Sci 58(9):1–47CrossRefGoogle Scholar
  27. Tang CA, Tang SB, Gong B, Bai HM (2015) Discontinuous deformation and displacement analysis: from continuous to discontinuous. Sci China Technol Sci 58(9):1567–1574CrossRefGoogle Scholar
  28. Wu JH (2008) New edge-to-edge contact calculating algorithm in three-dimensional discrete numerical analysis. Adv Eng Softw 39(1):15–24CrossRefGoogle Scholar
  29. Wu JH (2010) Seismic landslide simulations in discontinuous deformation analysis. Comput Geotech 37(5):594–601CrossRefGoogle Scholar
  30. Wu JH, Ohnishi Y, Nishiyama S (2004) Simulation of the mechanical behavior of inclined jointed rock masses during tunnel construction using Discontinuous Deformation Analysis (DDA). Int J Rock Mech Min Sci 41(5):731–743CrossRefGoogle Scholar
  31. Wu JH, Ohnishi Y, Shi GH, Nishiyama S (2005) Theory of three-dimensional discontinuous deformation analysis and its application to a slope toppling at Amatoribashi, Japan. Int J Geomech 5(3):179–195CrossRefGoogle Scholar
  32. Yagoda-Biran G, Hatzor YH (2016) Benchmarking the numerical discontinuous deformation analysis method. Comput Geotech 71:30–46CrossRefGoogle Scholar
  33. Yeung MR, Jiang QH, Sun N (2007) A model of edge-to-edge contact for three dimensional discontinuous deformation analysis. Comput Geotech 34(3):175–186CrossRefGoogle Scholar
  34. Zanbak C (1983) Design charts for rock slopes susceptible to toppling. J Geotech Eng ASCE 109(8):1039–1062CrossRefGoogle Scholar
  35. Zhang GX, Zhao Y, Peng XC (2010) Simulation of toppling failure of rock slope by numerical manifold method. Int Comput Method 7:167–189CrossRefGoogle Scholar
  36. Zhang YB, Xu Q, Chen GQ, Zhao JX, Zheng L (2014) Extension of discontinuous deformation analysis and application in cohesive-frictional slope analysis. Int J Rock Mech Min Sci 70:533–545CrossRefGoogle Scholar
  37. Zhang Z, Wang T, Wu S, Tang H (2015) Rock toppling failure mode influenced by local response to earthquakes. Bull Eng Geol Env 75(4):1361–1375CrossRefGoogle Scholar
  38. Zhang H, Liu SG, Zheng L, Zhong GH, Lou S, Han Z (2016) Extensions of edge-to-edge contact model in three-dimensional discontinuous deformation analysis for friction analysis. Comput Geotech 71:261–275CrossRefGoogle Scholar
  39. Zhang H, Liu SG, Wang W, Zheng L, Zhang YB, Wu YQ, Han Z, Li YG, Chen GQ (2018) A new DDA model for kinematic analyses of rockslides on complex 3-D terrain. Bull Eng Geol Environ 77:555–571CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Infrastructure Engineering, School of Hydraulic EngineeringDalian University of TechnologyDalianChina
  2. 2.School of EngineeringTibet UniversityLhasaChina

Personalised recommendations