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Step-path failure of rock slopes with intermittent joints

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Abstract

Step-path failure is a typical instable mode of rock slopes with intermittent joints. To gain deeper insight into the step-path failure mechanism, six rock slopes with different intermittent joints are studied using the 2D Particle Flow Code (PFC). Three different step-path failure modes, i.e., shear, tensile, and mixed tensile–shear failure, are observed by focusing on the crack initiation, propagation, and coalescence in the rock bridges. The cracks develop progressively in the rock bridges, which induce the intermittent joints to coalesce one by one from bottom to top under the action of gravity. The tensile cracks that often appear in the main body and at the crown are nearly vertical to the step-path failure surface. The step-path failure in a rock slope with intermittent joints can be divided into four stages in terms of both stress and crack development in the rock bridges, i.e., elastic deformation, failure of rock bridges at a lower position, progressive failure of rock bridges upward, and final block slide. Therefore, reinforcement is suggested to be applied to the lower part of the slopes. Three equations for calculating the factors of safety are derived with respect to the three failure modes, in which the degree of joint coalescence is considered.

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References

  • An XM, Ning YJ, Ma GW, He L (2014) Modeling progressive failures in rock slopes with non-persistent joints using the numerical manifold method. Int J Numer Anal Methods Geomech 38(7):679–701

    Article  Google Scholar 

  • Bahaaddini M, Sharrock G, Hebblewhite BK (2013a) Numerical investigation of the effect of joint geometrical parameters on the mechanical properties of a non-persistent jointed rock mass under uniaxial compression. Comput Geotech 49(4):206–225

    Article  Google Scholar 

  • Bahaaddini M, Sharrock G, Hebblewhite BK (2013b) Numerical direct shear tests to model the shear behaviour of rock joints. Comput Geotech 51(6):101–115

    Article  Google Scholar 

  • Bobet A, Einstein HH (1998) Numerical modeling of fracture coalescence in a model rock material. Int J Fract 92:221–252

    Article  Google Scholar 

  • Call RD, Nicholas DE (1978) Prediction of step path failure geometry for slope stability analysis. Proc. of 19th U.S. Symp. on Rock Mechanics, Lake Tahoe, NV, 8p

  • Chandler J (1999) Effective application of automated digital photogrammetry for geomorphological research. Earth Surf Process Landf 24(1):51–63

    Article  Google Scholar 

  • Chihsen TL, Bernard A, Joseph J, Jerry D (1996) Extensions of discontinuous deformation analysis for jointed rock masses. Int J Rock Mech Min Sci 33(7):671–694

    Article  Google Scholar 

  • Cho N, Martin CD, Sego DC (2007) A clumped particle model for rock. Int J Rock Mech Min Sci 44:997–1010

    Article  Google Scholar 

  • Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65

    Article  Google Scholar 

  • Eberhardt E, Stead D, Coggan JS (2004a) Numerical analysis of initiation and progressive failure in natural rock slopes—the 1991 Randa rockslide. Int J Rock Mech Min Sci 41:69–87

    Article  Google Scholar 

  • Eberhardt E, Stead D, Karami A, Coggan J (2004a) Numerical analysis of brittle fracture propagation and step-path failure in massive rock slopes. 57th Canadian Geotechnical Conference, 5th Joint CGS/IAH-CNC Conference, Quebec City

  • Erdogan F, Sih GC (1963) On the crack extension path in plates under plane loading and transverse shear. ASMEJ Basic Eng 85D:519

    Article  Google Scholar 

  • Ghazvinian A, Sarfarazi V, Schubert W, Blumel M (2012) A study of the failure mechanism of planar non-persistent open joints using PFC2D. Rock Mech Rock Eng 45:677–693

    Article  Google Scholar 

  • Gigli G, Casagli N (2011) Semi-automatic extraction of rock mass structural data from high resolution LIDAR point clouds. Int J Rock Mech Min Sci 48(2):187–198

    Article  Google Scholar 

  • Goncalves da Silva B, Einstein HH (2013) Modeling of crack initiation, propagation and coalescence in rocks. Int J Fract 182(2):167–186

    Article  Google Scholar 

  • Haeri H, Marji MF, Shahriar K, Moarefvand P (2014a) On the HDD analysis of micro crack initiation, propagation, and coalescence in brittle materials. Arab J Geosci. doi:10.1007/s12517-014-1290-5

    Google Scholar 

  • Haeri H, Shahriar K, Marji MF, Moarefvand P (2014b) Cracks coalescence mechanism and cracks propagation paths in rock-like specimens containing pre-existing random cracks under compression. J Cent South Univ 21(6):2404–2414

    Article  Google Scholar 

  • 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):813–832

    Article  Google Scholar 

  • Huang D, Cen DF (2013) Mechanical responses and energy dissipation mechanism of rock specimen with a single fissure under static and dynamic uniaxial compression using particle flow code simulations. Chin J Rock Mech Eng 32(9):1926–1936 (in Chinese)

    Google Scholar 

  • Hussain MA, Pu EL, Underwood JH (1974) Strain energy release rate for a crack under combined model I and mode II. ASTM STP 560:28

    Google Scholar 

  • Itasca Consulting Group Inc. (2008) PFC2D Particle Flow Code in 2 dimensions user’s guide

  • Jennings JE (1970) A mathematical theory for the calculation of the stability of slopes in open cast mine. Proceedings of the Symposium on Planning Open Pit Mines, Johannesburg

  • Kemeny J (2003) The time-dependent reduction of sliding cohesion due to rock bridges along discontinuities: a fracture mechanics approach. Rock Mech Rock Eng 36:27–38

    Article  Google Scholar 

  • Khan SMA, Khraisheh MK (2000) Analysis of mixed mode crack initiation angles under various loading conditions. Eng Fract Mech 67(5):397–419

    Article  Google Scholar 

  • Khan SMA, Khraisheh MK (2004) A new criterion for mixed mode fracture initiation based on the crack tip plastic core region. Int J Plast 20(1):55–84

    Article  Google Scholar 

  • Kulatilake PHSW, Malama B, Wang J (2001) Physical and particle flow modeling of jointed rock block behavior under uniaxial loading. Int J Rock Mech Min Sci 38(5):641–657

    Article  Google Scholar 

  • Lee H, Jeon S (2011) An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression. Int J Solids Struct 48(6):979–999

    Article  Google Scholar 

  • Li LC, Tang CA, Zhu WC, Liang ZZ (2009) Numerical analysis of slope stability based on the gravity increase method. Comput Geotech 36:1246–1258

    Article  Google Scholar 

  • Liu ZN, Koyi HA (2013) Kinematics and internal deformation of granular slopes: insights from discrete element modeling. Landslides 10:139–160

    Article  Google Scholar 

  • Ma GW, An XM, He L (2010) The numerical manifold method: a review. Int J Comput Method 7(1):1–32

    Article  Google Scholar 

  • Mas Ivars D, Potyondy DO, Pierce M, Cundall PA (2008) The smooth-joint contact model. In: Schrefler BA, Perego U (eds) Proceedings of WCCM8-ECCOMAS, Barcelona, 2008.

  • Mejía Camones LA, Amaral Vargas ED, Pelucí de Figueiredo R, Quadros Velloso R (2013) Application of the discrete element method for modeling of rock crack propagation and coalescence in the step-path failure mechanism. Eng Geol 153(2):80–94

    Article  Google Scholar 

  • Miller SM, Whyatt JK, Mchugh EL (2004) Applications of the point estimation method for stochastic rock slope engineering. Gulf Rocks 2004: Proceedings, Rock Mechanics Across Borders and Disciplines, 6th North American Rock Mechanics Conference, Houston, Texas. ARMA/NARMS (04–517)

  • Muller JR, Martel SJ (2000) Numerical models of translational landslide rupture surface growth. Pure Appl Geophys 157:1009–1038

    Article  Google Scholar 

  • Ning YJ, An XM, Ma GW (2011) Footwall slope stability analysis with the numerical manifold method. Int J Rock Mech Min Sci 48:964–975

    Article  Google Scholar 

  • Ning JG, Ren HL, Fang MJ (2012a) A constitutive model based on the evolution and coalescence of elliptical micro-cracks for quasi-brittle materials. Chin Sci Bull 57(28–29):3773–3781

    Article  Google Scholar 

  • Ning YJ, An XM, Lu Q, Ma GW (2012b) Modeling rock failure using the numerical manifold method followed by the discontinuous deformation analysis. Acta Mech Sinica 28(3):760–773

    Article  Google Scholar 

  • Ning JG, Ren HL, Fang MJ (2014) Research on the process of micro-crack damage evolution and coalescence in brittle materials. Eng Fail Anal 41:65–72

    Article  Google Scholar 

  • Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41:1239–1364

    Article  Google Scholar 

  • Prudencio M, Van Sint JM (2007) Strength and failure modes of rock mass models with non-persistent joints. Int J Rock Mech Min Sci 44(6):890–902

    Article  Google Scholar 

  • Sagong M, Bobet A (2002) Coalescence of multiple flaws in a rock-model material in uniaxial compression. Int J Rock Mech Min Sci 39(2):229–241

    Article  Google Scholar 

  • Scavia C (1990) Fracture mechanics approach to stability analysis of rock slopes. Eng Fract Mech 35(4/5):899–910

    Article  Google Scholar 

  • Sih GC (1974) Strain energy density factor applied to mixed mode crack problems. Int J Fract 10(3):305–321

    Article  Google Scholar 

  • Singh RN, Sun GX (1989) Fracture mechanics applied to slope stability analysis. International Symposium on Surface Mining-Future Concepts. University of Nottingham, England, p 93–97

  • Stead D, Coggan JS, Eberhardt E (2004) Realistic simulation of rock slope failure mechanisms: the need to incorporate principles of fracture mechanics. Int J Rock Mech Min Sci 41:563–568

    Article  Google Scholar 

  • Tang CA, Lin P, Wong RHC, Chau KT (2001) Analysis of crack coalescence in rock-like materials containing three flaws—Part II: numerical approach. Int J Rock Mech Min Sci 38:925–939

    Article  Google Scholar 

  • Tang CL, Hu JC, Lin ML, Angelier J, Lu CY, Chan YC, Chu HT (2009) The Tsaoling landslide triggered by the Chi-Chi earthquake, Taiwan: insights from a discrete element simulation. Eng Geol 106:1–19

    Article  Google Scholar 

  • Tharp TM, Coffin DF (1985) Field application of fracture mechanics analysis to small rock slopes. Proceedings, 26th U.S. Symposium on Rock Mechanics, South Dakota School on Mines and Technology, Rapid City, 26–28 June 1985

  • Wang C, Tannant DD, Lilly PA (2003) Numerical analysis of the stability of heavily jointed rock slopes using PFC2D. Int J Rock Mech Min Sci 40(3):415–424

    Article  Google Scholar 

  • Wong LNY, Einstein HH (2009) Crack coalescence in molded gypsum and carrara marble: part 1. Macroscopic observations and interpretation. Rock Mech Rock Eng 42(3):475–511

    Article  Google Scholar 

  • Wong LNY, Einstein HH (2012) Using high speed video imaging in the study of cracking processes in rock. Geotech Test J 32(2):1–17

    Google Scholar 

  • Wyllie DC, Mah CW (2004) Rock slope engineering: civil and mining, 4th edn. Taylor & Francis Group, London and New York

    Google Scholar 

  • Yoon J (2007) Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation. Int J Rock Mech Min Sci 44:871–889

    Article  Google Scholar 

  • Zhang XP, Wong LNY (2012) Cracking processes in rock-like material containing a single flaw under uniaxial compression: a numerical study based on parallel bonded-particle model approach. Rock Mech Rock Eng 45(5):711–737

    Google Scholar 

  • Zhang XP, Wong LNY (2013) Crack initiation, propagation and coalescence in rock-like material containing two flaws: a numerical study based on bonded-particle model approach. Rock Mech Rock Eng 46(5):1001–1021

    Article  Google Scholar 

  • Zhang K, Cao P, Meng J, Li K, Fan W (2014) Modeling the progressive failure of jointed rock slope using fracture mechanics and the strength reduction method. Rock Mech Rock Eng. doi:10.1007/s00603-014-0605-x

    Google Scholar 

  • Zhou XP, Yang HQ (2012) Multiscale numerical modeling of propagation and coalescence of multiple cracks in rock masses. Int J Rock Mech Min Sci 55:15–27

    Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China (No. 41172243, 41472245, and 41130745), the Fundamental Research Funds for the Central Universities (No. CDJZR12205501 and No. 106112014CDJZR200009), and the open Foundation of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (No. SKLGP2011K003).

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Correspondence to Da Huang.

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Huang, D., Cen, D., Ma, G. et al. Step-path failure of rock slopes with intermittent joints. Landslides 12, 911–926 (2015). https://doi.org/10.1007/s10346-014-0517-6

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