Abstract
Step-path failure is a typical unstable mode of rock slopes with intermittent joints, and the accurate prediction of their stability is of great significance. In the present study, an energy calculation programme for the slope system based on secondary development of two-dimensional particle flow code (PFC2D) was proposed. The step-path failure modes of slopes with intermittent joints were well reproduced and could be classified into three types according to the penetration modes of rock bridges: shear penetration, tensile penetration, and tensile–shear mixed penetration. The evolution of gravitational potential energy, elastic strain energy, and kinetic energy were also captured. Based on this, the failure criterion depending on the energy mutation was established. When the slope approached the critical instability state, the gravitational potential energy reduction, kinetic energy increment, and dissipative energy increment all increased suddenly, while the elastic strain energy increment suddenly decreased, indicating that the energy mutation could be used as the failure criterion for rock slopes with intermittent joints. The proposed energy mutation criterion has the advantages of clear physical meaning, strong integrity, easy judgement, and good applicability, which provides certain theoretical support for evaluation of rock mass stability and prediction of instability of jointed slopes.
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References
Atta-Ur-Rahman, Khan AN, Collins AE (2014) Erratum to: Analysis of landslide causes and associated damages in the Kashmir Himalayas of Pakistan. Nat Hazards 74:1307–1307. https://doi.org/10.1007/s11069-014-1298-x
Bobet A, Einstein HH (1998) Fracture coalescence in rock-type materials under uniaxial and biaxial compression. Int J Rock Mech Min Sci 35:863–888. https://doi.org/10.1016/S0148-9062(98)00005-9
Camones LAM, do Vargas EA, de Figueiredo RP, Velloso RQ (2013) Application of the discrete element method for modeling of rock crack propagation and coalescence in the step-path failure mechanism. Eng Geol 153:80–94. https://doi.org/10.1016/j.enggeo.2012.11.013
Cheng YM, Lansivaara T, Wei WB (2007) Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods. Comput Geotech 34:137–150. https://doi.org/10.1016/j.compgeo.2006.10.011
Chen G, Tang P, Huang R, Wang D, Lin Z, Huang D (2021a) Critical tension crack depth in rockslides that conform to the three-section mechanism. Landslides 18:79–88. https://doi.org/10.1007/s10346-020-01471-x
Chen Z, Hu X, Bu X (2021b) Effect of weak intercalation on failure mode of rock slopes under seismic excitation. Nat Hazards 105:363–381. https://doi.org/10.1007/s11069-020-04314-z
Cho SE (2013) First-order reliability analysis of slope considering multiple failure modes. Eng Geol 154:98–105. https://doi.org/10.1016/j.enggeo.2012.12.014
Dawson EM, Roth WH, Drescher A (1999) Slope stability analysis by strength reduction. Géotechnique 49:835–840. https://doi.org/10.1680/geot.1999.49.6.835
Du Y, Xie M (2022) Indirect method for the quantitative identification of unstable rock. Nat Hazards 112:1005–1012. https://doi.org/10.1007/s11069-021-05197-4
Eberhardt E, Stead D, Coggan JS, Willenberg H (2003) Hybrid finite-/discrete-element modelling of progressive failure in massive rock slopes. Presented at the 10th ISRM Congress, OnePetro
Gehle C, Kutter HK (2003) Breakage and shear behaviour of intermittent rock joints. Int J Rock Mech Min Sci 40:687–700. https://doi.org/10.1016/S1365-1609(03)00060-1
Huang D, Cen D, Ma G, Huang R (2015) Step-path failure of rock slopes with intermittent joints. Landslides 12:911–926. https://doi.org/10.1007/s10346-014-0517-6
Huang Y, Yang S, Tian W (2019a) Cracking process of a granite specimen that contains multiple pre-existing holes under uniaxial compression. Fatigue Fract Eng Mater Struct 42:1341–1356. https://doi.org/10.1111/ffe.12990
Huang Y-H, Yang S-Q, Tian W-L (2019b) Crack coalescence behavior of sandstone specimen containing two pre-existing flaws under different confining pressures. Theoret Appl Fract Mech 99:118–130. https://doi.org/10.1016/j.tafmec.2018.11.013
Jennings J (1970) A mathematical theory for the calculation of the stability of slopes in open cast mine. Presented at the Planning open pit mines, proceedings, Johannesburg
Kang Y, Zhao C, Zhang Q, Lu Z, Li B (2017) Application of InSAR techniques to an analysis of the Guanling Landslide. Remote Sensing 9:1046. https://doi.org/10.3390/rs9101046
Kokusho T, Ishizawa T (2007) Energy approach to earthquake-induced slope failures and its implications. J Geotech Geoenviron Eng 133:828–840. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:7(828)
Lv Q, Liu Y, Yang Q (2017) Stability analysis of earthquake-induced rock slope based on back analysis of shear strength parameters of rock mass. Eng Geol 228:39–49. https://doi.org/10.1016/j.enggeo.2017.07.007
Ma Q, Tan Y, Liu X, Zhao Z, Fan D (2021) Mechanical and energy characteristics of coal–rock composite sample with different height ratios: a numerical study based on particle flow code. Environ Earth Sci 80:309. https://doi.org/10.1007/s12665-021-09453-5
Sardana S, Verma AK, Verma R, Singh TN (2019) Rock slope stability along road cut of Kulikawn to Saikhamakawn of Aizawl, Mizoram, India. Nat Hazards 99:753–767. https://doi.org/10.1007/s11069-019-03772-4
Schlögl M, Gutjahr K, Fuchs S (2022) Correction to: The challenge to use multi-temporal InSAR for landslide early warning. Nat Hazards 113:1949–1949. https://doi.org/10.1007/s11069-022-05355-2
Sjöberg J (1996) Large scale slope stability in open pit mining : a review. Luleå tekniska universitet
Sloan SW (2013) Geotechnical stability analysis. Géotechnique 63:531–571. https://doi.org/10.1680/geot.12.RL.001
Solecki R, Conant RJ (2003) Advanced mechanics of materials. Oxford University Press
Tian W-L, Yang S-Q, Xie L-X, Wang Z-L (2018) Cracking behavior of three types granite with different grain size containing two non-coplanar fissures under uniaxial compression. Arch Civ Mech Eng 18:1580–1596. https://doi.org/10.1016/j.acme.2018.06.001
Tschuchnigg F, Schweiger HF, Sloan SW, Lyamin AV, Raissakis I (2015a) Comparison of finite-element limit analysis and strength reduction techniques. Géotechnique 65:249–257. https://doi.org/10.1680/geot.14.P.022
Tschuchnigg F, Schweiger HF, Sloan SW (2015b) Slope stability analysis by means of finite element limit analysis and finite element strength reduction techniques. Part I: numerical studies considering non-associated plasticity. Comput Geotech 70:169–177. https://doi.org/10.1016/j.compgeo.2015.06.018
Tu Y, Liu X, Zhong Z, Li Y (2016) New criteria for defining slope failure using the strength reduction method. Eng Geol 212:63–71. https://doi.org/10.1016/j.enggeo.2016.08.002
Wang H, Dyskin A, Pasternak E, Dight P, Sarmadivaleh M (2018) Effect of the intermediate principal stress on 3-D crack growth. Eng Fract Mech 204:404–420. https://doi.org/10.1016/j.engfracmech.2018.10.024
Wang W, Li J, Qu X, Han Z, Liu P (2019) Prediction on landslide displacement using a new combination model: a case study of Qinglong landslide in China. Nat Hazards 96:1121–1139. https://doi.org/10.1007/s11069-019-03595-3
Wang H, Dyskin A, Pasternak E, Dight P, Sarmadivaleh M (2020) Experimental and numerical study into 3D crack growth from a spherical pore in biaxial compression. Rock Mech Rock Eng 53:77–102. https://doi.org/10.1007/s00603-019-01899-1
Wei J, Zhao Z, Xu C, Wen Q (2019) Numerical investigation of landslide kinetics for the recent Mabian landslide (Sichuan, China). Landslides 16:2287–2298. https://doi.org/10.1007/s10346-019-01237-0
Wong RHC, Chau KT (1997) The coalescence of frictional cracks and the the shear zone formation in brittle solids under compressive stresses. Int J Rock Mech Min Sci 34:335.e1-335.e12. https://doi.org/10.1016/S1365-1609(97)00119-6
Wong RHC, Chau KT (1998) Crack coalescence in a rock-like material containing two cracks. Int J Rock Mech Min Sci 35:147–164. https://doi.org/10.1016/S0148-9062(97)00303-3
Wong RHC, Chau KT, Tang CA, Lin P (2001) Analysis of crack coalescence in rock-like materials containing three flaws—Part I: experimental approach. Int J Rock Mech Min Sci 38:909–924. https://doi.org/10.1016/S1365-1609(01)00064-8
Wu Z, Zhang D, Wang S, Liang C, Zhao D (2020) Dynamic-response characteristics and deformation evolution of loess slopes under seismic loads. Eng Geol 267:105507. https://doi.org/10.1016/j.enggeo.2020.105507
Yang S-Q, Yin P-F, Huang Y-H (2019a) Experiment and discrete element modelling on strength, deformation and failure behaviour of shale under Brazilian compression. Rock Mech Rock Eng 52:4339–4359. https://doi.org/10.1007/s00603-019-01847-z
Yang S-Q, Yin P-F, Zhang Y-C, Chen M, Zhou X-P, Jing H-W, Zhang Q-Y (2019b) Failure behavior and crack evolution mechanism of a non-persistent jointed rock mass containing a circular hole. Int J Rock Mech Min Sci 114:101–121. https://doi.org/10.1016/j.ijrmms.2018.12.017
Yin Y, Sun P, Zhu J, Yang S (2011) Research on catastrophic rock avalanche at Guanling, Guizhou, China. Landslides 8:517–525. https://doi.org/10.1007/s10346-011-0266-8
Zheng S, Jiang A-N, Feng K-S (2021) A reliability evaluation method for intermittent jointed rock slope based on evolutionary support vector machine. CMES 129:149–166. https://doi.org/10.32604/cmes.2021.016761
Zhou Y, Wu SC, Wang L, Yan Q, Zhang XP (2013) Application of equivalent rock mass technique to mesoscopic analysis of fracture mechanism of rock specimen containing two intermittent joint. Rock Soil Mech 34:2801–2809
Zhou Y, Zhao D, Li B, Wang H, Tang Q, Zhang Z (2021a) Fatigue damage mechanism and deformation behaviour of granite under ultrahigh-frequency cyclic loading conditions. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-021-02524-w
Zhou Z, Shen Y, Zhang H, Wang Y, Yang H, Pan J, Wei X (2021b) Sandstone-concrete interface debonding mechanism under freeze-thaw actions: fracture process and fracture criterion. Constr Build Mater 294:123526. https://doi.org/10.1016/j.conbuildmat.2021.123526
Zhou Z, Chen Z, Shen Y, Bao M, Nian G, Zhang L, Liu Y (2022) Failure of rock slopes with intermittent joints: failure process and stability calculation models. Lithosphere 2021:8923718. https://doi.org/10.2113/2022/8923718
Zienkiewicz OC, Humpheson C, Lewis RW (1975) Associated and non-associated visco-plasticity and plasticity in soil mechanics. Géotechnique 25:671–689. https://doi.org/10.1680/geot.1975.25.4.671
Acknowledgements
We would like to give great thanks to National Natural Science Foundation of China (Grant No. 52204146), China Postdoctoral Science Foundation (Grant Nos. 2022M721885 and 2022M712301), Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ21E040003), and Key Laboratory of Rock Mechanics and Geohazards of Zhejiang Province (No. ZJRMG-2022-01) for providing necessary support on this research.
Funding
This study is partially funded by the National Natural Science Foundation of China (Grant No. 52204146), China Postdoctoral Science Foundation (Grant Nos. 2022M721885 and 2022M712301), Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ21E040003), and Key Laboratory of Rock Mechanics and Geohazards of Zhejiang Province (No. ZJRMG-2022-01).
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Zhou, Y., Lv, W., Zhou, Z. et al. New failure criterion for rock slopes with intermittent joints based on energy mutation. Nat Hazards 118, 407–425 (2023). https://doi.org/10.1007/s11069-023-06011-z
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DOI: https://doi.org/10.1007/s11069-023-06011-z