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Quantitative description of stress-dependent post-peak brittle characteristics and numerical implementation

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Abstract

In this study, based on true-triaxial compression tests, five typical post-peak brittle characteristics are summarized, and the stress dependence is observed. Next, the quantitative description of this stress-dependent post-peak brittle characteristic is theoretically discussed. Then, combining the cluster analysis and the artificial recognition results on the brittleness, a new quantitative universal classification method based on stress-dependent brittleness is proposed, which is suitable for numerous hard rock types, with fewer parameters involved. Through implemented code and application to the actual field case, it is found that this stress-dependent post-peak characteristics model causes the higher energy concentration to occur at a deeper location comparing to traditional stress-independent models. The significance of the hard rock engineering is discussed, and the results indicate that it is necessary to consider the true-triaxial stress state of the rock mass and the influence of intermediate and minor principal stresses to the post-peak behaviour cannot be neglected. Finally, it is suggested to adopt the stress-dependent post-peak characteristic model in the design process of hard rock engineering, particularly for cases under high stress or severe engineering hazards such as rockbursts, which require more accurate calculation and prediction with lower error allowance.

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References

  • Alonso E, Alejano LR, Varas F, Fdez-Manin G, Carranza-Torres C (2003) Ground response curves for rock masses exhibiting strain-softening behaviour. Int J Numer Anal Meth Geomech 27(13):1153–1185

    Article  Google Scholar 

  • Amann F, Button EA, Evans KF, Gischig VS, Blümel M (2011) Experimental study of the brittle behaviour of clay shale in rapid unconfined compression. Rock Mech Rock Eng 44(4):415–430

    Article  Google Scholar 

  • Amari SI (1993) Backpropagation and stochastic gradient descent method. Neurocomputing 5(4–5):185–196

    Article  Google Scholar 

  • Aubertin M, Gill DE, Simon R (1994) On the use of the brittleness index modified (BIM) to estimate the post peak behaviour of rocks. In 1st North American Rock Mechanics Symposium. American Rock Mechanics Association

  • Brown ET, Bray JW, Ladanyi B, Hoek E (1983) Ground response curves for rock tunnels. J Geotech Eng 109(1):15–39

    Article  Google Scholar 

  • Byerlee JD (1968) Brittle-ductile transition in rocks. J Geophys Res 73(14):4741–4750

    Article  Google Scholar 

  • Crowder JJ, Bawden WF (2004) Review of post peak parameters and behaviour of rock masses: current trends and research. Rocnews, fall

  • Dreiseitl S, Ohno-Machado L (2002) Logistic regression and artificial neural network classification models: a methodology review. J Biomed Inform 35(5–6):352–359

    Article  Google Scholar 

  • Eberhardt E, Stead D, Coggan JS (2004) Numerical analysis of initiation and progressive failure in natural rock slopes—the 1991 Randa rockslide. Int J Rock Mech Min Sci 41(1):69–87

    Article  Google Scholar 

  • Edelbro C (2009) Numerical modelling of observed fallouts in hard rock masses using an instantaneous cohesion-softening friction-hardening model. Tunn Undergr Space Technol 24(4):398–409

    Article  Google Scholar 

  • Feng XT, Pan PZ, Zhou H (2006) Simulation of the rock microfracturing process under uniaxial compression using an elasto-plastic cellular automaton. Int J Rock Mech Min Sci 43(7):1091–1108

    Article  Google Scholar 

  • Feng XT, Hudson JA (2011) Rock engineering design. CRC Press

    Google Scholar 

  • Feng XT, Zhang X, Kong R, Wang G (2016) A novel mogi type true-triaxial testing apparatus and its use to obtain complete stress–strain curves of hard rocks. Rock Mech Rock Eng 49(5):1649–1662

    Article  Google Scholar 

  • Feng XT, Kong R, Yang C, Zhang X, Wang Z, Han Q, Wang G (2019a) A Three-Dimensional Failure Criterion for Hard Rocks Under True-triaxial Compression. Rock Mech Rock Eng 1–9

  • Feng XT (2017) Rockburst: mechanisms, monitoring, warning, and mitigation. Butterworth-Heinemann

    Google Scholar 

  • Feng XT, Yao ZB, Li SJ, Wu SY, Yang CX, Guo HS, Zhong S (2018a) In situ observation of hard surrounding rock displacement at 2400-m-deep tunnels. Rock Mech Rock Eng 51(3):873–892

    Article  Google Scholar 

  • Feng XT, Xu H, Qiu SL, Li SJ, Yang CX, Guo HS, Gao YH (2018b) In situ observation of rock spalling in the deep tunnels of the China Jinping underground laboratory (2400 m Depth). Rock Mech Rock Eng 51(4):1193–1213

    Article  Google Scholar 

  • Feng XT, Guo HS, Yang CX, Li SJ (2018c) In situ observation and evaluation of zonal disintegration affected by existing fractures in deep hard rock tunneling. Eng Geol 242:1–11

    Article  Google Scholar 

  • Feng XT, Zhou YY, Jiang Q (2019a) Rock mechanics contributions to recent hydroelectric developments in China. J Rock Mech Geotech Eng

  • Feng XT, Kong R, Zhang X, Yang C (2019b) Experimental Study of Failure Differences in Hard Rock Under True-triaxial Compression. Rock Mech Rock Eng 1–14

  • Feng XT, Wang Z, Zhou Y, Yang C, Pan PZ, Kong R (2021a) Modelling three-dimensional stress-dependent failure of hard rocks. Acta Geotech 16(6):1647–1677

    Article  Google Scholar 

  • Feng XT, Zhao J, Wang Z, Yang C, Han Q, Zheng Z (2021b) Effects of high differential stress and mineral properties on deformation and failure mechanism of hard rocks. Can Geotech J 58:411–426

    Article  Google Scholar 

  • Feng XT, Pan PZ, Wang Z, Zhang Y (2021c) Development of Cellular Automata Software for Engineering Rockmass Fracturing Processes. in International Conference of the International Association for Computer Methods and Advances in Geomechanics. Torino, Italy: Springer International Publishing

  • Gao YH, Feng XT, Zhang XW, Feng GL, Jiang Q, Qiu SL (2018) Characteristic stress levels and brittle fracturing of hard rocks subjected to true-triaxial compression with low minimum principal stress. Rock Mech Rock Eng 51(12):3681–3697

    Article  Google Scholar 

  • Hajiabdolmajid V, Kaiser PK, Martin CD (2002) Modelling brittle failure of rock. Int J Rock Mech Min Sci 39(6):731–741

    Article  Google Scholar 

  • Hajiabdolmajid V, Kaiser P (2003) Brittleness of rock and stability assessment in hard rock tunneling. Tunn Undergr Space Technol 18(1):35–48

    Article  Google Scholar 

  • Hill R (1998) The mathematical theory of plasticity (Vol. 11). Oxford university press

  • Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min Sci 34(8):1165–1186

    Article  Google Scholar 

  • Hoek E, Kaiser PK, Bawden WF (2000) Support of underground excavations in hard rock. CRC Press

    Book  Google Scholar 

  • Hudson JA, Brown ET, Fairhurst C (1971) Optimizing the control of rock failure in servo-controlled laboratory tests. Rock Mech 3(4):217–224

    Article  Google Scholar 

  • Jansen DC, Shah SP (1997) Effect of length on compressive strain softening of concrete. J Eng Mech 123(1):25–35

    Google Scholar 

  • Jiang Q, Feng XT, Xiang TB, Su GS (2010) Rockburst characteristics and numerical simulation based on a new energy index: a case study of a tunnel at 2,500 m depth. Bull Eng Geol Env 69(3):381–388

    Article  Google Scholar 

  • Joshi A, Kaur R (2013) A review: Comparative study of various clustering techniques in data mining. Int J Adv Res Comp Sci Software Eng 3(3)

  • Kodinariya TM, Makwana PR (2013) Review on determining number of Cluster in K-Means Clustering. Int J 1(6):90–95

    Google Scholar 

  • Lee YK, Pietruszczak S (2008) A new numerical procedure for elasto-plastic analysis of a circular opening excavated in a strain-softening rock mass. Tunn Undergr Space Technol 23(5):588–599

    Article  Google Scholar 

  • Mogi K (1972) Effect of the triaxial stress system on fracture and flow of rocks. Phys Earth Planet Inter 5:318–324

    Article  Google Scholar 

  • Mei W, Li M, Pan PZ, Pan J, Liu K (2021) Blasting induced dynamic response analysis in a rock tunnel based on combined inversion of Laplace transform with elasto-plastic cellular automaton. Geophys J Int 225:699–710

    Article  Google Scholar 

  • Mei W, Xia Y, Pan PZ, Li M, Tan S, Zhang Y (2022) Transient responses of deep-buried unlined tunnels subjected to blasting P wave. Comput Geotech 146:104729

    Article  Google Scholar 

  • Pan PZ, Feng XT, Hudson JA (2009) Study of failure and scale effects in rocks under uniaxial compression using 3D cellular automata. Int J Rock Mech Min Sci 46(4):674–685

    Article  Google Scholar 

  • Pan P-Z, Feng X-T, Zhou H (2012) Development and applications of the elasto-plastic cellular automaton. Acta Mech Solida Sin 25(2):126–143

    Article  Google Scholar 

  • Park KH, Kim YJ (2006) Analytical solution for a circular opening in an elastic–brittle–plastic rock. Int J Rock Mech Min Sci 43(4):616–622

    Article  Google Scholar 

  • Read H, Hegemier GA (1984) Strain softening of rock, soil and concrete—a review article. Mech Mater 3(4):271–294

    Article  Google Scholar 

  • Ross JV, Lewis PD (1989) Brittle-ductile transition: Semi-brittle behaviour. Tectonophysics 167(1):75–79

    Article  Google Scholar 

  • Rummel F, Fairhurst C (1970) Determination of the post-failure behaviour of brittle rock using a servo-controlled testing machine. Rock Mech 2(4):189–204

    Article  Google Scholar 

  • Sharan SK (2003) Elastic–brittle–plastic analysis of circular openings in Hoek-Brown media. Int J Rock Mech Min Sci 40(6):817–824

    Article  Google Scholar 

  • Vermeer PA, De Borst R (1984) Non-associated plasticity for soils, concrete and rock. HERON 29(3):1984

    Google Scholar 

  • Wawersik WR, Fairhurst CH (1970) A study of brittle rock fracture in laboratory compression experiments. In Int J Rock Mech Min Sci Geomech Abs 7(5):561–575 Pergamon

  • Wawersik WR, Brace WF (1971) Post-failure behaviour of a granite and diabase. Rock Mech 3(2):61–85

    Article  Google Scholar 

  • Wawersik WR, Olsson WA, Holcomb DJ, Rudnicki JW, Chau KT (1990) Localization of deformation in brittle rock: Theoretical and laboratory investigations (No. SAND-90–0507C; CONF-9006122–2). Sandia National Labs., Albuquerque, NM (USA)

  • Yang CX, Wu YH, Hon T (2010) A no-tension elastic–plastic model and optimized back-analysis technique for modelling nonlinear mechanical behaviour of rock mass in tunneling. Tunn Undergr Space Technol 25(3):279–289

    Article  Google Scholar 

  • Zhao XG, Cai M (2010a) A mobilized dilation angle model for rocks. Int J Rock Mech Min Sci 47(3):368–384

    Article  Google Scholar 

  • Zhao XG, Cai M (2010b) Influence of plastic shear strain and confinement-dependent rock dilation on rock failure and displacement near an excavation boundary. Int J Rock Mech Min Sci 47(5):723–738

    Article  Google Scholar 

  • Zhao J, Feng XT, Zhang XW, Zhang Y, Zhou YY, Yang CX (2018) Brittle-ductile transition and failure mechanism of Jinping marble under true-triaxial compression. Eng Geol 232:160–170

    Article  Google Scholar 

Download references

Acknowledgements

This work was funded by the National Natural Science Foundation of China (Grant Nos. 52125903, 51621006). We would like to thank Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University for giving us the opportunities to conduct the experimental and simulating tests. Appreciation is extended to all the teachers and staffs here.

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Authors and Affiliations

  1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, China

    Zhaofeng Wang & Peng-Zhi Pan

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    Zhaofeng Wang & Peng-Zhi Pan

  3. Power China Kunming Engineering Corporation Limited, Kunming, 650000, Yunnan, China

    Shijie Yang

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  1. Zhaofeng Wang
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Correspondence to Peng-Zhi Pan.

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Wang, Z., Pan, PZ. & Yang, S. Quantitative description of stress-dependent post-peak brittle characteristics and numerical implementation. Bull Eng Geol Environ 81, 451 (2022). https://doi.org/10.1007/s10064-022-02919-1

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