Abstract
The failure and instability of a kind of specific rock structural bodies, such as the spalling-induced thin rock plates and the slender rock pillars, are the key inducing factors of rock engineering disasters and they are closely related to the shape effect, i.e., the height-to-width (H/W) ratio. For application in engineering practice, the strength characteristics and failure modes of the rock structural bodies when their H/W ratios vary in a wide range should be specially concerned, whereas this seems to be seriously ignored in previous studies. To support this purpose, a numerical scheme that integrates the statistical meso-damage constitutive model and the finite deformation formulation is proposed, to consider both the material failure and buckling instability of the rock structural bodies. The numerical results of a series of uniaxial compression tests of rock samples with relatively low H/W ratios (0.5–4) are completely consistent with the findings obtained from experiments. The behaviors of rock samples with high H/W ratios (6–28) show that the failure of rock samples is affected by both the H/W ratio and the strength of the rock material. That is, as the H/W ratio increases, the failure of rock samples gradually transforms from material failure dominated to structural (buckling) instability dominated, and the increase of the strength of rock material can facilitate this transition. The presented results have established an envelope about the failure and instability of rocks, and obtained the critical boundary line (CBL) for distinguishing different failure modes and determining the boundary between low and high H/W ratio.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
ASTM (1994) American Society for Testing and Materials. Annual book of ASTM standards, vol 04.08, Philadeplhia. https://doi.org/10.1016/0029-1021(71)90107-1
Bathe K, Ramm E, Wilson EL (1975) Finite element formulations for large deformation dynamic analysis. Int J Numer Meth Eng 9(2):353–386. https://doi.org/10.1002/nme.1620090207
Cai M (2008) Influence of intermediate principal stress on rock fracturing and strength near excavation boundaries-Insight from numerical modeling. Int J Rock Mech Min 45(5):763–772. https://doi.org/10.1016/j.ijrmms.2007.07.026
Cai M (2013) Principles of rock support in burst-prone ground. Tunn Undergr Sp Tech 36:46–56. https://doi.org/10.1016/j.tust.2013.02.003
Cai M, Kaiser PK (2014) In-situ rock spalling strength near excavation boundaries. Rock Mech Rock Eng 47(2):659–675. https://doi.org/10.1007/s00603-013-0437-0
Chen ZH, Huang LQ, Li XB, Weng L, Wang SF (2020) Influences of the height to diameter ratio on the failure characteristics of marble under unloading conditions. Int J Geomech 20(9):4020148. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001777
Cording EJ, Hashash YMA, Oh J (2015) Analysis of pillar stability of mined gas storage caverns in shale formations. Eng Geol 184:71–80. https://doi.org/10.1016/j.enggeo.2014.11.001
Dehghan S, Shahriar K, Maarefvand P, Goshtasbi K (2013) 3-D modeling of rock burst in pillar No. 19 of Fetr6 chromite mine. Int J Min Sci Technol 23(2):231–236. https://doi.org/10.1016/j.ijmst.2013.04.014
Deng J, Gu DS (2018) Buckling mechanism of pillar rockbursts in underground hard rock mining. Geomech Geoeng 13(3):168–183
Diederichs MS (2007) The 2003 Canadian Geotechnical Colloquium: mechanistic interpretation and practical application of damage and spalling prediction criteria for deep tunnelling. Can Geotech J 44(9):1082–1116. https://doi.org/10.1139/T07-033
Du K, Su R, Tao M, Yang CZ, Momeni A, Wang SF (2019) Specimen shape and cross-section effects on the mechanical properties of rocks under uniaxial compressive stress. B Eng Geol Environ 78(8):6061–6074. https://doi.org/10.1007/s10064-019-01518-x
Elmo D, Stead D (2010) An integrated numerical modelling–discrete fracture network approach applied to the characterisation of rock mass strength of naturally fractured pillars. Rock Mech Rock Eng 43(1):3–19. https://doi.org/10.1007/s00603-009-0027-3
Esterhuizen GS, Ellenberger JL (2007) Effects of weak bands on pillar stability in stone mines: Field observations and numerical model assessment.
Gong QM, Yin LJ, Wu SY, Zhao J, Ting Y (2012) Rock burst and slabbing failure and its influence on TBM excavation at headrace tunnels in Jinping II hydropower station. Eng Geol 124:98–108. https://doi.org/10.1016/j.enggeo.2011.10.007
Goodno BJ, Gere JM (2020) Mechanics of materials. Cengage Learning
Hawkins AB (1998) Aspects of rock strength. B Eng Geol Environ 57(1):17–30. https://doi.org/10.1007/s100640050017
Hoek E, Martin CD (2014) Fracture initiation and propagation in intact rock – A review. J Rock Mech Geotech 6(4):287–300. https://doi.org/10.1016/j.jrmge.2014.06.001
Hu LH, Liang X, Liang ZZ, Li YC, Zhang ZH, Tang CA (2021) Influence of radial stress on strainbursts under true triaxial conditions: Insights from a distinct element modelling. Int J Rock Mech Min 138:104577. https://doi.org/10.1016/j.ijrmms.2020.104577
Huang BF, Lu WS (2020) Experimental investigation of the uniaxial compressive behavior of thin building granite. Constr Build Mater. https://doi.org/10.1016/j.conbuildmat.2020.120967
Hudson JA, Crouch SL, Fairhurst C (1972) Soft, stiff and servo-controlled testing machines: a review with reference to rock failure. Eng Geol 6(3):155–189. https://doi.org/10.1016/0013-7952(72)90001-4
Jessu KV, Spearing AJS (2019) Direct strain evaluation method for laboratory-based pillar performance. J Rock Mech Geotech Eng 11(4):860–866. https://doi.org/10.1016/j.jrmge.2018.12.017
Jr Z (2001) Pillar design to prevent collapse of room-and-pillar mines in underground mining methods: engineering fundamentals and international case studies. Soc Min Metall Explor 493–511
Karampinos E, Hadjigeorgiou J, Hazzard J, Turcotte P (2015) Discrete element modelling of the buckling phenomenon in deep hard rock mines. Int J Rock Mech Min 80:346–356. https://doi.org/10.1016/j.ijrmms.2015.10.007
Kazakidis VN (2002) Confinement effects and energy balance analyses for buckling failure under eccentric loading conditions. Rock Mech Rock Eng 35(2):115–126. https://doi.org/10.1007/s006030200015
Labuz JF, Biolzi L (1991) Class I vs class II stability: a demonstration of size effect. Int J Rock Mech Min Sci Geomech Abstr 28(2/3):199–205
Li G, Tang CA (2015) A statistical meso-damage mechanical method for modeling trans-scale progressive failure process of rock. Int J Rock Mech Min 74:133–150. https://doi.org/10.1016/j.ijrmms.2014.12.006
Li DY, Li CC, Li XB (2011) Influence of sample Height-to-Width ratios on failure mode for rectangular prism samples of hard rock loaded in uniaxial compression. Rock Mech Rock Eng 44(3):253–267. https://doi.org/10.1007/s00603-010-0127-0
Li G, Liang ZZ, Tang CA (2015) Morphologic interpretation of rock failure mechanisms under uniaxial compression based on 3D multiscale high-resolution numerical modeling. Rock Mech Rock Eng 48(6):2235–2262. https://doi.org/10.1007/s00603-014-0698-2
Li G, Tang CA, Liang ZZ (2017) Development of a parallel FE simulator for modeling the whole trans-scale failure process of rock from meso- to engineering-scale. Comput Geosci UK 98:73–86. https://doi.org/10.1016/j.cageo.2016.08.014
Li G, Cheng XF, Hu LH, Tang CA (2021) The material-structure duality of rock mass: insight from numerical modeling. Int J Rock Mech Min 144:104821
Liang CY, Zhang QB, Li X, Xin P (2016) The effect of specimen shape and strain rate on uniaxial compressive behavior of rock material. B Eng Geol Environ 75(4):1669–1681. https://doi.org/10.1007/s10064-015-0811-0
Malan DF (2012) Pillar design in the hard rock mines of south africa. Int J Min Geoeng 46(2):163–191. https://doi.org/10.22059/ijmge.2012.51326
Mallı T, Yetkin ME, Özfırat MK, Kahraman B (2017) Numerical analysis of underground space and pillar design in metalliferous mine. J Afr Earth Sci 134:365–372. https://doi.org/10.1016/j.jafrearsci.2017.07.018
Mark C (1999) The state-of-the-art in coal pillar design. Proc Soc Min Metall Explor 308:1–8
Martin CD (1997) Seventeenth Canadian Geotechnical Colloquium: the effect of cohesion loss and stress path on brittle rock strength. Can Geotech J 34(5):698–725. https://doi.org/10.1139/t97-030
Martin CD, Maybee WG (2000) The strength of hard-rock pillars. Int J Rock Mech Min 37(8):1239–1246. https://doi.org/10.1016/S1365-1609(00)00032-0
Mogi K (2006) Experimental rock mechanics. CRC Press
Mortazavi A, Hassani FP, Shabani M (2009) A numerical investigation of rock pillar failure mechanism in underground openings. Comput Geotech 36(5):691–697. https://doi.org/10.1016/j.compgeo.2008.11.004
Ortlepp WD (2001) The behaviour of tunnels at great depth under large static and dynamic pressures. Tunn Undergr Sp Tech 16(1):41–48. https://doi.org/10.1016/S0886-7798(01)00029-3
Ozkan I, Ozarslan A, Genis M, Ozsen H (2009) Assessment of scale effects on uniaxial compressive strength in rock salt. Environ Eng Geosci 15(2):91–100
Peng J, Wong LNY, Teh CI (2018) A re-examination of slenderness ratio effect on rock strength: Insights from DEM grain-based modelling. Eng Geol 246:245–254. https://doi.org/10.1016/j.enggeo.2018.10.003
Qiu SL, Feng XT, Zhang CQ, Xiang TB (2014) Estimation of rockburst wall-rock velocity invoked by slab flexure sources in deep tunnels. Can Geotech J 51(5):520–539. https://doi.org/10.1139/cgj-2013-0337
Rafiei Renani H, Martin CD (2018) Modeling the progressive failure of hard rock pillars. Tunn Undergr Sp Tech 74:71–81. https://doi.org/10.1016/j.tust.2018.01.006
Reed G, Mctyer K, Frith R (2017) An assessment of coal pillar system stability criteria based on a mechanistic evaluation of the interaction between coal pillars and the overburden. Int J Min Sci Technol 27(1):9–15. https://doi.org/10.1016/j.ijmst.2016.09.031
Sinha S, Walton G (2018) A progressive S-shaped yield criterion and its application to rock pillar behavior. Int J Rock Mech Min 105:98–109. https://doi.org/10.1016/j.ijrmms.2018.03.014
Tang CA (1997) Numerical simulation of progressive rock failure and associated seismicity. Int J Rock Mech Min 34(2):249–261. https://doi.org/10.1016/S0148-9062(96)00039-3
Tuncay E, Hasancebi N (2009) The effect of length to diameter ratio of test specimens on the uniaxial compressive strength of rock. B Eng Geol Environ 68(4):491. https://doi.org/10.1007/s10064-009-0227-9
Tuncay E, Özcan NT, Kalender A (2019) An approach to predict the length-to-diameter ratio of a rock core specimen for uniaxial compression tests. B Eng Geol Environ 78(7):5467–5482. https://doi.org/10.1007/s10064-019-01482-6
Zienkiewicz OC, Taylor RL, Fox D (2014) Chapter 5—Geometrically nonlinear problems: finite deformation. Butterworth-Heinemann, Oxford
Acknowledgements
This work is supported in part by the National Natural Science Foundation of China (Grant Nos. 52079019, 52009016, 51879034 and 41941018).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare they have no conflicts of interest to this work.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Li, G., Cheng, X., Hu, L. et al. Rock Failure and Instability from a Structural Perspective: Insights from the Shape Effect. Rock Mech Rock Eng 55, 937–952 (2022). https://doi.org/10.1007/s00603-021-02703-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00603-021-02703-9