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Full-field quantification of time-dependent and -independent deformation and fracturing of double-notch flawed rock using digital image correlation

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Abstract

The quantitative characterization of time-dependent and -independent deformation and fracturing of rock is crucial to reveal the short-term and long-term instability mechanisms of structural rocks. In the present paper, we conduct uniaxial constant strain rate and stress-stepping creep tests on double-notched sandstone samples with different rock bridge and flaw inclination angles. Full-field measurements of strain and crack evolution by using digital image correlation (DIC) are presented to understand time-dependent and -independent deformation, fracturing and associated crack types and failure modes of cracked rock. Results from uniaxial and creep experiments show that the flaw inclination, rock bridge inclination and time significantly affect the evolution of the strain field, and in turn change the crack propagation behaviour, and the final strength and failure mode of the rock. The vertical maximum principal stress direction is often in compression near the flaw tips, and as it moves away from the tip, the compression gradually changes to tension, while the parallel maximum principal stress direction is often in tension. Compared with short-term loading, tensile cracks such as wing cracks and far-field cracks, are prominent under creep loading conditions and can be fully developed and characterized by a longer expanded trajectory.

Highlights

  1. 1.

    Full-field measurements of strains and crack evolution in rock with three flaw configurations by the DIC.

  2. 2.

    Comparative analysis of time-dependent and -independent crack types and failure modes.

  3. 3.

    Tensile cracks are prominent under creep loading conditions and can be fully developed.

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References

  • Atkinson BK (1984) Subcritical crack growth in geological materials. J Geophys Res 89:4077–4114

    Article  Google Scholar 

  • Atkinson BK, Meredith PG (1981) Stress corrosion cracking of quartz: a note on the influence of chemical environment. Tectonophys 77:T1–T11

    Article  Google Scholar 

  • Atkinson BK, Meredith PG (1987) The theory of subcritical crack growth with applications to minerals and rocks. Academic Press, London

    Book  Google Scholar 

  • Baud P, Meredith PG (1997) Damage accumulation during triaxial creep of darley dale sandstone from pore volumometry and acoustic emission. Int J Rock Mech Min Sci 34:24.e21-24.e10

    Article  Google Scholar 

  • Bi J, Zhou XP, Qian QH (2016) The 3D numerical simulation for the propagation process of multiple pre-existing flaws in rock-like materials subjected to biaxial compressive loads. Rock Mech Rock Eng 49:1611–1627

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Brantut N, Baud P, Heap MJ, Meredith PG (2012) Micromechanics of brittle creep in rocks. Journal of Geophysical Research: Solid Earth 117:8412

    Article  Google Scholar 

  • Brantut N, Heap MJ, Meredith PG, Baud P (2013) Time-dependent cracking and brittle creep in crustal rocks: a review. J Struct Geol 52:17–43

    Article  Google Scholar 

  • Chen CF, Xu T, Heap MJ, Baud P (2018) Influence of unloading and loading stress cycles on the creep behavior of Darley Dale Sandstone. Int J Rock Mech Min Sci 112:55–63

    Article  Google Scholar 

  • Feng P, Dai F, Liu Y, Xu NW, Zhao T (2018) Effects of strain rate on the mechanical and fracturing behaviors of rock-like specimens containing two unparallel fissures under uniaxial compression. Soil Dyn Earthq Eng 110:195–211

    Article  Google Scholar 

  • Fu TF, Xu T, Heap MJ, Meredith PG, Mitchell TM (2020) Mesoscopic time-dependent behavior of rocks based on three-dimensional discrete element grain-based model. Comput Geotech 121:103472

    Article  Google Scholar 

  • Fu T-F, Xu T, Meredith PG, Mitchell TM, Heap MJ, Nara Y (2021) A meso-mechanical approach to time-dependent deformation and fracturing of partially saturated sandstone. Int J Rock Mech Min Sci 145:104840

    Article  Google Scholar 

  • Gehle C, Kutter HK (2003) Breakage and shear behaviour of intermittent rock joints. Int J Rock Mech Min Sci 40:687–700

    Article  Google Scholar 

  • Griffiths L, Heap MJ, Xu T, Chen CF, Baud P (2017) The influence of pore geometry and orientation on the strength and stiffness of porous rock. J Struct Geol 96:149–160

    Article  Google Scholar 

  • Heap MJ, Baud P, McBeck JA, Renard F, Carbillet L, Hall SA (2020) Imaging strain localisation in porous andesite using digital volume correlation. J Volcanol Geotherm Res 404:107038

    Article  Google Scholar 

  • Heap M. J., Baud P. , Meredith P. G. (2009a) Influence of temperature on brittle creep in sandstones. Geophysical Research Letters 36

  • Heap M. J., Baud P., Meredith P. G., Bell A. F. , Main I. G. (2009b) Time-dependent brittle creep in Darley Dale sandstone. J Geophys Res-Solid Earth 114

  • Heap MJ, Brantut N, Baud P, Meredith PG (2015) Time-dependent compaction band formation in sandstone. J Geophys Res-Solid Earth 120:4808–4830

    Article  Google Scholar 

  • Hild F, Roux S (2012) Digital image correlation. Wiley-VCH, Weinheim

    MATH  Google Scholar 

  • Huang D, Gu DM, Yang C, Huang RQ, Fu GY (2016) Investigation on mechanical behaviors of sandstone with two preexisting flaws under triaxial compression. Rock Mech Rock Eng 49:375–399

    Article  Google Scholar 

  • Ji YT, Hall SA, Baud P, Wong TF (2015) Characterization of pore structure and strain localization in Majella limestone by X-ray computed tomography and digital image correlation. Geophys J Int 200:699–717

    Article  Google Scholar 

  • Jiang MJ, Sun C, Rodriguez-Dono A, Zhang N, Shao JF (2015) Influence of time-dependence on failure of echelon rock joints through a novel DEM model. Eur J Environ Civ Eng 19:S108–S118

    Article  Google Scholar 

  • Louis L, Wong TF, Baud P (2007) Imaging strain localization by X-ray radiography and digital image correlation: Deformation bands in Rothbach sandstone. J Struct Geol 29:129–140

    Article  Google Scholar 

  • Ngwenya BT, Main IG, Elphick SC, Crawford BR, Smart BGD (2001) A constitutive law for low-temperature creep of water-saturated sandstones. J Geophys Res-Solid Earth 106:21811–21826

    Article  Google Scholar 

  • Park CH, Bobet A (2009) Crack coalescence in specimens with open and closed flaws: a comparison. Int J Rock Mech Min Sci 46:819–829

    Article  Google Scholar 

  • Renard F, McBeck J, Kandula N, Cordonnier B, Meakin P, Ben-Zion Y (2019) Volumetric and shear processes in crystalline rock approaching faulting. Proc Natl Acad Sci USA 116:16234–16239

    Article  Google Scholar 

  • Shen BT, Stephansson O, Einstein HH, Ghahreman B (1995) Coalescence of fractures under shear stresses in experiments. J Geophys Res-Solid Earth 100:5975–5990

    Article  Google Scholar 

  • Sutton MA, Orteu JJ, Schreier H (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer, New York

    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 SB, Yu CY, Heap MJ, Chen PZ, Ren YG (2018) The influence of water saturation on the short- and long-term mechanical behavior of red sandstone. Rock Mech Rock Eng 51:2669–2687

    Article  Google Scholar 

  • Tudisco E, Hall SA, Charalampidou EM, Kardjilov N, Hilger A, Sone H (2015) Full-field measurements of strain localisation in sandstone by neutron tomography and 3D-volumetric digital image correlation. Phys Procedia 69:509–515

    Article  Google Scholar 

  • Voigtländer A, Leith K, Krautblatter M (2018) Subcritical crack growth and progressive failure in carrara marble under wet and dry conditions. J Geophys Res: Solid Earth 123:3780–3798

    Article  Google Scholar 

  • Wang YT, Zhou XP, Wang Y, Shou YD (2018) A 3-D conjugated bond-pair-based peridynamic formulation for initiation and propagation of cracks in brittle solids. Int J Solids Struct 134:89–115

    Article  Google Scholar 

  • Wang YT, Zhou XP, Kou MM (2019) Three-dimensional numerical study on the failure characteristics of intermittent fissures under compressive-shear loads. Acta Geotech 14:1161–1193

    Article  Google Scholar 

  • Wang YT, Zhang X, Liu XS (2021) Machine learning approaches to rock fracture mechanics problems: Mode-I fracture toughness determination. Eng Fract Mech 253:107890

    Article  Google Scholar 

  • Wong LNY (2013) A review of field occurrence of crack types and crack coalescence in rocks. Appl Mech Mater 405–408:191–202

    Article  Google Scholar 

  • Wong LNY, Einstein HH (2009) Crack coalescence in molded gypsum and carrara marble: part 2-microscopic observations and interpretation. Rock Mech Rock Eng 42:513–545

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Xu T., Fu T. F., Heap M. J., Meredith P. G., Mitchell T. M. , Baud P. (2020) Mesoscopic damage and fracturing of heterogeneous brittle rocks based on three-dimensional polycrystalline discrete element method. Rock Mech Rock Eng

  • Xu T, Ranjith PG, Wasantha PLP, Zhao J, Tang CA, Zhu WC (2013) Influence of the geometry of partially-spanning joints on mechanical properties of rock in uniaxial compression. Eng Geol 167:134–147

    Article  Google Scholar 

  • Xu T, Tang CA, Yang TH, Zhu WC, Liu J (2006) Numerical investigation of coal and gas outbursts in underground collieries. Int J Rock Mech Min Sci 43:905–919

    Article  Google Scholar 

  • Xu T, Tang CA, Zhao J, Li LC, Heap MJ (2012) Modelling the time-dependent rheological behaviour of heterogeneous brittle rocks. Geophys J Int 189:1781–1796

    Article  Google Scholar 

  • Yang SQ (2011) Crack coalescence behavior of brittle sandstone samples containing two coplanar fissures in the process of deformation failure. Eng Fract Mech 78:3059–3081

    Article  Google Scholar 

  • Yang SQ (2015) Strength failure and crack evolution behavior of rock materials containing pre-existing fissures. Springer, Berlin, Heidelberg

    Book  Google Scholar 

  • Yang SQ, Huang YH (2017) An experimental study on deformation and failure mechanical behavior of granite containing a single fissure under different confining pressures. Environ Earth Sci 76(10):1–22

    Article  MathSciNet  Google Scholar 

  • Yang SQ, Jiang YZ (2010) Triaxial mechanical creep behavior of sandstone. Min Sci Technol (china) 20(3):339–349

    Article  Google Scholar 

  • Yang SQ, Jiang YZ, Xu WY, Chen XQ (2008) Experimental investigation on strength and failure behavior of pre-cracked marble under conventional triaxial compression. Int J Solids Struct 45:4796–4819

    Article  MATH  Google Scholar 

  • Yang W. D., Bo C. J., Chen X. G., Huang C. C. , Li G. Z. (2021) Time-dependent behavior of rock-like specimen containing multiple discontinuous joints under uniaxial step-loading compression. Int J Damage Mech

  • Yao W, Cai YY, Yu J, Zhou JF, Liu SY, Tu BX (2019) Experimental and numerical study on mechanical and cracking behaviors of flawed granite under triaxial compression. Meas 145:573–582

    Article  Google Scholar 

  • Yin P, Wong RHC, Chau KT (2014) Coalescence of two parallel pre-existing surface cracks in granite. Int J Rock Mech Min Sci 68:66–84

    Article  Google Scholar 

  • Yu XY, Xu T, Heap MJ, Baud P, Reuschlé T, Heng Z, Zhu WC, Wang XW (2021) Time-dependent deformation and failure of granite based on the virtual crack incorporated numerical manifold method. Comput Geotech 133:104070

    Article  Google Scholar 

  • Yuan Y, Xu T, Heap MJ, Meredith PG, Yang TH, Zhou GL (2021) A three-dimensional mesoscale model for progressive time-dependent deformation and fracturing of brittle rock with application to slope stability. Comput Geotech 135:104160

    Article  Google Scholar 

  • Zhang JZ, Zhou XP (2020) AE event rate characteristics of flawed granite: from damage stress to ultimate failure. Geophys J Int 222:795–814

    Article  Google Scholar 

  • Zhang JZ, Zhou XP, Zhou LS, Berto F (2019) Progressive failure of brittle rocks with non-isometric flaws: Insights from acousto-optic-mechanical (AOM) data. Fatigue Fract Eng Mater Struct 42:1787–1802

    Article  Google Scholar 

  • Zhao J, Feng XT, Yang CX, Zhang XW, Jiang MF (2021) Differential time-dependent fracturing and deformation characteristics of Jinping marble under true triaxial stress. Int J Rock Mech Min Sci 138:104651

    Article  Google Scholar 

  • Zhou GL, Xu T, Heap MJ, Meredith PG, Mitchell TM, Sesnic ASY, Yuan Y (2020) A three-dimensional numerical meso-approach to modeling time-independent deformation and fracturing of brittle rocks. Comput Geotech 117:103274

    Article  Google Scholar 

  • Zhou XP, Wang YT, Zhang JZ, Liu FN (2019a) Fracturing behavior study of three-flawed specimens by uniaxial compression and 3D digital image correlation: sensitivity to brittleness. Rock Mech Rock Eng 52:691–718

    Article  Google Scholar 

  • Zhou XP, Zhang JZ, Qian QH, Niu Y (2019b) Experimental investigation of progressive cracking processes in granite under uniaxial loading using digital imaging and AE techniques. J Struct Geol 126:129–145

    Article  Google Scholar 

  • Zhu WC, Li SH, Li S, Niu LL (2018) Influence of dynamic disturbance on the creep of sandstone: an experimental study. Rock Mech Rock Eng 52:1023–1039

    Article  Google Scholar 

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Acknowledgements

The work was jointly supported by NSFC (51974062, 42172312, 51950410595), Fundamental Research Funds for the Central Universities of China (N180101028), and National Key Research and Development Program of China (2017YFC1503100). M. Heap acknowledges support from the Institut Universitaire de France (IUF).

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Correspondence to Tao Xu.

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Xue, Y., Xu, T., Zhu, W. et al. Full-field quantification of time-dependent and -independent deformation and fracturing of double-notch flawed rock using digital image correlation. Geomech. Geophys. Geo-energ. Geo-resour. 7, 100 (2021). https://doi.org/10.1007/s40948-021-00302-0

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