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Analysis of stress-strain relationship of brittle rock containing microcracks under water pressure

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Abstract

Brittle rock contains many microcracks under natural conditions. The theoretical models of brittle rock containing microcracks under the effect of water pressure, axial stress, and confining pressure have not yet been fully elucidated. Therefore, a new model based on a wing crack model and an improved Weibull model was established to analyse the effects of water on the progress of crack initiation, growth, and coalescence. In this improved wing crack model, the water pressure was introduced as a variable, and the analytical stress-crack relationship considering the water pressure was revealed. The relationship between the stress and strain was also obtained. The results revealed that the cracks more readily propagated and failure occurred under higher water pressure. The proposed theoretical curves agree with the experimental data obtained under various water pressures. The effects of water pressure with the change of the crack inclination angle, friction coefficient, crack initiation length, and wing crack length on the wedging force, internal stress, and stress-strain relationship were analysed. The analytical results were validated by experiments. The effect of water pressure on the stress-strain relationship was quantified using an analytical equation whereby the most disadvantageous angle cases, that is, cases wherein the wedging force was maximum, with zero friction were determined.

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References

  • Ashby MF, Hallam SD (1986) The failure of brittle solids containing small cracks under compressive stress states. Acta Metall 34(3):497–510

    Article  Google Scholar 

  • Ashby MF, Sammis CG (1990) The damage mechanics of brittle solids in compression. Pure Appl Geophys 133(3):489–521

    Article  Google Scholar 

  • Brantut N, Baud P, Heap MJ, Meredith PG (2012) Micromechanics of brittle creep in rocks. J Geophys Res 117:B08412

    Article  Google Scholar 

  • Bridgeman PW (1912) Breaking tests under hydrostatic pressure and conditions of rupture. Phil.Mag 24:63–80

    Article  Google Scholar 

  • Bruno MS, Nakagawa FM (1991) Pore pressure influence on tensile fracture propagation in sedimentary rock. Int J Rock Mech Min Sci 28(4):261–273

    Article  Google Scholar 

  • Cai M, Kaiser PK, Tasaka Y, Maejima T, Morioka H, Minami M, Minami M (2004a) Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations. Int J Rock Mech Min Sci 41(5):833–847

    Article  Google Scholar 

  • Cai M, Kaiser PK, Uno H, Tasakam Y, Minami M (2004b) Estimation of rock mass deformation modulus and strength of jointed hard rock masses using the GSI system. Int J Rock Mech Min Sci 41(1):3–19

    Article  Google Scholar 

  • Cao P, Liu T, Pu C et al (2015) Crack propagation and coalescence of brittle rock-like specimens with pre-existing cracks in compression. Eng Geol 187:113–121

    Article  Google Scholar 

  • Chen ZH, Tang CA, Huang RQ (1997) A double rock sample model for rock bursts. Int J Rock Mech Min Sci 34(6):991–1000

    Article  Google Scholar 

  • Costin LS (1983) A microcrack model for the deformation and failure of brittle rock. J Geophys Res 88(B11):9485–9492

    Article  Google Scholar 

  • Eberhardt E (1998) Brittle rock fracture and progressive damage in uniaxial compression. Canada: Saskatoon

  • Fan H, Xu JG, Yan XZ (2014) Reservoir rock mechanics parameters test and analysis of tight sandstone. 2014 Cross-Strait Academic Conference on Destruction Science and Materials Testing and the 12th Symposium on Destruction Science/ The 10th National MTS Materials Testing Conference

  • Fu JW, Liu SL, Zhu WS et al (2018) Experiments on failure process of new rock-like specimens with two internal cracks under biaxial loading and the 3-D simulation. Acta Geotech 13:853–867

    Article  Google Scholar 

  • Gallagher JJ, Friedman M, Handin J, Sowers GM (1974) Experimental studies relating to microfracture in sandstone. Tectonophysics 21(3):203–247

    Article  Google Scholar 

  • Guéguen Y, Kachanov M (2011) Effective elastic properties of cracked and porous rocks - an overview. In: Mechanics of crustal rocks. Springer, Berlin

    Google Scholar 

  • Haeri H, Shahriar K, Marji MF et al (2014) Experimental and numerical study of crack propagation and coalescence in pre-cracked rock-like disks. Int J Rock Mech Min Sci 67:20–28

    Article  Google Scholar 

  • Hao RQ, Li JT, Cao P et al (2015) Test of subcritical crack growth and fracture toughness under water-rock interaction in three types of rocks. J Cent South Univ 22(2):662–668

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Homand-Etienne F, Hoxha D, Shao JF (1998) A continuum damage constitutive law for brittle rocks. Comput Geotech 22(2):135–151

    Article  Google Scholar 

  • Huang YH, Yang SQ, Tian WL et al (2016a) An experimental study on fracture mechanical behavior of rock-like materials containing two unparallel fissures under uniaxial compression. Acta Mech Sinica 32(3):442–455

    Article  Google Scholar 

  • Huang Z, Jiang Z, Zhu S, Wu X, Yang L, Guan Y (2016b) Influence of structure and water pressure on the hydraulic conductivity of the rock mass around underground excavations. Eng Geol 202:74–84

    Article  Google Scholar 

  • Kachanov M (1994) Elastic solids with many cracks and related problems. Appl Mech 30(114):256–445

    Google Scholar 

  • Lajtai EZ, Schmidtke RH, Bielus LE (1987) The effect of water on the time-dependent deformation and fracture of a granite. Int J Rock Mech Min Sci Geomech Abstr 24(4):247–255

    Article  Google Scholar 

  • Levasseur S, Collin F, Charlier R, Kondo D (2013) A micro macro approach of permeability evolution in rocks excavation damaged zones. Comput Geotech 49:245–252

    Article  Google Scholar 

  • Li X, Huai Z, Konietzky H et al (2018) A numerical study of brittle failure in rocks with distinct microcrack characteristics. Int J Rock Mech Min Sci 106:289–299

    Article  Google Scholar 

  • Lu Y, Elsworth D, Wang L (2013) Microcrack-based coupled damage and flow modeling of fracturing evolution in permeable brittle rocks. Comput Geotech 49:226–244

    Article  Google Scholar 

  • Pouya A, Ghoreychi M (1998) Determination of rock mass strength properties by homogenization. In: Cividini A (ed) Application of numerical methods to geotechnical problems. International Centre for Mechanical Sciences (Courses and Lectures), vol 397. Springer, Vienna

    Google Scholar 

  • Rice JR, Cleary MP (1976) Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents. Rev Geophys 14:227–241

    Article  Google Scholar 

  • Tang SB (2018) The effects of water on the strength of black sandstone in a brittle regime. Eng Geol S0013795218300310

  • Vergara MR, Jan MVS, Lorig L (2016) Numerical model for the study of the strength and failure modes of rock containing non-persistent joints. Rock Mech Rock Eng 49(4):1211–1226

    Article  Google Scholar 

  • **ng Z, Sanderson DJ, Barker AJ (2002) Numerical study of fluid flow of deforming fractured rocks using dual permeability model. Geophys.J.Int 151:452–468

    Article  Google Scholar 

  • Xu P, Yang SQ (2017) A fracture damage constitutive model for fissured rock mass and its experimental verification. Arab J Geosci 10(7):164

    Article  Google Scholar 

  • Yang HW (2011) Study on coupling mechanism of rock and pore water under cyclic loading. Ph.D. Thesis, Chongqing University, Chongqing, China

  • Yang SQ, **g HW (2011) Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression. Int J Fract 168(2):227–250

    Article  Google Scholar 

  • Yang SQ, **g HW, Xu T (2014) Mechanical behavior and failure analysis of brittle sandstone specimens containing combined flaws under uniaxial compression. J Cent South Univ 21(5):2059–2073

    Article  Google Scholar 

  • Yang WM, Fang ZD, Wang H, Li LP, Shi SS (2019) Analysis on water inrush process of tunnel with large buried depth and high water pressure. Processes. https://doi.org/10.3390/pr7030134

  • Yin Q, **g HW, Zhu TT (2016) Experimental study on mechanical properties and cracking behavior of pre-cracked sandstone specimens under uniaxial compression. Indian Geotech J 47(3):1–15

    Google Scholar 

  • Zhao Y, Zhang L, Wang W, Tang J, Lin H, Wan W (2017) Transient pulse test and morphological analysis of single rock fractures. Int J Rock Mech Min Sci 91:139–154

    Article  Google Scholar 

  • Zhao C, Niu J, Zhang Q et al (2019a) Weakening effects of the presence of water on the brittleness of hard sandstone. Bull Eng Geol Environ 78:593. https://doi.org/10.1007/s10064-018-1379-2

    Article  Google Scholar 

  • Zhao Y, Cao SG, Shang DL, Yang HW et al (2019b) Crack propagation and crack direction changes during the hydraulic fracturing of coalbed. Comput Geotech 111:229–242

    Article  Google Scholar 

  • Zhao Y, Wang Y, Wang W, Tang L, Liu Q, Cheng G (2019c) Modeling of rheological fracture behavior of rock cracks subjected to hydraulic pressure and far field stresses. Theor Appl Fract Mech. https://doi.org/10.1016/j.tafmec.2019.01.026

  • Zhou ZH, Cao P, Ye ZY (2014) Crack propagation mechanism of compression-shear rock under static-dynamic loading and seepage water pressure. J Cent South Univ 21(4):1565–1570

    Article  Google Scholar 

  • Zhou X, Fan L, Wu Z (2017) Effects of microfracture on wave propagation through rock mass. Int J Geomech 17(9):04017072

    Article  Google Scholar 

  • Zhou J, Wei J, Yang T, Zhu W, Li L, Zhang P (2018) Damage analysis of rock mass coupling joints, water and microseismicity. Tunn. Undergr. Space Technol 71:366–381

    Article  Google Scholar 

Download references

Acknowledgements

We thank Liwen Bianji and Edanz Editing China (www.liwenbianji.cn/ac) for editing the English text of the draft of this manuscript.

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Authors and Affiliations

  1. State Key Laboratory for Disaster Prevention & Mitigation of Explosion & Impact, Army Engineering University of PLA, Nan**g, 210007, Jiangsu, China

    Zhihao Li, Ziming **ong, Haoxiang Chen, Hao Lu, Mu Huang, Chao Ma & Yiming Liu

  2. Bei**g University of Civil Engineering and Architecture, Bei**g, 100044, China

    Haoxiang Chen

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  1. Zhihao Li
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  2. Ziming **ong
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  3. Haoxiang Chen
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  4. Hao Lu
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  7. Yiming Liu
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Correspondence to Ziming **ong.

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Li, Z., **ong, Z., Chen, H. et al. Analysis of stress-strain relationship of brittle rock containing microcracks under water pressure. Bull Eng Geol Environ 79, 1909–1918 (2020). https://doi.org/10.1007/s10064-019-01660-6

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  • DOI: https://doi.org/10.1007/s10064-019-01660-6

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