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Laboratory investigation on microcrack fracturing behaviour of granite under quasi-static combined compression and shear

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Abstract

The mechanical characteristics of brittle materials submitted to combined compression and shear loading (CCSL) have received considerable attention recently. Both dynamic and quasi-static CCSL tests have been experimented to simulate the realistic working conditions encountered by different materials. Nevertheless, how the external shear loading affects the microcrack fracturing of rock still excludes explanation. In this paper, a self-developed loading device, instrumented with acoustic emission monitoring, is used to uncover the effect of sample inclination on the microcrack fracturing thresholds of granite samples sourced from two different places. Our laboratory results show that the microcrack damage thresholds (σcd) of the granite samples drop almost linearly with higher sample inclination whereas the microcrack initiation thresholds (σci) only decline when the inclination angle is elevated to a certain magnitude. The changes of the σci/σc ratios (the σci to peak strength ratios) and the σcd/σc ratios against the sample inclination are rock origin dependent. Multiple regression analysis is conducted to unveil the correlation among microcrack fracturing thresholds, peak strength and sample inclination. Both σci and σcd are more sensitive to the combined influence of the peak strength and the inclination angle compared with the individual effect of these two factors. Finally, empirical formulae are proposed to provide reliable predictions of σci and σcd at different sample inclination based on the peak strength acquired from the CCSL tests.

Article Highlights

  • Microcrack fracturing of granite specimen under quasi-static CCSL is studied with a self-developed loading device and acoustic emission monitoring.

  • How the specimen inclination affects the microcrack fracturing thresholds of granite specimens and their ratios to the specimen peak strength are understood.

  • Microcrack fracturing thresholds of granite specimens are found to be more sensitive to the combined effect of the specimen peak strength and the inclination angle compared with the individual effect of these two factors.

  • Empirical formulae are proposed to give quick, reliable prediction of the microcrack fracturing thresholds of granite specimens at different specimen inclination.

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Abbreviations

a, b, c :

Regression coefficients, 1

F θ :

The inclination factor, 1

m i :

The material constant in the Hoek–Brown strength envelope, 1

N :

Sample number, 1

R 2 :

Coefficient of determination, 1

x 1, x 2 :

Independent factors, 1

y :

A dependent factor, 1

y i :

Measured value, 1

\(y_{i}^{*}\) :

Estimated value, 1

σc :

Peak strength of the granite sample at a given sample inclination, MPa

σci :

Microcrack initiation threshold of the granite sample at a given sample inclination, MPa

σcd :

Microcrack damage threshold of the granite sample at a certain sample inclination, MPa

θ :

Sample inclination angle, ˚

AE:

Acoustic emission

CCSL:

Combined compression and shear loading

C-CAST:

Combined compression and shear test

CI:

Microcrack initiation

CD:

Microcrack damage

EPS:

Expanded polystyrene

FG:

Fujian granite

HDT:

Hit definition time

HLT:

Hit locking time

INSTRON:

A manufacturer of test equipment to evaluate the mechanical properties of materials

ISRM:

International Society of Rock Mechanics

MTS:

Material Testing System

PBX:

Polymer bonded explosive

PDT:

Peak definition time

PMMA:

Polymethyl methacrylate

RMSE:

Root mean square error

SCS:

Shear-compression sample

SG:

Shandong granite

SHPB:

Split Hopkinson Pressure Bar

UCS:

Uniaxial compressive strength

VAF:

Variance account for

var :

Variation

References

  • Alkan H, Cinar Y, Pusch G (2007) Rock salt dilatancy boundary from combined acoustic emission and triaxial compression tests. Int J Rock Mech Min Sci 44:108–119

    Google Scholar 

  • Arslan AT, Koca MY, Aydogmus T, Klapperich H, Yılmaz HR (2008) Correlation of unconfined compressive strength with Young’s Modulus and Poisson’s ratio in gypsum from sivas (Turkey). Rock Mech Rock Eng 41:941–950

    Google Scholar 

  • Ashab A, Ruan D, Lu GX, Wong YC (2015) Combined compression-shear behavior of aluminum honeycombs. Key Eng Mater 626:127–132

    Google Scholar 

  • Ashab ASM, Ruan D, Lu G, Wong YC (2016) Quasi-static and dynamic experiments of aluminum honeycombs under combined compression-shear loading. Mater Des 97:183–194

    Google Scholar 

  • Azimian A, Ajalloeian R (2015) Empirical correlation of physical and mechanical properties of Marly rocks with P wave velocity. Arab J Geosci 8:2069–2079

    Google Scholar 

  • Bieniawski Z (1968) Propagation of brittle fracture in rock. In: The 10th U.S. symposium on rock mechanics. American Rock Mechanics Association, Austin, Texas, pp 409–427

  • Bieniawski ZT (1967a) Mechanism of brittle fracture of rock: part II—experimental studies. Int J Rock Mech Min Sci 4:407–423

    Google Scholar 

  • Bieniawski ZT (1967b) Mechanism of brittle fracture of rock: Part III—fracture in tension and under long-term loading. Int J Rock Mech Min Sci 4:425–430

    Google Scholar 

  • Brace WF, Paulding BW, Scholz C (1966) Dilatancy in the fracture of crystalline rocks. J Geophys Res 71:3939–3953

    Google Scholar 

  • Cai M (2010) Practical estimates of tensile strength and Hoek–Brown strength parameter mi of brittle rocks. Rock Mech Rock Eng 43:167–184

    Google Scholar 

  • Cargill JS, Shakoor A (1990) Evaluation of empirical methods for measuring the uniaxial compressive strength of rock. Int J Rock Mech Min Sci 27:495–503

    Google Scholar 

  • Chang SH, Lee CI (2004) Estimation of cracking and damage mechanisms in rock under triaxial compression by moment tensor analysis of acoustic emission. Int J Rock Mech Min Sci 41:1069–1086

    Google Scholar 

  • Çobanoğlu İ, Çelik SB (2008) Estimation of uniaxial compressive strength from point load strength, Schmidt hardness and P-wave velocity. Bull Eng Geol Environ 67:491–498

    Google Scholar 

  • Eberhardt E, Stead D, Stimpson B, Read RS (1997) Changes in acoustic event properties with progressive fracture damage. Int J Rock Mech Min Sci 34:71.e71-71.e12

    Google Scholar 

  • Eberhardt E, Stead D, Stimpson B, Read RS (1998) Identifying crack initiation and propagation thresholds in brittle rock. Can Geotech J 35:222–233

    Google Scholar 

  • Eberhardt E, Stead D, Stimpson B (1999a) Effects of sample disturbance on the stress induced microfracturing characteristics of brittle rock. Can Geotech J 36:239–250

    Google Scholar 

  • Eberhardt E, Stead D, Stimpson B (1999b) Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression. Int J Rock Mech Min Sci 36:361–380

    Google Scholar 

  • Eberhardt E, Stimpson B, Stead D (1999c) Effects of grain size on the initiation and propagation thresholds of stress-induced brittle fractures. Rock Mech Rock Eng 32:81–99

    Google Scholar 

  • Eberhardt E, Stimpson B, Stead D (1999d) The influence of mineralogy on the initiation of microfractures in granite. In: Proceedings of the 8th international congress on rock mechanics, Paris, pp 1007–1010

  • Farrokhrouz M, Asef MR, Kharrat R (2014) Empirical estimation of uniaxial compressive strength of shale formations. Geophysics 79:227–233

    Google Scholar 

  • Feng X, Nong Z, Zheng X, Pan D (2015) Strength restoration of cracked sandstone and coal under a uniaxial compression test and correlated damage source location based on acoustic emissions. PLoS ONE 10:1–20

    Google Scholar 

  • Ganne P, Vervoort A, Wevers M (2007) Quantification of pre-peak brittle damage: correlation between acoustic emission and observed micro-fracturing. Int J Rock Mech Min Sci 44:720–729

    Google Scholar 

  • He Q, Li Y, She S (2019) Mechanical properties of basalt specimens under combined compression and shear loading at low strain rates. Rock Mech Rock Eng 52:4101–4112

    Google Scholar 

  • He Q, Li Y, Xu J, Zhang C (2020) Prediction of mechanical properties of igneous rocks under combined compression and shear loading through statistical analysis. Rock Mech Rock Eng 53:841–859

    Google Scholar 

  • He Q, Zhu L, Li Y, Li D, Zhang B (2021) Simulating hydraulic fracture re-orientation in heterogeneous rocks with an improved discrete element method. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-021-02422-1

    Article  Google Scholar 

  • Hoek E, Bieniawski ZT (1965) Brittle fracture propagation in rock under compression. Int J Fract 1:137–155

    Google Scholar 

  • Hou B, Ono A, Abdennadher S, Pattofatto S, Li YL, Zhao H (2011a) Impact behavior of honeycombs under combined shear-compression. Part I: experiments. Int J Solids Struct 48:687–697

    MATH  Google Scholar 

  • Hou B, Pattofatto S, Li YL, Zhao H (2011b) Impact behavior of honeycombs under combined shear-compression. Part II: analysis. Int J Solids Struct 48:698–705

    MATH  Google Scholar 

  • Jamshidi A, Nikudel MR, Khamehchiyan M, Sahamieh RZ (2016) The effect of specimen diameter size on uniaxial compressive strength, P-wave velocity and the correlation between them. Geomech Geoeng 11:13–19

    Google Scholar 

  • Jamshidi A, Zamanian H, Sahamieh RZ (2018) The effect of density and porosity on the correlation between uniaxial compressive strength and P-wave velocity. Rock Mech Rock Eng 51:1279–1286

    Google Scholar 

  • Katz O, Reches Z, Roegiers JC (2000) Evaluation of mechanical rock properties using a Schmidt Hammer. Int J Rock Mech Min Sci 37:723–728

    Google Scholar 

  • Kim JS, Lee KS, Cho WJ, Choi HJ, Cho GC (2015) A comparative evaluation of stress-strain and acoustic emission methods for quantitative damage assessments of brittle rock. Rock Mech Rock Eng 48:495–508

    Google Scholar 

  • Kumari WGP, Beaumont DM, Ranjith PG, Perara MSA, Avanthi Isaka BL, Khandelwal M (2019) An experimental study on tensile characteristics of granite rocks exposed to different high-temperature treatments. Geomech Geophys Geo-energy Geo-resour 5:47–64

    Google Scholar 

  • Kwasniewski M (2007) Mechanical behaviour of rocks under true triaxial compression conditions: volumetric strain and dilatancy. Arch Min Sci 52:409–435

    Google Scholar 

  • Lajtai EZ, Carter BJ, Duncan EJS (1991) Mapping the state of fracture around cavities. Eng Geol 31:277–289

    Google Scholar 

  • Ling C, Ivens J, Cardiff P, Gilchrist MD (2018) Deformation response of EPS foam under combined compression-shear loading. Part I: experimental design and quasi-static tests. Int J Mech Sci 144:480–489

    Google Scholar 

  • Martin CD, Chandler NA (1994) The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min Sci 31:643–659

    Google Scholar 

  • Meyer LW, Staskewitsch E, Burblies A (1994) Adiabatic shear failure under biaxial dynamic compression/shear loading. Mech Mater 17:203–214

    Google Scholar 

  • Mohr D, Doyoyo M (2002) Analysis of the Arcan apparatus in the clamped configuration. J Compos Mater 36:2583–2594

    Google Scholar 

  • Moradian Z, Einstein HH, Ballivy G (2016) Detection of cracking levels in brittle rocks by parametric analysis of the acoustic emission signals. Rock Mech Rock Eng 49:785–800

    Google Scholar 

  • Nicksiar M, Martin CD (2014) Factors affecting crack initiation in low porosity crystalline rocks. Rock Mech Rock Eng 47:1165–1181

    Google Scholar 

  • Nie X, Chen WW, Sun X, Templeton DW (2007) Dynamic failure of a borosilicate glass under compression/shear loading. J Am Ceram Soc 90:2556–2562

    Google Scholar 

  • Palchik V, Hatzor YH (2002) Crack Damage stress as a composite function of porosity and elastic matrix stiffness in dolomites and limestones. Eng Geol 63:233–245

    Google Scholar 

  • Rittel D, Lee S, Ravichandran G (2002) A shear-compression sample for large strain testing. Exp Mech 42:58–64

    Google Scholar 

  • Rongved M, Holt RM, Larsen I (2019) The effect of heterogeneity on multiple fracture interaction and on the effect of a non-uniform perforation cluster distribution. Geomech Geophys Geo-energy Geo-resour 5:315–332

    Google Scholar 

  • Sandeep CS, Senetakis K (2019) Influence of morphology on the micro-mechanical behavior of soil grain contacts. Geomech Geophys Geo-energy Geo-resour 5:103–119

    Google Scholar 

  • Schmidtke RH, Lajtai EZ (1985) The long-term strength of Lac Du Bonnet granite. Int J Rock Mech Min Sci 22:461–465

    Google Scholar 

  • Shalabi FI, Cording EJ, Al-Hattamleh OH (2007) Estimation of rock engineering properties using hardness tests. Eng Geol 90:138–147

    Google Scholar 

  • Sharma PK, Singh TN (2008) A Correlation between P-wave velocity, impact strength index, slake durability index and uniaxial compressive strength. Bull Eng Geol Environ 67:17–22

    Google Scholar 

  • Souley M, Homand F, Pepa S, Hoxha D (2001) Damage-induced permeability changes in granite: a case example at the URL in Canada. Int J Rock Mech Min Sci 38:297–310

    Google Scholar 

  • Su K, Ghoreychi M, Chanchole S (2000) Experimental study of damage in granite. Géotechnique 50:235–241

    Google Scholar 

  • Suorineni FT, Kaiser PK, Mgumbwa JJ, Thibodeau D (2013) Mining of orebodies under shear loading: part 1 case histories. Min Technol 120:137–147

    Google Scholar 

  • Tan S, Yao X, Long S, Zhang X, Zang S (2019) Static and dynamic strength of soda-lime glass under combined compression-shear loading. J Non-Cryst Solids 516:14–25

    Google Scholar 

  • Tao J, Zhou Z, Wang Z, Wu G, Liu Z, Shu X (2015) Quasi-static failure behaviour of pmma under combined shear-compression loading. Polym Test 42:181–184

    Google Scholar 

  • Tounsi R, Markiewicz E, Haugou G, Chaari F, Zouari B (2016) Dynamic behaviour of honeycombs under mixed shear-compression loading: experiments and analysis of combined effects of loading angle and cells in-plane orientation. Int J Solids Struct 80:501–511

    Google Scholar 

  • Ulusay R (2014) The ISRM suggested methods for rock characterization, testing and monitoring: 2007–2014. Springer, Berlin

    Google Scholar 

  • Wen T, Tang H, Ma J, Wang Y (2018) Evaluation of methods for determining crack initiation stress under compression. Eng Geol 235:81–97

    Google Scholar 

  • Xiong LX, Xu ZY, Li TB, Zhang Y (2019) Bonded-particle discrete element modeling of mechanical behaviors of interlayered rock mass under loading and unloading conditions. Geomech Geophys Geo-energy Geo-resour 5:1–16

    Google Scholar 

  • Xu S, Huang J, Wang P, Chao Z, Zhou L, Hu S (2015) Investigation of rock material under combined compression and shear dynamic loading: an experimental technique. Int J Impact Eng 86:206–222

    Google Scholar 

  • Xue L, Qin S, Sun Q, Wang Y, Lee LM, Li W (2014) A study on crack damage stress thresholds of different rock types based on uniaxial compression tests. Rock Mech Rock Eng 47:1183–1195

    Google Scholar 

  • Yao Q, Chen T, Ju M, Liang S, Liu Y, Li X (2016) Effects of water intrusion on mechanical properties of and crack propagation in coal. Rock Mech Rock Eng 49:4699–4709

    Google Scholar 

  • Yasar E, Erdogan Y (2004) Correlating sound velocity with the density, compressive strength and Young’s modulus of carbonate rocks. Int J Rock Mech Min Sci 41:871–875

    Google Scholar 

  • Yasin Q, Du Q, Sohail GM, Ismail A (2018) Fracturing index-based brittleness prediction from geophysical logging data: application to Longmaxi shale. Geomech Geophys Geo-energy Geo-resour 4:301–325

    Google Scholar 

  • Yilmaz I (2010) Influence of water content on the strength and deformability of gypsum. Int J Rock Mech Min Sci 47:342–347

    Google Scholar 

  • Yuan X, Feng D (2018) Dynamic response and failure mechanism of brittle rocks under combined compression-shear loading experiments. Rock Mech Rock Eng 51:747–764

    Google Scholar 

  • Zhang J, Tao J, Wang Z, Zhao L (2016) Experimental investigation on yield behavior of PMMA under combined shear-compression loading. Results Phys. 6:265–269

    Google Scholar 

  • Zhang D, Lu G, Ruan D, Fei Q, Duan W (2019) Quasi-static combined compression-shear crushing of honeycombs: an experimental study. Mater Des 167:107632

    Google Scholar 

  • Zhao PD, Lu FY, Chen R, Sun GL, Lin YL, Li JL, Lu L (2011) A new technique for combined dynamic compression-shear test. Dyn Behav Mater 1:417–424

    Google Scholar 

  • Zhao PD, Lu FY, Lin YL, Chen R, Li JL, Lu L (2012) Technique for combined dynamic compression-shear testing of PBXs. Exp Mech 52:205–213

    Google Scholar 

  • Zhao XG, Cai M, Wang J, Ma LK (2013) Damage stress and acoustic emission characteristics of the Beishan granite. Int J Rock Mech Min Sci 64:258–269

    Google Scholar 

  • Zhao XG, Cai M, Wang J, Li PF, Ma LK (2015) Objective determination of crack initiation stress of brittle rocks under compression using AE measurement. Rock Mech Rock Eng 48:2473–2484

    Google Scholar 

  • Zhou Z, Wang Z, Zhao L, Shu X (2012) Experimental investigation on the yield behavior of nomex honeycombs under combined shear-compression. Lat Am J Solids Struct 9:515–530

    Google Scholar 

  • Zhou Z, Su B, Wang Z, Li Z, Shu X, Zhao L (2013) Shear-compression failure behavior of PMMA at different loading rates. Mater Lett 109:151–153

    Google Scholar 

  • Zhou L, Xu S, Shan J, Liu Y, Wang P (2018) Heterogeneity in deformation of granite under dynamic combined compression/shear loading. Mech Mater 123:1–18

    Google Scholar 

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Acknowledgements

We thank the financial support from the Fundamental Research Funds for the Central Universities (Grant No. 2018QNA31). Particularly, the first author would like to show his deep yearning for his deceased grandmother, Mrs. Chongfen Ran, for the love and care received from childhood.

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Authors and Affiliations

  1. State Key Laboratory of Coal Resources and Safe Mining, School of Mines, China University of Mining and Technology, Xuzhou, 221116, China

    Qingyuan He & Zhibing Liu

  2. State Key Laboratory of Coastal and Offshore Engineering, School of Civil Engineering, Dalian University of Technology, Dalian, 116024, China

    Yingchun Li

  3. School of Minerals and Energy Resources Engineering, UNSW Sydney, Sydney, 2051, Australia

    Qingyuan He

  4. WA School of Mines: Minerals, Energy and Chemical Engineering, Curtin University, Kalgoorlie, WA, 6430, Australia

    Danqi Li

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  1. Qingyuan He
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Correspondence to Yingchun Li.

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He, Q., Liu, Z., Li, Y. et al. Laboratory investigation on microcrack fracturing behaviour of granite under quasi-static combined compression and shear. Geomech. Geophys. Geo-energ. Geo-resour. 7, 52 (2021). https://doi.org/10.1007/s40948-021-00244-7

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