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Semi-analytical and Numerical Studies on the Flattened Brazilian Splitting Test Used for Measuring the Indirect Tensile Strength of Rocks

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Abstract

Based on the two-dimensional elasticity theory, this study established a mechanical model under chordally opposing distributed compressive loads, in order to perfect the theoretical foundation of the flattened Brazilian splitting test used for measuring the indirect tensile strength of rocks. The stress superposition method was used to obtain the approximate analytic solutions of stress components inside the flattened Brazilian disk. These analytic solutions were then verified through a comparison with the numerical results of the finite element method (FEM). Based on the theoretical derivation, this research carried out a contrastive study on the effect of the flattened loading angles on the stress value and stress concentration degree inside the disk. The results showed that the stress concentration degree near the loading point and the ratio of compressive/tensile stress inside the disk dramatically decreased as the flattened loading angle increased, avoiding the crushing failure near-loading point of Brazilian disk specimens. However, only the tensile stress value and the tensile region were slightly reduced with the increase of the flattened loading angle. Furthermore, this study found that the optimal flattened loading angle was 20°–30°; flattened load angles that were too large or too small made it difficult to guarantee the central tensile splitting failure principle of the Brazilian splitting test. According to the Griffith strength failure criterion, the calculative formula of the indirect tensile strength of rocks was derived theoretically. This study obtained a theoretical indirect tensile strength that closely coincided with existing and experimental results. Finally, this paper simulated the fracture evolution process of rocks under different loading angles through the use of the finite element numerical software ANSYS. The modeling results showed that the Flattened Brazilian Splitting Test using the optimal loading angle could guarantee the tensile splitting failure initiated by a central crack.

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Abbreviations

FEM:

Finite element method

ISRM:

International Society for Rock Mechanics

SBT:

Standard Brazilian test

SBD:

Standard Brazilian disk

FBST:

Flattened Brazilian splitting test

FBD:

Flattened Brazilian disk

DEM:

Discrete element method

A, B, A’, B’, M, N :

Points in the flattened Brazilian disk

A i , B i and C i (i = 1, 2, 3 and 4):

Variables in specific equations

b :

Half of the flattened width (m)

dA :

Infinitesimal area (m2)

dF :

Infinitesimal force (N)

ds :

Infinitesimal length (m)

E:

Elastic modulus (Pa)

n :

Normal line at point M on the disk

P :

Experimental load (N)

q :

Distributed load (Pa)

R :

Radius of the flattened Brazilian disk (m)

r 1 :

Distance between point M and action point of infinitesimal force in the top semi-infinite plane (m)

r 2 :

Distance between point M and action point of infinitesimal force in the bottom semi-infinite plane (m)

S :

Distance between central point and action point of infinitesimal force (m)

t :

Thickness of the flattened Brazilian disk (m)

2α :

Loading angle of flattened Brazilian disk (rad)

θ 1 :

Included angle between the direction of radial stress and vertical direction in the top semi-infinite plane (rad)

θ 2 :

Included angle between the direction of radial stress and vertical direction in the bottom semi-infinite plane (rad)

∆:

Triangle symbol

σ G :

Griffith equivalent stress (Pa)

σ T :

Tensile strength of the rock (Pa)

σ 1 , σ 2 , σ 3 :

Maximum, intermediate and minimum principal stresses of the disk (Pa)

σ n :

Normal stress component under the polar coordinate (Pa)

σ r :

Radial stress component under the polar coordinate (Pa)

σ τ :

Tangential stress component under the polar coordinate (Pa)

σ x :

X-direction stress component under the cartesian coordinates (Pa)

σ y :

Y-direction stress component under the cartesian coordinates (Pa)

τ xy :

Shear stress component under the cartesian coordinates (Pa)

τ :

Tangential line at point M on the disk

d :

Differential operator

∫ :

Integral operator

References

  • Erarslan N, Williams DJ (2012) Experimental, numerical and analytical studies on tensile strength of rocks. Int J Rock Mech Min Sci 49:21–30

    Article  Google Scholar 

  • Erarslan N, Liang ZZ, Williams DJ (2012) Experimental and numerical studies on determination of indirect tensile strength of rocks. Rock Mech Rock Eng 45(5):739–751

    Google Scholar 

  • Griffith A (1921) The Phenomena of Rupture and Flow in Solids. Philos Trans R Soc London A Contain Papers Math Phys Character 221:163–198

    Google Scholar 

  • Hong J, Tsai C, Dong P (1998) Assessment of numerical procedures for residual stress analysis of multipass welds. Weld J 77:372s–382s

    Google Scholar 

  • ISRM (1978) Suggested methods for determining tensile strength of rock materials. Int J Rock Mech Min Sci Geomech Abstr 15(3):99–103

    Article  Google Scholar 

  • Kwon OH, Jenkins MG (2002) Mechanical behavior and numerical estimation of fracture resistance of a SCS6 fiber reinforced reaction bonded S13N4 continuous fiber ceramic composite. KSME Int J 16(9):1093–1101

    Google Scholar 

  • Lu Y, Yang S, Chen L, Lei J (2011) Mechanism of the spatial distribution and migration of the strong earthquakes in China inferred from numerical simulation. J Asian Earth Sci 40(4):990–1001

    Article  Google Scholar 

  • Ma C-C, Hung K-M (2008) Exact full-field analysis of strain and displacement for circular disks subjected to partially distributed compressions. Int J Mech Sci 50(2):275–292

    Article  Google Scholar 

  • Markides CF, Kourkoulis S (2012) The stress field in a standardized Brazilian disc: the influence of the loading type acting on the actual contact length. Rock Mech Rock Eng 45(2):145–158

    Article  Google Scholar 

  • Markides CF, Pazis D, Kourkoulis S (2010) Closed full-field solutions for stresses and displacements in the Brazilian disk under distributed radial load. Int J Rock Mech Min Sci 47(2):227–237

    Article  Google Scholar 

  • Meng J-J, Cao P, Zhang K, Tan P (2013) Brazil split test of flattened disk and rock tensile strength using particle flow code. J Cent South Univ (Science and Technology) 44(6):2454–2499

    Google Scholar 

  • Pu H, Huang Y-G, Chen R-H (2011) Mechanical analysis for X-O type fracture morphology of stope roof. J China Univ Min Technol 6(40):835–840

    Google Scholar 

  • Satoch Y (1987) Position and load of failure in Brazilian test a numerical analysis by Griffith criterion. J Soc Mater Sci Jpn 36(410):1219–1224

    Article  Google Scholar 

  • Van Cauwelaert F, Eckmann B (1994) Indirect tensile test applied to anisotropic materials. Mater Struct 27(1):54–60

    Article  Google Scholar 

  • Wang Q-Z, Jia X-M (2002) Determination of elastic modulus tensile strength and fracture toughness of brittle rocks by using flattened Brazilian disk specimen—part I: analytical and numerical results. Chin J Rock Mech Eng 21(9):1285–1289

    Google Scholar 

  • Wang Q-Z, Wu L-Z (2004) Determination of elastic modulus tensile strength and fracture toughness of brittle rocks by using flattened Brazilian disk specimen—part II: analytical and numerical results. Chin J Rock Mech Eng 23(2):199–204

    Google Scholar 

  • Wang Q-Z, Xing L (1999) Determination of fracture toughness K IC by using the flattened Brazilian disk specimen for rocks. Eng Fract Mech 64(2):193–201

    Article  Google Scholar 

  • Wang QZ, Jia XM, Kou SQ, Zhang ZX, Lindqvist PA (2004) The flattened Brazilian disc specimen used for testing elastic modulus, tensile strength and fracture toughness of brittle rocks: analytical and numerical results. Int J Rock Mech Min Sci 41(2):245–253

    Article  Google Scholar 

  • Xu Z-L (2006) Elasticity, 4th Edn. Higher Education Press, Beijing, pp 54–85

  • Ye J, Wu F, Sun J (2009) Estimation of the tensile elastic modulus using Brazilian disc by applying diametrically opposed concentrated loads. Int J Rock Mech Min Sci 46(3):568–576

    Article  Google Scholar 

  • You M-Q, Su C-D (2004a) Experimental study on split test with flattened disk and tensile strength of rock. Chin J Rock Mech Eng 23(18):3106–3112

    Google Scholar 

  • You M-Q, Su C-D (2004b) Split test of flattened rock disk and related theory. Chin J Rock Mech Eng 23(1):170–174

    Google Scholar 

  • Yu Y, Xu Y-L (2006) Method to determine tensile of rock using flattened Brazilian disk. Chin J Rock Mech Eng 25(7):1457–1462

    Google Scholar 

  • Yu Q-L, Tang C-A, Yang T-H, Tang S-B, Liu H-L (2008) Numerical analysis of influence of central angle of flats on tensile strength of granite in split test with flattened disk. Rock Soil Mech 29(12):3251–3255

    Google Scholar 

  • Yu Y, Zhang J, Zhang J (2009) A modified Brazilian disk tension test. Int J Rock Mech Min Sci 46(2):421–425

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National 973 Programs (2014CB046905), the National Natural Science Foundation of China (Grant No. 51274191, 51404245 and 51204159), the Doctoral Fund of Ministry of Education of China (20130095110018), the China Postdoctoral Science Foundation (2014M551699) and the Fundamental Research Funds for the Central Universities (2014QNB42).The authors also thank two anonymous referees for their careful reading of this paper and valuable suggestions.

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Authors and Affiliations

  1. State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu, 221008, China

    Y. G. Huang, L. G. Wang, Y. L. Lu, J. R. Chen & J. H. Zhang

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  1. Y. G. Huang
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  2. L. G. Wang
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  3. Y. L. Lu
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  4. J. R. Chen
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  5. J. H. Zhang
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Correspondence to L. G. Wang.

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Huang, Y.G., Wang, L.G., Lu, Y.L. et al. Semi-analytical and Numerical Studies on the Flattened Brazilian Splitting Test Used for Measuring the Indirect Tensile Strength of Rocks. Rock Mech Rock Eng 48, 1849–1866 (2015). https://doi.org/10.1007/s00603-014-0676-8

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