Skip to main content
SpringerLink
Log in

Bending Properties of Granite Beams with Various Section-Sizes in Three-Point Bending Tests

  • Original paper
  • Published:
Geotechnical and Geological Engineering Aims and scope Submit manuscript

Abstract

To examine the size effects on the bending strength of rock and determine the relation between Brazilian splitting strength and bending strength, Brazilian splitting tests were performed to measure the indirect tensile strength of rock materials. Three-point bending tests were used to evaluate the bending properties of rock beam by changing the sample cross section size including height, width, and diameter. The peak load increases as section size linearly expands. An exponential relation between the peak load and the cross section area ratio is found for rectangular section with different heights and circular section with different diameters samples, whereas a linear one is observed for rectangular section with different widths samples. The measured peak load ratio for all tested samples actually differs from the theoretical one. The maximum shear stress on the cross section of the sample is linearly affected by the section height and diameter but hardly influenced by the section width. Bending strength is barely affected by section size which leads to the conclusion that no size effect is observed in the tested size range. However, the ratio of bending strength to Brazilian tensile strength is found within 3.81–4.26 for rectangular samples and 3.14–3.48 for circular samples. The obtained bending strength is higher than the Brazilian tensile strength, which is in good agreement with the previous results, and the bending strength to Brazilian tensile strength ratio is associated with the sample section size.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Abbreviations

t :

Vertical distance, mm

P :

Vertical load, kN

RSDH:

Rectangular section with different heights

RSDW:

Rectangular section with different widths

CSDD:

Circular section with different diameters

L s :

Length of sample in three-point bending test, mm

H :

Height of rectangular cross-section, mm

W :

Width of rectangular cross-section, mm

L :

Support span length, mm

H b :

Height of cylindrical sample in Brazilian test, mm

D :

Diameter of cylindrical sample, mm

σ t :

Indirect tensile strength obtained from Brazilian splitting test, MPa

\(\bar{\sigma }_{t}\) :

Average value of indirect tensile strength, MPa

\(\bar{\sigma }_{f}\) :

Average value of bending strength, MPa

r :

Ratio of \(\bar{\sigma }_{f}\) to \(\bar{\sigma }_{t}\)

References

  • Agioutantis Z, Kaklis K, Mavrigiannakis S et al (2016) Potential of acoustic emissions from three point bending tests as rock failure precursors. Int J Min Sci Technol 26:155–160

    Article  Google Scholar 

  • Aliha MRM, Hosseinpour GR, Ayatollahi MR (2013) Application of cracked triangular specimen subjected to three-point bending for investigating fracture behavior of rock materials. Rock Mech Rock Eng 46:1023–1034

    Article  Google Scholar 

  • Aliha MRM, Bahmani A, Akhondi S (2016) Mixed mode fracture toughness testing of PMMA with different three-point bend type specimens. Eur J Mech A Solids 58:148–162

    Article  Google Scholar 

  • Ayatollahi MR, Aliha MRM (2007) Fracture toughness study for a brittle rock subjected to mixed mode I/II loading. Int J Rock Mech Min 44:617–624

    Article  Google Scholar 

  • Cabrero JM, Vargas G (2015) Analysis of the validity of the three-point off-axis bending method. Appl Math Model 39:5265–5277

    Article  Google Scholar 

  • Chang SH, Lee CI, Jeon S (2002) Measurement of rock fracture toughness under modes I and II and mixed-mode conditions by using disc-type specimens. Eng Geol 66:79–97

    Article  Google Scholar 

  • Chen CS, Pan E, Amadei B (1998) Determination of deformability and tensile strength of anisotropic rock using Brazilian tests. Int J Rock Mech Min 35:43–61

    Article  Google Scholar 

  • Cooper GA (1977) Optimization of the three-point bend test for fracture energy measurement. J Mater Sci 12:277–289

    Article  Google Scholar 

  • Efimov VP (2009) The rock strength in different tension conditions. J Min Sci 45:569–575

    Article  Google Scholar 

  • Erarslan N, Williams DJ (2012) Experimental, numerical and analytical studies on tensile strength of rocks. Int J Rock Mech Min 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 45:739–751

    Article  Google Scholar 

  • Fahimifar A, Malekpour M (2012) Experimental and numerical analysis of indirect and direct tensile strength using fracture mechanics concepts. Bull Eng Geol Environ 71:269–283

    Article  Google Scholar 

  • Hayashi K, Ono A, Abe H (1989) BEM analysis of a cylindrical three point bend specimen with a chevron crack for fracture toughness test of rock. Nihon Kikai Gakkai Ronbunshu A Hen/Trans Jpn Soc Mech Eng Part A 54:1541–1545

    Google Scholar 

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

    Article  Google Scholar 

  • Khan K, Al-Shayea NA (2000) Effect of specimen geometry and testing method on mixed mode I–II fracture toughness of a limestone rock from Saudi Arabia. Rock Mech Rock Eng 33:179–206

    Article  Google Scholar 

  • Komurlu E, Kesimal A (2015) Evaluation of indirect tensile strength of rocks using different types of jaws. Rock Mech Rock Eng 48:1723–1730

    Article  Google Scholar 

  • Lim IL, Johnston IW, Choi SK et al (1994) Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 1—mode I. Int J Rock Mech Min 31:185–197

    Article  Google Scholar 

  • Lin H, Xiong W, Zhong WW et al (2014) Location of the crack initiation points in the Brazilian disc test. Geotech Geol Eng 32:1339–1345

    Article  Google Scholar 

  • Lin H, Xiong W, Xiong Z et al (2015) Three-dimensional effects in a flattened Brazilian disk test. Int J Rock Mech Min 74:10–14

    Article  Google Scholar 

  • Lin H, Xiong W, Yan Q (2016) Modified formula for the tensile strength as obtained by the flattened Brazilian disk test. Rock Mech Rock Eng 49:1579–1586

    Article  Google Scholar 

  • Nuri TM, Ali ANY, Ahmed S (2012) Correlation study between point load test and uniaxial compressive strength and tensile strength of some sedimentary rocks in Mosul city. Eng Tech J 30:155–166

    Google Scholar 

  • Park SJ, Lee JR (1998) Bending fracture and acoustic emission studies on carbon–carbon composites: effect of sizing treatment on carbon fibres. J Mater Sci 33:647–651

    Article  Google Scholar 

  • Prasad BKR, Sagar RV (2008) Relationship between AE energy and fracture energy of plain concrete beams-experimental study. J Mater Civ Eng 20:212–220

    Article  Google Scholar 

  • Shan Z, Porter I, Nemcik J et al (2014) Effect of different curing conditions on the compressive and flexural properties of Plaster of Paris. Microform Publications, College of Health, Physical Education and Recreation, University of Oregon

  • Wei MD, Dai F, Xu NW et al (2016) Experimental and numerical study on the cracked chevron notched semi-circular bend method for characterizing the mode I fracture toughness of rocks. Rock Mech Rock Eng 49:1595–1609

    Article  Google Scholar 

  • Weinberger R, Reches Z, Eidelman A et al (1994) Tensile properties of rocks in four-point beam tests under confining pressure. American Rock Mechanics Association, Alexandria

    Google Scholar 

  • Xu N, Dai F, Sha C et al (2015) Microseismic signal characterization and numerical simulation of concrete beam subjected to three-point bending fracture. J Sens, article ID: 987232

  • Zhang ZX (2016) An empirical relation between mode I fracture toughness and the tensile strength of rock. Int J Rock Mech Min 39:401–406

    Article  Google Scholar 

  • Zhao Y, Wang Y, Wang W et al (2017) Modeling of non-linear rheological behavior of hard rock using triaxial rheological experiment. Int J Rock Mech Min 93:66–75

    Article  Google Scholar 

  • Zhou XP, Qian QH, Yang HQ (2010) Effect of loading rate on fracture characteristics of rock. J Cent South Univ 17:150–155

    Article  Google Scholar 

  • Zietlow WK, Labuz JF (1998) Measurement of the intrinsic process zone in rock using acoustic emission. Int J Rock Mech Min 35:291–299

    Article  Google Scholar 

Download references

Acknowledgements

This paper gets its funding from project (51474249, 51774322) supported by National Natural Science Foundation of China; Project (2016CX019) supported by Innovation-driven Plan in Central South University; Project (2016M602742) supported by China Postdoctoral Science Foundation; Open Fund of Key Laboratory of Bridge Engineering Safety Control by Hunan Province, Department of Education (Changsha University of Science and Technology) (15KB02); Open Fund of Engineering Research Center of Catastrophic Prophylaxis and Treatment of Road and Traffic Safety of Ministry of Education (Changsha University of Science and Technology kfj150405); Opening fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (SKLGP2016K009). The authors wish to acknowledge these supports.

Author information

Authors and Affiliations

  1. School of Highway, Chang’an University, Xi’an, 710064, Shanxi, China

    Xiang Fan

  2. School of Resources and Safety Engineering, Central South University, Changsha, 410083, Hunan, China

    Hang Lin & Rihong Cao

  3. Key Laboratory of Bridge Engineering Safety Control by Hunan Province, Department of Education, Changsha University of Science and Technology, Changsha, 410114, China

    Xiang Fan

  4. Engineering Research Center of Catastrophic Prophylaxis and Treatment of Road and Traffic Safety of Ministry of Education, Changsha University of Science and Technology, Changsha, 410004, China

    Xiang Fan

  5. State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu, 610059, China

    Xiang Fan

Authors
  1. Xiang Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hang Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rihong Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hang Lin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, X., Lin, H. & Cao, R. Bending Properties of Granite Beams with Various Section-Sizes in Three-Point Bending Tests. Geotech Geol Eng 37, 1–11 (2019). https://doi.org/10.1007/s10706-018-0504-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10706-018-0504-0

Keywords

Search

Navigation