SpringerLink
Log in

Mixed-Mode Fracture Behaviour of Semicircular Bend Shale with Bedding Layer

  • Research Article-Petroleum Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

The intersection of fractures, particularly the intersection of discontinuities, occurs frequently in practical engineering, mainly manifesting as a mixed-mode failure. In the present study, the three-point bend test was conducted on the semicircular bend (SCB) of pre-cracked shale samples with a bedding layer. A numerical model for simulating mixed-mode fracture propagation was constructed using the extended finite element method. The minimum strain energy density criterion was applied for crack initiation and propagation. According to the experimental results, the minimum strain energy density criterion better indicates the fracture path. When the approach angle was set at 30°, the mode I fracture toughness was 0.85 MPa m1/2 and the mode II fracture toughness was 0.38 MPa  m1/2. Furthermore, the mixed-mode fracture path and the crack initiation angle of the SCB with a bedding layer were discussed. As the approach angle became smaller and more prone to crack propagation, a tendency for the fracture propagation path to transfer to the fracture diversion was observed. If the Young's modulus of the layer is greater than the Young's modulus of the shale, the propagation path of the fracture would be far away from the layer. With the decrease in the tensile strength of the bedding layer, the fracture was more likely to propagate along the bedding layer orientation. The present study aimed to better understand the crack initiation and expansion in the mixed-mode fracture process with a bedding layer.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

Abbreviations

a :

Crack length

β :

Crack approach angle

B :

Specimen thickness

CCNBD:

Cracked chevron-notched Brazilian disc

CNB:

Cut notched bend

D:

Specimen diameter

K :

Stress intensity factor

K IC :

Fracture toughness

K I :

Mode I stress intensity factor

KgI I :

Mode II stress intensity factor

K I II :

Mode III stress intensity factor

K 1C :

Mode I fracture toughness

K 2C :

Mode II fracture toughness

R :

Specimen radius

Rs:

Saw radius

P :

Load on specimen

S :

Strain energy density factor

SCB:

Semicircular bend

SR:

Short rod

t :

Notch width

W :

Strain energy density

Y*:

Minimum value of the dimensionless stress intensity factor

Y1 :

The dimensionless parameter

Y2 :

The dimensionless parameter

r :

The radius

u :

Parameter depends on α0 and αB

ν :

Parameter depends on α0 and αB

References

  1. Wang, D.; Bian, X.; Qin, H.; Sun, D.; Bo, Yu.: Experimental investigation of mechanical properties and failure behavior of fluid-saturated hot dry rocks. Nat. Resour. Res. (2020). https://doi.org/10.1007/s11053-020-09760-x

    Article  Google Scholar 

  2. Guo, T., et al. Physical simulation of hydraulic fracturing of large-sized tight sandstone outcrops. SPE J. 2020.

  3. He, Y., et al.: Improving oil recovery through fracture injection and production of multiple fractured horizontal wells. J. Energy Resour. Technol. 142(5), 053002 (2020)

    Article  Google Scholar 

  4. Wang, D.; Dong, Y.; Sun, D.; Bo, Yu.: A three-dimensional numerical study of hydraulic fracturing with degradable diverting materials via CZM-based FEM. Eng. Fract. Mech. 237, 107251 (2020). https://doi.org/10.1016/j.engfracmech.2020.107251

    Article  Google Scholar 

  5. Li, Y., et al.: A rock physics model for the characterization of organic-rich shale from elastic properties. Pet. Sci. 12(2), 264–272 (2015)

    Article  Google Scholar 

  6. Liu, S.; Zhang, D.; Liu, H.: Rock crack propagation mechanism of oriented perforation hydraulic fracture under different perforation parameters. Arab. J. Sci. Eng. 45(10), 8711–8725 (2020)

    Article  Google Scholar 

  7. Guo, Y., et al.: Study on the influence of bedding density on hydraulic fracturing in shale. Arab. J. Sci. Eng. 43(11), 6493–6508 (2018)

    Article  Google Scholar 

  8. Li, Y., et al.: Experimental of hydraulic fracture propagation using fixed-point multistage fracturing in a vertical well in tight sandstone reservoir. J. Pet. Sci. Eng. 171, 704–713 (2018)

    Article  Google Scholar 

  9. Warpinski, N.; Teufel, L.: Influence of geologic discontinuities on hydraulic fracture propagation (includes associated papers 17011 and 17074). J. Pet. Technol. 39, 209–220 (1987)

    Article  Google Scholar 

  10. Zhang, X.; Jeffrey, R.G.; Thiercelin, M.: Deflection and propagation of fluid-driven fractures at frictional bedding interfaces: a numerical investigation. J. Struct. Geol. 29, 396–410 (2007)

    Article  Google Scholar 

  11. Gu, H.; Weng, X.; Lund, J.B.; Mack, M.G.; Ganguly, U.; Suarez-rivera, R.: Hydraulic fracture crossing natural fracture at non-orthogonal angles, a criterion, its validation and applications. SPE Hydraulic Fracturing Technology Conference, 2011. Society of Petroleum Engineers (2011).

  12. Lamont, N.; Jessen, F.: The effects of existing fractures in rocks on the extension of hydraulic fractures. J Pet Technol 15, 203–209 (1963)

    Article  Google Scholar 

  13. Daneshy, A.A.: Hydraulic fracture propagation in the presence of planes of weakness. SPE European spring meeting. Society of Petroleum Engineers (1974)

  14. Zhou, J.; **, Y.; Chen, M.: Experimental investigation of hydraulic fracturing in random naturally fractured blocks. Int. J. Rock Mech. Min. Sci. 7, 1193–1199 (2010)

    Article  Google Scholar 

  15. Olson, J.E.; Bahorich, B.; Holder, J.: Examining hydraulic fracture: natural fracture interaction in hydrostone block experiments. SPE hydraulic fracturing technology conference, 2012. Society of Petroleum Engineers.

  16. Guo, T.; Zhang, S.; Qu, Z.; Zhou, T.; **ao, Y.; Gao, J.: Experimental study of hydraulic fracturing for shale by stimulated reservoir volume. Fuel 128, 373–380 (2014)

    Article  Google Scholar 

  17. Tan, P.; **, Y.; Han, K.; Hou, B.; Chen, M.; Guo, X.; Gao, J.: Analysis of hydraulic fracture initiation and vertical propagation behaviour in laminated shale formation. Fuel 206, 482–493 (2017)

    Article  Google Scholar 

  18. Jeffrey, R.; Vandamme, L.; Roegiers, J.-C.: Mechanical interactions in branched or subparallel hydraulic fractures. Low Permeability Reservoirs Symposium, 1987. Society of Petroleum Engineers.

  19. Zhang, X., Thiercelin, M.J., & Jeffrey, R.G.: Effects of frictional geological discontinuities on hydraulic fracture propagation. SPE hydraulic fracturing technology conference, 2007. Society of Petroleum Engineers.

  20. Suo, Y.; Chen, Z.; Rahman, S.; Xu, W. Effects of formation properties and treatment parameters on hydraulic fracture geometry in poro-viscoelasticity shale gas reservoirs using cohesive zone method in a 3D model. Abu Dhabi International Petroleum Exhibition & Conference, 2018. Society of Petroleum Engineers.

  21. Yao, Y.; Wang, W.; Keer, L.M.: An energy based analytical method to predict the influence of natural fractures on hydraulic fracture propagation. Civ. Environ. Eng. 189, 232–245 (2018)

    Google Scholar 

  22. Xu, W.; Zhao, J.; Rahman, S.S.; Li, Y.; Yuan, Y.: A comprehensive model of a hydraulic fracture interacting with a natural fracture: analytical and numerical solution. Rock Mech. Rock Eng. 52, 1095–1113 (2019)

    Article  Google Scholar 

  23. Lee, H.P.; Olson, J.E.; Schultz, R.: Interaction analysis of propagating opening mode fractures with veins using the discrete element method. Int. J. Rock Mech. Min. Sci. 103, 275–288 (2018)

    Article  Google Scholar 

  24. Whittaker, B.N.; Singh, R.N.; Sun, G.: Rock Fracture Mechanics: Principles, Design, and Applications. Elsevier, Amsterdam (1992)

    Google Scholar 

  25. Carpinteri, A.; Ronchei, C.; Scorza, D.; Vantadori, S.: Fracture mechanics based approach to fatigue analysis of welded joints. Eng. Fail. Anal. 49, 67–78 (2015)

    Article  Google Scholar 

  26. Sih, G.J.: Strength of stress singularities at crack tips for flexural and torsional problems. J. Appl. Mech. 30, 419–425 (1963)

    Article  Google Scholar 

  27. Nuismer, R.: An energy release rate criterion for mixed mode fracture. Int. J. Fract. 11, 245–250 (1975)

    Article  Google Scholar 

  28. Sih, C.J.; Heather, J.; Sood, R.; Price, P.; Peruzzotti, G.; Lee, L.H.; Lee, S.: Total synthesis of prostaglandins. VII. Symmetric total synthesis of (-)-prostaglandin E1 and (-)-prostaglandin E2. J. Am. Chem. Soc 97, 865–874 (1975)

    Article  Google Scholar 

  29. Meneghetti, G.; Ricotta, M.: Evaluating the heat energy dissipated in a small volume surrounding the tip of a fatigue crack. Int. J. Fatigue 92, 605–615 (2016)

    Article  Google Scholar 

  30. Mirsayar, M.; Hartl, D.J.: On the validity of strain energy density criterion for mixed mode I/II fracture analysis of notched shape memory alloy components. Eng. Fract. Mech. 214, 270–288 (2019)

    Article  Google Scholar 

  31. Dwivedi, R.; Soni, A.; Goel, R.; Dube, A.: Fracture toughness of rocks under sub-zero temperature conditions. Int. J. Rock Mech. Min. Sci. 37, 1267–1275 (2000)

    Article  Google Scholar 

  32. Keles, C.; Tutluoglu, L.: Investigation of proper specimen geometry for mode I fracture toughness testing with flattened Brazilian disc method. Int. J. Fract. 169, 61–75 (2011)

    Article  Google Scholar 

  33. Suo, Y.; Chen, Z.; Rahman, S.S.; Song, H.: Experimental and numerical investigation of the effect of bedding layer orientation on fracture toughness of shale rocks. Rock Mech. Rock Eng. 53, 1–11 (2020)

    Article  Google Scholar 

  34. Kuruppu, M.D.; Chong, K.P.: Fracture toughness testing of brittle materials using semi-circular bend (SCB) specimen. Eng. Fract. Mech. 91, 133–150 (2012)

    Article  Google Scholar 

  35. Aliha, M.; Ayatollahi, M.: Mixed mode I/II brittle fracture evaluation of marble using SCB specimen. Proc. Eng. 10, 311–318 (2011)

    Article  Google Scholar 

  36. Li, C., Hu, Y., Meng, T., Zhang, C., Gao, R., **, P., & Hu, Y.: Mode-I fracture toughness and mechanisms of salt-rock gypsum interlayers under real-time high-temperature conditions. Eng. Fract. Mech. 107357 (2020)

  37. Zhang, S.; Wang, H.; Li, X.; Zhang, X.; An, D.; Yu, B.: Experimental study on development characteristics and size effect of rock fracture process zone. Eng. Fract. Mech. 241, 107377 (2020)

    Article  Google Scholar 

  38. Aliha, M.R.M.; Ziari, H.; Mojaradi, B.; Sarbijan, M.J.: Heterogeneity effects on mixed-mode I/II stress intensity factors and fracture path of laboratory asphalt mixtures in the shape of SCB specimen. Fatigue Fract. Eng. Mater. Struct. 43(3), 586–604 (2020)

    Article  Google Scholar 

  39. Ameri, M.; Mansourian, A.; Pirmohammad, S.; Aliha, M.; Ayatollahi, M.R.: Mixed mode fracture resistance of asphalt concrete mixtures. Eng. Fract. Mech. 93, 153–167 (2012)

    Article  Google Scholar 

  40. Yan, C.; Zhang, Y.; Bahia, H.U.: Comparison between SCB-IFIT, un-notched SCB-IFIT and IDEAL-CT for measuring cracking resistance of asphalt mixtures. Construct. Build. Mater. 252, 119060 (2020)

    Article  Google Scholar 

  41. Ayatollahi, M.; Aliha, M.; Hassani, M.M.: Mixed mode brittle fracture in PMMA—an experimental study using SCB specimens. Mater. Sci. Eng A 417, 348–356 (2006)

    Article  Google Scholar 

  42. Mousavi, A.; Aliha, M.R.M.; Imani, D.M.: Effects of biocompatible Nanofillers on mixed-mode I and II fracture toughness of PMMA base dentures. J. Mech. Behav. Biomed. Mater. 103, 103566 (2020)

    Article  Google Scholar 

  43. Lee, H.P.; Olson, J.E.; Holder, J.; Gale, J.F.; Myers, R.D.: The interaction of propagating opening mode fractures with preexisting discontinuities in shale. J. Geophys. Res. Solid Earth 120, 169–181 (2015)

    Article  Google Scholar 

  44. Chandler, M.R.; Meredith, P.G.; Brantut, N.; Crawford, B.R.: Fracture toughness anisotropy in shale. J. Geophys. Res. Solid Earth 121, 1706–1729 (2016)

    Article  Google Scholar 

  45. Zuo, J.-P.; Yao, M.-H.; Li, Y.-J.; Zhao, S.-K.; Jiang, Y.-Q.; Li, Z.-D.: Investigation on fracture toughness and micro-deformation field of SCB sandstone including different inclination angles cracks. Eng. Fract. Mech. 208, 27–37 (2019)

    Article  Google Scholar 

  46. Ayatollahi, M.; Aliha, M.: Wide range data for crack tip parameters in two disc-type specimens under mixed mode loading. Comput. Mater. Sci. 38, 660–670 (2007)

    Article  Google Scholar 

  47. Lim, I.; Johnston, I.; Choi, S.; Boland, J.: Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 2—mixed-mode. Int. J. Rock Mech. Min Sci. Geomech. Abstr. 31, 199–212 (1994)

    Article  Google Scholar 

  48. **e, Y.; Cao, P.; **, J.; Wang, M.: Mixed mode fracture analysis of semi-circular bend (SCB) specimen: a numerical study based on extended finite element method. Comput. Geotech. 82, 157–172 (2017)

    Article  Google Scholar 

  49. Wang, W.; Olson, J.E.; Prodanović, M.; Schultz, R.A.: Interaction between cemented natural fractures and hydraulic fractures assessed by experiments and numerical simulations. J. Pet. Sci. Eng. 167, 506–516 (2018)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Petroleum Engineering, Northeast Petroleum University, Daqing, China

    Yu Suo

  2. School of Minerals and Energy Resources Engineering, University of New South Wales, Sydney, Australia

    Yu Suo, Zhixi Chen & Sheik Rahman

Authors
  1. Yu Suo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhixi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sheik Rahman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu Suo.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Data availability statement

All data generated or used during the study are available from the corresponding author by request.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Suo, Y., Chen, Z. & Rahman, S. Mixed-Mode Fracture Behaviour of Semicircular Bend Shale with Bedding Layer. Arab J Sci Eng 46, 6967–6978 (2021). https://doi.org/10.1007/s13369-021-05376-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-021-05376-2

Keywords

Search

Navigation