Rock Mechanics and Rock Engineering

, Volume 49, Issue 12, pp 4681–4698 | Cite as

Estimation Criteria for Rock Brittleness Based on Energy Analysis During the Rupturing Process

Original Paper
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Abstract

Brittleness is one of the most important mechanical properties of rock: it plays a significant role in evaluating the risk of rock bursts and in analysis of borehole-wall stability during shale gas development. Brittleness is also a critical parameter in the design of hydraulic fracturing. However, there is still no widely accepted definition of the concept of brittleness in rock mechanics. Although many criteria have been proposed to characterize rock brittleness, their applicability and reliability have yet to be verified. In this paper, the brittleness of rock under compression is defined as the ability of a rock to accumulate elastic energy during the pre-peak stage and to self-sustain fracture propagation in the post-peak stage. This ability is related to three types of energy: fracture energy, post-peak released energy and pre-peak dissipation energy. New brittleness evaluation indices B 1 and B 2 are proposed based on the stress–strain curve from the viewpoint of energy. The new indices can describe the entire transition of rock from absolute plasticity to absolute brittleness. In addition, the brittle characteristics reflected by other brittleness indices can be described, and the calculation results of B 1 and B 2 are continuous and monotonic. Triaxial compression tests on different types of rock were carried out under different confining pressures. Based on B 1 and B 2, the brittleness of different rocks shows different trends with rising confining pressure. The brittleness of red sandstone decreases with increasing confining pressure, whereas for black shale it initially increases and then decreases in a certain range of confining pressure. Granite displays a constant increasing trend. The brittleness anisotropy of black shale is discussed. The smaller the angle between the loading direction and the bedding plane, the greater the brittleness. The calculation B 1 and B 2 requires experimental data, and the values of these two indices represent only relative brittleness under certain conditions. In field operations, both the relative brittleness and the brittleness obtained from seismic data or mineral composition should be considered to gain a more comprehensive knowledge of the brittleness of rock material.

Keywords

Brittleness Type II rock behavior Fracture mechanism Energy change Anisotropy of brittleness 

List of Symbols

VQuartz, VCarbonate, VClay

The content of quartz, carbonate and clay content, respectively (Eq. 1)

a

The weight coefficient of each mineral (Eq. 2)

i

The types of brittle minerals (Eq. 2)

j

The types of all minerals (Eq. 2)

M

The mineral content (volume fraction) (Eq. 2)

σc, σt

Uniaxial compressive strength and tensile strength of rock material (Eq. 3)

σci

Initiation stress of rock material (Eq. 4)

E, v

The elastic modulus and Poisson’s ratio based on the seismic data (Eq.5)

Emax, Emin

The maximum and minimum values of the Elastic modulus (Eq. 5)

vmax, vmin

The maximum and minimum values of the Poisson’s ratio (Eq. 5)

εel, εpl

The elastic strain and plastic strain at the pre-peak stage of stress–strain curves (Eq. 6)

εTOT

Total strain of pre-peak stage (Eq. 6)

σp, σr

The peak strength and the residual strength of the whole stress–strain curve (Eq. 7)

εp, εr

The peak strain and the residual strain of the whole stress–strain curve (Eq. 7)

dWf

The fracture energy (Eq. 8)

dWue

The unloading elastic energy (Eq. 8)

dWd

The dissipation energy of pre-peak stage (Eq. 8)

dWx

The extra energy required (type I behavior) or the excess energy released(type II behavior) (Eq. 9)

dWe

The total elastic energy accumulated in the rock specimen when reaching the peak strength (Eq. 10)

dWt

The energy which unconsumed or converts into other forms (Eq. 10)

σP

The peak strength of the rock specimen under compression (Eq. 10)

σR

The residual strength; σ i represents the function of pre-peak curve (Eq. 10)

E

Elastic modulus of stress–strain curve (Eq. 11)

M

Post-peak modulus of stress–strain curve (Eq. 11)

σi

The function of pre-peak curve (Eq. 13)

εp

The strain corresponding to the peak strength (Eq. 13)

Notes

Acknowledgments

The research was supported by Natural Science for Youth Foundation of China (No. 51504068).

References

  1. Altindag R, Guney A (2010) Predicting the relationships between brittleness and mechanical properties (UCS, TS and SH) of rocks. Int J Sci Res Essays 5(16):2107–2118Google Scholar
  2. Aswegen GV (2008) Ortlepp shears-dynamic brittle shears of South African Gold Mines. In: Proceedings of the first southern hemisphere international rock mechanics symposium, vol 11, pp 1–9Google Scholar
  3. Bishop AW (1967) Progressive failure with special reference to the mechanism causing it. In: Proceedings of the geotechnical conference, Oslo, pp 142–150Google Scholar
  4. Buller D, Hughes S, Market J, Petre E (2010) Petrophysical evaluation for enhancing hydraulic stimulation in horizontal shale gas-wells. In: SPE annual technical conference and exhibition held in Florence, Italy, SPE 132990Google Scholar
  5. Diao HY (2013) Rock mechanical properties and brittleness evaluation of shale reservoir. Acta Petrol Sin 29(9):3300–3306Google Scholar
  6. George EA (1995) Brittle failure of rock material-test results and constitutive models. A.A. Balkema Publishers, Rotterdam, pp 123–128Google Scholar
  7. Goktan RM, Yilmaz NG (2005) A new methodology for the analysis of the relationship between rock brittleness index and drag pick cutting efficiency. Int J S Afr Inst Min Metall 105:727–734Google Scholar
  8. Hajiabdolmajid V, Kaiser PK (2003) Brittleness of rock and stability assessment in hard rock tunneling. Int J Tunn Undergr Space Technol 18(1):35–48CrossRefGoogle Scholar
  9. He C, Okubo S, Nishimatsu Y (1990) A study of the class II behavior of rock. Int J Rock Mech Rock Eng 23:261–273CrossRefGoogle Scholar
  10. Hetenyi M (1966) Handbook of experimental stress analysis. Wiley, New York, pp 23–25Google Scholar
  11. Holt RM, Fjaer E, Nes OM, Alassi HT (2011) A shaly look at brittleness. ARMA 11-366Google Scholar
  12. Holt RM, Fjær E, Stenebraten JF, Nes OM (2015) Brittleness of shales: relevance to borehole collapse and hydraulic fracturing. J Pet Sci Eng 131:200–209CrossRefGoogle Scholar
  13. Honda H, Sanada Y (1956) Hardness of coal. Fuel 35:451–460Google Scholar
  14. Huang XR, Huang JP, Li ZC, Yang QY, Sun QX, Cui W (2015) Brittleness index and seismic rock physics model for anisotropic tight-oil sandstone reservoir. Appl Geophys 12(1):11–22CrossRefGoogle Scholar
  15. Hucka V, Das B (1974) Brittleness determination of rocks by different methods. Int J Rock Mech Min Sci 11(10):389–392CrossRefGoogle Scholar
  16. Jarvie DM, Hill RJ, Ruble TE, Pollastro RM (2007) Unconventional shale-gas systems: the Mississippian Barnett Shale of north-central Texas as one model for thermogenic shale-gas assessment. AAPG Bull 9(4):475–499CrossRefGoogle Scholar
  17. Jin XC, Shah SN, Truax JA, Roegiers JC (2014) A practical petrophysical approach for brittleness prediction from porosity and sonic logging in shale reservoirs. In: SPE Conference, 170972-MSGoogle Scholar
  18. King GCP, Sammis CG (1992) The mechanisms of finite brittle strain. Pure appl Geophys 138:611–640CrossRefGoogle Scholar
  19. Li QH, Chen M, Jin Y (2012) Rock mechanical properties and brittleness evaluation of shale gas reservoir. Chin J Pet Drill Tech 40(4):17–22Google Scholar
  20. Liu ZB, Sun ZD (2015) New brittleness indexes and their application in shale/clay gas reservoir prediction. Chin J Pet Explor Dev 42(1):117–123Google Scholar
  21. Liu WH, Zhou LP, Deng Y, Li YQ, Ren YJ, Pang Q (2014) Tight sand brittleness prediction and reservoirs evaluation in Jimsar, Junggar Basin. In: SEG Conference, 2014-0463Google Scholar
  22. Luan XY, Di BR, Wei JX, Li XY, Qian KR, Xie JY, Ding PB (2014) Laboratory measurements of brittleness anisotropy in synthetic shale with different cementation. SEG. doi: 10.1190/segam2014-0432.1 Google Scholar
  23. Mikaeil R, Ataei M, Yousefi R (2011) Correlation of production rate of ornamental stone with rock brittleness indexes. Arabian J Geosci 6(1):115–121CrossRefGoogle Scholar
  24. Morley A (1944) Strength of materials. Longman Green, London, pp 71–72Google Scholar
  25. Obert L, Duvall WI (1967) Rock mechanics and the design of structures in rock. Wiley, New York, pp 78–82Google Scholar
  26. Ortlepp WD (1997) Rock fracture and rockbursts-an illustrative study. Johannesburg, J S Afr Inst Min Metall, p 98Google Scholar
  27. Pan YS, Xu BY, Wang MY (1999) The study of plastic strain gradient and class II behavior of rock. Chin J Geotech Eng 21(4):82–89Google Scholar
  28. Paterson MS, Wong TF (2005) Experimental rock deformation: the brittle field. Springer, BerlinGoogle Scholar
  29. Perez R, Marfurt K (2013) Brittleness estimation from seismic measurements in unconventional reservoirs: application to the Barnett Shale. Ph.D. dissertation, The University of Oklahoma, USAGoogle Scholar
  30. Ramsay JG (1967) Folding and fracturing of rocks. McGraw-Hill, London, pp 44–47Google Scholar
  31. Reches Z (1999) Mechanisms of slip nucleation during earthquakes. Earth Planet Sci Lett 170:475–486CrossRefGoogle Scholar
  32. Reches Z, Lockner DA (1994) Nucleation and growth of faults in brittle rocks. J Geophys Res 99(B9):59–73CrossRefGoogle Scholar
  33. Rickman R, Mullen M, Petre E, Grieser B, Kundert D (2008) A practical use of shale petrophysics for stimulation design optimization: all shale plays are not clones of the Barnett Shale. In: SPE annual technical conference and exhibition, society of petroleum engineers, SPE-115258Google Scholar
  34. Sun SZ, Wang KN, Yang P, Li XG, Sun JX, Liu BH, Jin K (2013) Integrated prediction of shale oil reservoir using pre-tack algorithms for brittleness and fracture detection. In: IPTC conference, 17048-MSGoogle Scholar
  35. Tarasov BG (2010) Superbrittleness of rocks at high confining pressure. In: Proceedings of the fifth international seminar on deep and high stress mining, pp 119–133Google Scholar
  36. Tarasov BG (2011) Universal scale of brittleness for rocks failed at compression. In: Proceedings of the 13th international conference of the international association for computer methods and advances in geomechanics, pp 669–673Google Scholar
  37. Tarasov B, Potvinb Y (2013) Universal criteria for rock brittleness estimation under triaxial compression. Int J Rock Mech Min Sci 59:57–69Google Scholar
  38. Tarasov BG, Randolph MF (2011) Super brittleness of rocks and earthquake activity. Int J Rock Mech Min Sci 48:888–898CrossRefGoogle Scholar
  39. Wang YN (2014) Simulation test research on the rules of local deformation and energy evolution of fractured rock. Ph.D. dissertation, Chengdu University of Technology, Si Chuan, ChinaGoogle Scholar
  40. Wang Y, Li X, Wu YF, Fen YX, Li DD, He JM (2014) Research on relationship between crack initiation stress level and brittleness indices for brittle rocks. Chin J Rock Mech Eng 33(2):265–275Google Scholar
  41. Yang Y, Sone H, Hows A, Zoback MD (2013) Comparison of brittleness indices in organic-rich shale formation. ARMA 13-403Google Scholar
  42. Zhang ZZ, Gao F (2012) Experimental reason on energy evolution of red sandstone samples under uniaxial compression. Chin J Rock Mech Eng 31(5):953–962CrossRefGoogle Scholar
  43. Zhang ZZ, Gao F (2015a) Confining pressure effect on rock energy. Chin J Rock Mech Eng 34(1):1–11CrossRefGoogle Scholar
  44. Zhang ZZ, Gao F (2015b) Experimental investigations on energy evolution characteristics of coal, sandstone and granite during loading process. Chin J Univ Min Tech 44(3):416–422Google Scholar
  45. Zhang ZZ, Gao F, Gao YN, Xu XL (2010) Experimental study of brittle stress drop coefficient of granite endured high temperature. Chin J Exper Mech 25(5):589–594Google Scholar
  46. Zhou H, Meng FZ, Liu HT, Zhang CQ, Lu JJ, Xu RC (2014a) Experimental study on characteristics and mechanics and mechanism of brittle failure of granite. Chin J Rock Mech Eng 33(9):1822–1832Google Scholar
  47. Zhou H, Meng FZ, Zhang CQ, Xu RC, Lu JJ (2014b) Quantitative evaluation of rock brittleness based on stress–strain curve. Chin J Rock Mech Engi 33(6):1114–1122Google Scholar
  48. Zuo JP, Huang YM, Xiong GJ (2014) Study of energy-drop coefficient of brittle rock failure. Chin J Rock Soil Mech 2(35):321–327Google Scholar

Copyright information

© Springer-Verlag Wien 2016

Authors and Affiliations

  1. 1.Department of Petroleum EngineeringNortheast Petroleum UniversityDaqingChina

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