Fracture energy release and size effect in borehole breakout
10.1002/nag.1610170102
Crossref journal-article
Wiley
International Journal for Numerical and Analytical Methods in Geomechanics (311)
Abstract

AbstractThe paper presents a simple approximate analytical solution of the remote stresses that cause the collapse of a borehole or other circular cylindrical cavity in an infinite elastic space. Regions of parallel equidistant splitting cracks are assumed to form on the sides of the cavity. Their boundary is assumed to be an ellipse of a growing horizontal axis, the other axis remaining equal to the borehole diameter. The slabs of rock between the splitting cracks are assumed to buckle as slender columns, and their post‐critical stress is considered as the residual stress in the cracked rock. The buckling of these slab columns is assumed to be resisted not only by their elastic bending stiffness but also shear stresses produced on rough crack faces by relative shear displacements. The energy release from the infinite medium caused by the growth of the elliptical cracking region is evaluated according to Eschelby's theorem. This release is set equal to the energy dissipated by the formation of all the splitting cracks, which is calculated under the assumption of constant fracture energy. This yields the collapse stress as a function of the elastic moduli, fracture energy, ratio of the remote principal stresses, crack shear resistance characteristic and borehole diameter. The collapse stress as a function of crack spacing is found to have a minimum, and the correct crack spacing is determined from this minimum. For small enough diameters, the crack spacing increases as the (4/5)‐power of the borehole diameter, while for large enough diameters a constant spacing is approached. In contrast to plastic solutions, the breakout stress exhibits a size effect, such that for small enough diameters the breakout stress decreases as the (− 2/5)‐power of the borehole diameter, while for large enough diameters a constant limiting value is approached. Finally, some numerical estimates are given and the validity of various simplifying assumptions made is discussed.

Bibliography

Bažant, Z. P., Lin, F., & Lippmann, H. (1993). Fracture energy release and size effect in borehole breakout. International Journal for Numerical and Analytical Methods in Geomechanics, 17(1), 1–14. Portico.

Authors 3
  1. Zdeněk P. Bažant (first)
  2. Feng‐Bao Lin (additional)
  3. Horst Lippmann (additional)
References 42 Referenced 67
  1. 10.1115/1.3149548 / Appl. Mech. Rev. ASME / Mechanics of ‘bumps’ in coal mines: a discussion of violent deformation in the sides of roadways in coal seams by Lippmann H. (1987)
  2. 10.1007/BF00534325 / Ingenieur‐Archiv / Mechanik des Bohrens in vorgespanntem sproden oder granularen Material, speziell in Kohleflözen by Lippmann H. (1979)
  3. {'key': 'e_1_2_1_4_2', 'first-page': '25', 'volume-title': 'Advances in Analysis of Geotechnical Instabilities', 'author': 'Lippmann H.', 'year': '1979'} / Advances in Analysis of Geotechnical Instabilities by Lippmann H. (1979)
  4. {'key': 'e_1_2_1_5_2', 'first-page': '169', 'article-title': 'Zur Theorie des Gebirgsschlages', 'volume': '37', 'author': 'Bräuner G.', 'year': '1976', 'journal-title': 'Glückauf—Forschungshefte'} / Glückauf—Forschungshefte / Zur Theorie des Gebirgsschlages by Bräuner G. (1976)
  5. G.Tokar ‘Gebirgsschlaggefahr und Testbohren’ Doctor‐Ingenieur Dissertation Technische Universität München 1987.
  6. {'key': 'e_1_2_1_7_2', 'first-page': '17', 'volume-title': 'Proc. Drilling Symp. at ETCE', 'author': 'Haimson B.', 'year': '1989'} / Proc. Drilling Symp. at ETCE by Haimson B. (1989)
  7. 10.1016/0148-9062(84)91531-6
  8. 10.1002/nag.1610120404
  9. 10.1002/nag.1610130206
  10. {'key': 'e_1_2_1_11_2', 'first-page': '4', 'article-title': 'Die Mechanik des Gebirgsschlages bei elastischem Nebestein', 'volume': '43', 'author': 'Lippmann H.', 'year': '1982', 'journal-title': 'Glückauf—Forschungshefte'} / Glückauf—Forschungshefte / Die Mechanik des Gebirgsschlages bei elastischem Nebestein by Lippmann H. (1982)
  11. {'key': 'e_1_2_1_12_2', 'first-page': '539', 'volume-title': 'Mechanics of Geomaterials', 'author': 'Mroz Z.', 'year': '1985'} / Mechanics of Geomaterials by Mroz Z. (1985)
  12. 10.1016/0148-9062(88)91872-4 / Int. J. Rock Mech. Min. Sci. / Simulation of Borehole Breakouts in a Model Material by Périé P. J.
  13. {'key': 'e_1_2_1_14_2', 'first-page': 'D113', 'volume-title': 'Proc. 5th Congress Int. Soc. Rock. Mech.', 'author': 'Petukhov I. M.', 'year': '1983'} / Proc. 5th Congress Int. Soc. Rock. Mech. by Petukhov I. M. (1983)
  14. 10.1016/0013-7944(90)90172-D / Eng. Fracture Mech. / Experimental analysis of the elasto‐plastic zone surrounding a borehole in a specimen of rock‐like material under multiaxial pressure by Tokar G. (1990)
  15. {'key': 'e_1_2_1_16_2', 'first-page': '109', 'volume-title': 'Proc. 6th Int. Congr., Soc. Rock Mech.', 'author': 'Guénot A.', 'year': '1987'} / Proc. 6th Int. Congr., Soc. Rock Mech. by Guénot A. (1987)
  16. 10.1016/0148-9062(88)92298-X / Int. J. Rock. Mech. Min. Sci. / Borehole instabilities as bifurcation phenomena by Vardoulakis I. (1988)
  17. {'key': 'e_1_2_1_18_2', 'first-page': '835', 'volume-title': 'Rock at Great Depth', 'author': 'Veeken C. A.', 'year': '1989'} / Rock at Great Depth by Veeken C. A. (1989)
  18. {'key': 'e_1_2_1_19_2', 'first-page': '309', 'volume-title': 'Mech. Mater.', 'author': 'Gates D. J.', 'year': '1990'} / Mech. Mater. by Gates D. J. (1990)
  19. {'key': 'e_1_2_1_20_2', 'first-page': '436', 'article-title': 'Rock mechanics applied to the study of rockbursts', 'volume': '66', 'author': 'Cook N. G. W.', 'year': '1966', 'journal-title': 'J. South African Inst. Min. Met.'} / J. South African Inst. Min. Met. / Rock mechanics applied to the study of rockbursts by Cook N. G. W. (1966)
  20. 10.1007/BF01042360 / Rock Mech. Rock Eng. / Numerical simulation of rock burst processes treated as problems of dynamic instability by Zubelewicz A.
  21. G.Bräuner Gebirgsdruck und Gebirgsschläge Glückauf Essen 1981.
  22. {'key': 'e_1_2_1_23_2', 'first-page': '317', 'article-title': 'Mechanics of coal mine bumps', 'volume': '256', 'author': 'Crouch S. L.', 'year': '1974', 'journal-title': 'Trans., Soc. Min. Engrs AIME'} / Trans., Soc. Min. Engrs AIME / Mechanics of coal mine bumps by Crouch S. L. (1974)
  23. B.HaimsonandC.Herrick Borehole breakouts—a new tool for estimatingin situ stress? Proc. Int. Symp. on Rock Stress and Rock Measurements Stockholm 1986.
  24. {'key': 'e_1_2_1_25_2', 'first-page': '63', 'volume-title': 'Proc. Drilling Symp. at ETCE', 'author': 'Ewy R.', 'year': '1989'} / Proc. Drilling Symp. at ETCE by Ewy R. (1989)
  25. {'key': 'e_1_2_1_26_2', 'volume-title': 'Micromechanics of Defects in Solids', 'author': 'Mura T.'} / Micromechanics of Defects in Solids by Mura T.
  26. 10.1007/978-94-009-4333-9
  27. {'key': 'e_1_2_1_28_2', 'volume-title': 'Fundamentals of Fracture Mechanics', 'author': 'Knott J. F.', 'year': '1973'} / Fundamentals of Fracture Mechanics by Knott J. F. (1973)
  28. {'key': 'e_1_2_1_29_2', 'first-page': '32', 'volume-title': 'Proc. Drilling Symp. at ETCE', 'author': 'Périé P.', 'year': '1989'} / Proc. Drilling Symp. at ETCE by Périé P. (1989)
  29. E.Papamichos J. F.LabuzandI.Vardoulakis ‘Surface instabilities in brittle rock’ Int. Conf. on Micromechanics of Failure of Quasibrittle Materials S. P. Shah and M. Wang (ed.) Albuquerque NM.
  30. Z. P.Baz̆ant ‘Fracture analysis of compression failure and borehole collapse’ Note privately communicated toF.‐B.Lin(1990).
  31. {'key': 'e_1_2_1_32_2', 'first-page': '99', 'article-title': "L'instabilité d'un milieu continu et la résistence en compression", 'volume': '35', 'author': 'Baz̆ant Z. P.', 'year': '1967', 'journal-title': 'Bull. RILEM (Paris)'} / Bull. RILEM (Paris) / L'instabilité d'un milieu continu et la résistence en compression by Baz̆ant Z. P. (1967)
  32. {'key': 'e_1_2_1_33_2', 'volume-title': 'Stability of Structures: Elastic, Inelastic, Damage and Fracture Theories', 'author': 'Baz̆ant Z. P.', 'year': '1991'} / Stability of Structures: Elastic, Inelastic, Damage and Fracture Theories by Baz̆ant Z. P. (1991)
  33. N. G. W.Cook Private communication to Z. P. Baz̆ant University of California Berkeley 1990.
  34. 10.1061/(ASCE)0733-9399(1984)110:4(518)
  35. 10.1016/0148-9062(91)93232-U
  36. 10.1007/BF00047063
  37. P. C.Papanastasiou Numerical analysis of localization phenomena with application in deep boreholes Ph.D. Dissertation University of Minnesota Minneapolis 1990.
  38. 10.1007/BF00017341 / Int. J. Fracture / Bifurcation and stability of structures with interacting propagating cracks by Baz̆ant Z. P. (1992)
  39. 10.1061/(ASCE)0733-9399(1985)111:4(559)
  40. T.PaulayandP. J.Loeber Shear transfer by aggregate interlock Special Publication SP42 Am. Concrete Institute Detroit pp.1–15(1974).
  41. 10.1061/JSDEAG.0005400 / J. Struct. Div. ASCE / Rough cracks in reinforced concrete by Baz̆ant Z. P. (1980)
  42. 10.1061/(ASCE)0733-9399(1990)116:8(1686)
Dates
Type When
Created 20 years ago (Aug. 8, 2005, 3:19 p.m.)
Deposited 1 year, 9 months ago (Oct. 26, 2023, 2:18 a.m.)
Indexed 2 months, 4 weeks ago (May 27, 2025, 1:37 p.m.)
Issued 32 years, 7 months ago (Jan. 1, 1993)
Published 32 years, 7 months ago (Jan. 1, 1993)
Published Online 20 years, 1 month ago (July 7, 2005)
Published Print 32 years, 7 months ago (Jan. 1, 1993)
Funders 0

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@article{Ba_ant_1993, title={Fracture energy release and size effect in borehole breakout}, volume={17}, ISSN={1096-9853}, url={http://dx.doi.org/10.1002/nag.1610170102}, DOI={10.1002/nag.1610170102}, number={1}, journal={International Journal for Numerical and Analytical Methods in Geomechanics}, publisher={Wiley}, author={Bažant, Zdeněk P. and Lin, Feng‐Bao and Lippmann, Horst}, year={1993}, month=jan, pages={1–14} }