Advertisement

Scaling Laws for Sea Ice Fracture

  • Zdeněk P. Bažant
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 94)

Abstract

Based on the premise (recently validated by Dempsey’s in-situ tests) that large-scale failure of sea ice is governed by cohesive fracture mechanics, the paper presents simplified analytical solutions for (1) the load capacity of floating ice plate subjected to vertical load and (2) the horizontal force exerted by an ice plated moving against a fixed structure. The solutions clarify the fracture mechanism and agree with the previous numerical simulations based on cohesive fracture mechanics. They confirm the presence of a strong deterministic size effect. For the case of vertical load, the size effect approximately follows the size effect law proposed in 1984 by Bazant. In the case of an ice plate moving against a fixed obstacle, radial cleavage of the ice plate in the direction opposite to ice movement causes a size effect of structure diameter which follows linear elastic fracture mechanics for small enough diameters but becomes progressively weaker as the diameter increases. The present solutions contradict the earlier solutions based on material strength or plasticity theories, which exhibit no size effect.

Keywords

Linear Elastic Fracture Mechanic Fracture Process Zone Radial Crack Polygonal Crack Fracture Process Zone Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ashton, G. (ed.) 1986. River and Lake Ice Engineering. Water Resources Publications.Google Scholar
  2. Atkins, A.G. 1975. Icebreaking modeling. J. of Ship Research 19(1): 40–43.Google Scholar
  3. Bažant, Z.P. 1984. Size effect in blunt fracture: concrete, rock, ana metal. J. of Engrg. Mech. ASCE 110: 518–535.CrossRefGoogle Scholar
  4. Bažant, Z.P. 1985. Fracture mechanics and strain-softening in concrete. Preprints, U.S.Japan Seminar on Finite Element Analysis of Reinforced Concrete Structures, Tokyo, Vol. 1, pp. 47–69.Google Scholar
  5. Bažant, Z.P. 1987. Fracture energy of heterogeneous material and similitude. Preprints, SEM-RILEM Int. Conf. on Fracture of Concrete and Rock (held in Houston, Texas), ed. by S. P. Shah and S. E. Swartz, publ. by SEM (Soc. for Exper. Mech.) 390–402.Google Scholar
  6. Bažant, Z.P. 1992. Large-scale thermal bending fracture of sea ice plates. J. of Geophysical Research 97 (C11): 17,739–17,751.ADSGoogle Scholar
  7. Bažant, Z.P. 1997a. Scaling of quasibrittle fracture: asymptotic analysis. Int. J. of Fracture 83 (1): 19–40.CrossRefGoogle Scholar
  8. Bažant, Z.P. 1997b. Scaling of quasibrittle fracture: Hypotheses of invasive and lacunar fractality, their critique and Weibull connection. Int. J. of Fracture 83 (1): 41–65.CrossRefGoogle Scholar
  9. Bažant, Z.P. 1999. Size effect on structural strength: a review. Archives of Applied Mechanics (Ingenieur-Archiv, Springer Verlag) 69: 703–725.zbMATHGoogle Scholar
  10. Bažant, Z.P. 2000. Scaling laws for brittle failure of sea ice. Preprints distributed at IUTAM Workshop on Scaling Laws in Ice Mechanics and Ice Dynamics, held at University of Alaska, Fairbanks, June 2000, J.P. Dempsey et al., eds., pp. 1–23.Google Scholar
  11. Bažant, Z.P. 2001a. Scaling of Structural Strength. Hermes Scientific Publications, Oxford and Paris.Google Scholar
  12. Bažant, Z.P. 2001b. Scaling of failure of beams, frames and plates with softening hinges. Meccanica (Italy) (special issue honoring Giulio Maier), in press.Google Scholar
  13. Bažant, Z.P. 2002. Scaling of Sea Ice Fracture. I. Vertical Penetration. II. Horizontal Load from Moving Ice. ASME Journal of Applied Mechanics, in press.Google Scholar
  14. Bažant, Z.P., and Cedolin, L. 1991. Stability of structures: Elastic, inelastic, fracture and damage theories, Oxford University Press, New York.zbMATHGoogle Scholar
  15. Bažant, Z.P., & Chen, E.-P. 1997. Scaling of structural failure. Applied Mechanics Reviews ASME 50 (10): 593–627.ADSCrossRefGoogle Scholar
  16. Bažant, Z.P., and Guo, Z. 2001. Size effect of softening inelastic hinges: II. Sea ice under vertical line load. ASCE J. of Engrg. Mech., submitted to.Google Scholar
  17. Bažant, Z.P., and Kim, J.-K. 1985. Fracture theory for nonhomogeneous brittle materials with application to ice. Proc. ASCE Nat. Conf. on Civil Engineering in the Arctic OffshoreARCTIC 85, San Francisco, L. F. Bennett (ed.), ASCE, New York, pp. 917–930.Google Scholar
  18. Bažant, Z.P., and Kim, Jang-Jay H. 1998. Size effect in penetration of sea ice plate with part-through cracks. I. Theory. J. of Engrg. Mechanics ASCE 124 (12): 1310–1315; with discussions and closure in 126 (4): 438–442 (2000).CrossRefGoogle Scholar
  19. Bažant, Z.P., and Kim, Jang-Jay H. 1998. Size effect in penetration of sea ice plate with part-through cracks. II. Results. J. of Engrg. Mechanics ASCE 124 (12): 1316–1324; with discussions and closure in 126 (4): 438–442 (2000).Google Scholar
  20. Bažant, Z.P., Kim, J.J., & Li, Y.-N. 1995. Part-through bending cracks in sea ice plates: Mathematical modeling. ICE MECHANICS-1995, J.P. Dempsey & Y. Ra-Japakse (eds.), ASME AMD-Vol. 207, 97–105.Google Scholar
  21. Bažant, Z.P., and Li, Y.-N. 1994. Penetration fracture of sea ice plate: Simplified analysis and size effect. J. of Engrg. Mech. ASCE 120 (6): 1304–1321.CrossRefGoogle Scholar
  22. Bažant, Z.P., and Li, Y.-N. 1995. Penetration fracture of sea ice plate. Int. J. Solids Structures 32 (No. 3/4): 303–313.zbMATHGoogle Scholar
  23. Bažant, Z.P., and Planas, J. 1998. Fracture and size effect in concrete and other quasibrittle materials. CRC Press, Boca Raton, Florida.Google Scholar
  24. Bažant, Z.P., and Xiang, Y. 1997. Size effect in compression fracture: splitting crack band propagation. J. of Engrg. Mechanics ASCE 123 (2): 162–172.Google Scholar
  25. Dempsey, J.P. 1991. The fracture toughness of ice. Ice Structure Interaction, S.J. Jones, R.F. McKenna, J. Tilotson and I.J. Jordaan, Eds., Springer-Verlag, Berlin, pp. 109–145.Google Scholar
  26. Dempsey, P.P. 2000. Discussion of Size effect in penetration of ice plate with part-through cracks. I. Theory, II. Results, by Z.P. Bažant and J.J.H. Kim, J. of Engrg. Mech. 126 (4): 438; with authors’ rebuttal, 438–442.CrossRefGoogle Scholar
  27. Dempsey, J.P., Adamson, R.M., and Mulmule, S.V. 1995, Large-scale in-situ fracture of ice. Proc, FRAMCOS-2, Wittmann, F.H., ed., AEDIFICATIO Publishers, D-79104 Freiburg, Germany, pp. 675–684.Google Scholar
  28. Dempsey, J.P., Adamson, R.M., and Mulmule, S.V. 1999b. Scale effects on the in situ tensile strength and fracture of ice: Part II.: First-year sea ice at Resolute, N.W.T..Int. J. of Fracture 95: 346–378.Google Scholar
  29. Dempsey, J.P., DeFranco, S.J., Adamson, R.M., and Mulmule, S.V. 1999a. Scale effects on the in situ tensile strength and fracture of ice: Part I.: Large grained freshwater ice at Spray Lakes Reservoir, Alberta. Int. J. of Fracture 95: 325–345.CrossRefGoogle Scholar
  30. Dempsey, J.P., Slepyan, L.I., and Shekhtman, I.I. 1995. Radial cracking with closure. Int. J. of Fracture 73 (3): 233–261.CrossRefGoogle Scholar
  31. DeFranco, S.J., and Dempsey, J.P. 1992. Nonlinear fracture analysis of saline ice: Size, rate and temperature effects. Proc. of the 11th IAHR Symposium, Banff, Alberta, Vol.3, pp. 1420–1435.Google Scholar
  32. DeFranco, S.J., and Dempsey, J.P. 1994. Crack propagation and fracture resistance in saline ice. J. Glaciology 40: 451–462.ADSGoogle Scholar
  33. DeFranco, S.J., Wei, Y., and Dempsey, J.P. 1991. Notch acuity effects on fracture of saline ice. Annals of Glaciology 15: 230–235.ADSGoogle Scholar
  34. Frankenstein, E.G. 1963. Load test data for lake ice sheet. Technical Report 89, U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire.Google Scholar
  35. Frankenstein, E.G. 1966. Strength of ice sheets. Proc, Conf. on Ice Pressures against Struct.; Tech. Memor. No. 92, NRCC No. 9851, Laval University, Quebec, National Research Council of Canada, Canada, pp. 79–87.Google Scholar
  36. Goldstein, R.V., and Osipenko, N.M. 1993. Fracture mechanics in modeling of icebreaking capability of ships. J. of Cold Regions Engrg. ASCE 7 (2): 33–43.CrossRefGoogle Scholar
  37. Li, Y.-N., and Bazant, Z.P. 1994. Penetration fracture of ice plate: 2D analysis and size effect. J. of Engrg. Mech. ASCE 120 (7): 1481–1498.CrossRefGoogle Scholar
  38. Li, Z., and Bažant, Z.P. 1998. Acoustic emissions in fracturing sea ice plate simulated by particle system. J. of Engrg. Mechanics ASCE 124 (1): 69–79.CrossRefGoogle Scholar
  39. Lichtenberger, G.J., Jones, J.W., Stegall, R.D., and Zadow, D.W. 1974. Static ice loading tests Resolute Bay — Winter 1973/74. APOA Proj. No. 64, Rep. No. 745B-74–14 (CREEL Bib # 34–3095), Sunoco Sci. & Technol., Rechardson, Texas.Google Scholar
  40. Kerr, A.D. 1996. Bearing capacity of floating ice covers subjected to static, moving, and oscillatory loads. Appl. Mech. Rev., ASME Reprint 49 (11): 463–476.ADSCrossRefGoogle Scholar
  41. Mulmule, S.V., Dempsey, J.P., and Adamson, R.M., 1995. Large-scale in-situ ice fracture experiments — part II: modeling efforts, in ice mechanics — 1995 . ASME Joint Applied Mechanics and Materials Summer Conference, AMD — MD 1995, University of California, Loas Angeles, June, pp. 28–30.Google Scholar
  42. Palmer, A.C., et al. 1983. Annals of Glaciology 4: 216–221.MathSciNetADSGoogle Scholar
  43. Ponter, A.R.S. 1983. Cold Regions Sci. & Tech. 8: 189–118.CrossRefGoogle Scholar
  44. Rice, J.R. and Levy, N. 1972. The part-through surface crack in an elastic plate. J. Appl. Mech. ASME 39: 185–194.ADSzbMATHCrossRefGoogle Scholar
  45. Sanderson, T.J.O. 1988. Ice Mechanics: Risks to Offshore Structures, Graham and Trot-man Limited, London.Google Scholar
  46. Slepyan, L.I. 1990. Modeling of fracture of sheet ice. Mechanics of Solids (transl. of Izv. AN SSSR Mekhanika Tverdoga Tela), pp. 155–161.Google Scholar
  47. Sodhi, D.S. 2000. Discussion of Size effect in penetration of ice plate with part-through cracks. I. Theory, II. Results, by Z.P. Bažant and J.J.H. Kim, J. of Engrg. Mech. 126 (4): 438–440; with authors’ rebuttal, 438–442.CrossRefGoogle Scholar
  48. Timoshenko, S.P., & Goodier, J.N. 1970. Theory of elasticity. 3rd ed. McGraw Hill, NY.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Zdeněk P. Bažant
    • 1
  1. 1.Civil Engineering and Materials ScienceNorthwestern UniversityEvanstonUSA

Personalised recommendations