International Journal of Fracture

, Volume 179, Issue 1–2, pp 9–33 | Cite as

A mesh-free approach for fracture modelling of gravity dams under earthquake

Original Paper


Fracture is a major cause of failure for concrete gravity dams. This can result in the large-scale loss of human lives and enormous economic consequences. Numerical modelling can play a crucial role in understanding and predicting complex fracture processes, providing useful input to fracture-resistant designs. In this paper, the use of a mesh-free particle method called smoothed particle hydrodynamics (SPH) for modelling of gravity dam failure subject to fluctuating dynamic earthquake loads is explored. The structural response of the Koyna dam is analysed with the base of the dam being subjected to high-intensity periodic ground excitations. The SPH prediction of the crack initiation location and propagation pattern is found to be consistent with existing FEM predictions and experimental results from physical models. The transient stress field and the resulting damage evolution in the dam structure were monitored. The amplitude and frequency of the ground excitation is shown to have considerable influence on the fracture pattern and the associated energy dissipation. The fluctuations in the kinetic energy of the dam wall and its fragments are found to vary with different frequencies and amplitudes as the structure undergoes progressive fracture. The dynamic responses and the fracture patterns predicted establish the strong potential of SPH for fracture modelling of dams and similar large structures.


Dam Failure Damage Fracture Earthquake Mesh-free method Smoothed particle hydrodynamics 


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  1. Aliabadi MH, Rooke DP (1991) Numerical fracture mechanics. Computational Mechanics Publications and Kluwer Academic PublishersGoogle Scholar
  2. Amirreze G, Mohsen G (2006) Large-scale testing on specific fracture energy determination of dam concrete. Int J Fract 141(1–2): 247–254Google Scholar
  3. Anderson TL (1991) Fracture mechanics: fundamentals and applications. CRC Press, Boca RatonGoogle Scholar
  4. Ayari ML, Saouma VE (1990) Fracture mechanics based seismic analysis of concrete gravity dams using discrete cracks. Eng Fract Mech 35(1–3): 587–598CrossRefGoogle Scholar
  5. Barani OR, Khoei AR, Mofid M (2011) Modeling of cohesive crack growth in partially saturated porous media; a study on the permeability of cohesive fracture. Int J Fract 167(1): 15–31CrossRefGoogle Scholar
  6. Barker DB, Fourney WL, Dally JW (1978) The influence of stress waves on explosive induced fragmentation-borehole crack network. In: 19th US symposium on rock mechanics, Lake TahoeGoogle Scholar
  7. Batta V, Pekau OA (1996) Application of boundary element analysis for multiple seismic cracking in concrete gravity dams. Earthq Eng Struct Dyn 25(1): 15–30CrossRefGoogle Scholar
  8. Baustadter K, Widmann R (1985) The behavior of the Kolnbrein arch dam. In: Proceedings of the 15th ICOLD, pp 633–651Google Scholar
  9. Bhattacharjee SS, Leger P (1993) Seismic cracking and energy dissipation in concrete gravity dams. Earthq Eng Struct Dyn 22(11): 991–1007CrossRefGoogle Scholar
  10. Calayir Y, Karaton M (2005a) Seismic fracture analysis of concrete gravity dams including dam–reservoir interaction. Comput Struct 83: 1595–1606CrossRefGoogle Scholar
  11. Calayir Y, Karaton M (2005b) A continuum damage concrete model for earthquake analysis of concrete gravity dam-reservoir systems. Soil Dyn Earthq Eng 25(11): 857–869CrossRefGoogle Scholar
  12. Cervera M, Oliver J, Faria R (1995) Seismic evaluation of concrete dams via continuum damage models. Earthq Eng Struct Dyn 24(9): 1225–1245CrossRefGoogle Scholar
  13. Chopra AK, Gupta S (1982) Hydrodynamic and foundation interaction effects in frequency response functions for concrete gravity dams. Earthq Eng Struct Dyn 10(1): 89–106CrossRefGoogle Scholar
  14. Cleary PW, Prakash M (2004) discrete-element modelling and smoothed particle hydrodynamics: potential in the environmental sciences. Phil Trans R Soc Math Phys Eng Sci 362(1822): 2003–2030CrossRefGoogle Scholar
  15. Cleary P, Ha J, Alguine V, Nguyen T (2002) Flow modelling in casting processes. Appl Math Model 26(2): 171–190CrossRefGoogle Scholar
  16. Cleary PW, Prakash M, Ha J (2006) Novel applications of smoothed particle hydrodynamics (SPH) in metal forming. J Mater Process Technol 177(1–3): 41–48CrossRefGoogle Scholar
  17. Cleary PW, Prakash M, Ha J, Stokes N, Scott C (2007) Smooth particle hydrodynamics: status and future potential. Prog Comput Fluid Dyn 7(2–4): 70–90CrossRefGoogle Scholar
  18. Cleary PW, Prakash M, Rothauge K (2010) Combining digital terrain and surface textures with large-scale particle-based computational models to predict dam collapse and landslide events. Int J Image Data Fusion 1(4): 337–357CrossRefGoogle Scholar
  19. Das R, Cleary PW (2008a) Modelling 3D fracture and fragmentation in a thin plate under high velocity projectile impact using SPH. In: 3rd SPHERIC workshop, LausanneGoogle Scholar
  20. Das R, Cleary PW (2008b) Modelling brittle fracture and fragmentation of a column during projectile impact using a mesh-free method. In: 6th International conference on CFD in Oil & Gas, Metallurgical and Process Industries, TrondheimGoogle Scholar
  21. Das R, Cleary PW (2010) Effect of rock shapes on brittle fracture using Smoothed Particle Hydrodynamics. Theor Appl Fract Mech 53: 47–60CrossRefGoogle Scholar
  22. DeKay ML, McClelland GH (1993) Predicting loss of life in cases of dam failure and flash flood. Risk Anal 13(2): 193–205CrossRefGoogle Scholar
  23. Fang X, Jin F, Wang J (2008) Seismic fracture simulation of the Koyna gravity dam using an extended finite element method. J Tsinghua Univ (Sci Technol) 48(12): 2065–2069Google Scholar
  24. Fujiwara A (1989) Experiments and scaling laws for catastrophic collisions, pp 240–265Google Scholar
  25. Ghosh B, Madabhushi SPG (2003) A numerical investigation into effects of single and multiple frequency earthquake motions. Soil Dyn Earthq Eng 23(8): 691–704CrossRefGoogle Scholar
  26. Ghrib F, Tinawi R (1995) Application of damage mechanics for seismic analysis of concrete gravity dams. Earthq Eng Struct Dyn 24(2): 157–173CrossRefGoogle Scholar
  27. Grady DE, Kipp ME (1980) Continuum modelling of explosive fracture in oil shale. Int J Rock Mech Min Sci Geomech Abstr 17(3): 147–157CrossRefGoogle Scholar
  28. Gray JP, Monaghan JJ (2004) Numerical modelling of stress fields and fracture around magma chambers. J Volcanol Geotherm Res 135: 259–283CrossRefGoogle Scholar
  29. Grady DE, Kipp ME, Smith CS (1980) Explosive fracture studies on oil shale. Soc Petrol Eng J 5: 349–356Google Scholar
  30. Gray JP, Monaghan JJ, Swift RP (2001) SPH elastic dynamics. Comput Methods Appl Mech Eng 190(49–50): 6641–6662CrossRefGoogle Scholar
  31. Guanglun W, Pekau OA, Chuhan Z, Shaomin W (2000) Seismic fracture analysis of concrete gravity dams based on nonlinear fracture mechanics. Eng Fract Mech 65(1): 67–87CrossRefGoogle Scholar
  32. Hori T, Mohri Y, Kohgo Y (2006) Model test and deformation analysis for failure of a loose sandy embankment dam by seepage. In: Carefree, AZ, USA. 2359-2370. American Society of Civil Engineers, Reston, 20191-4400, USAGoogle Scholar
  33. Imaeda Y, Inutsuka S-I (2002) Shear flows in smoothed particle hydrodynamics. Astrophys J 569(1): 501–518CrossRefGoogle Scholar
  34. Ingraffea AR (1990) Case studies of simulation of fracture in concrete dams. Eng Fract Mech 35(1–3): 553–564CrossRefGoogle Scholar
  35. Khan IH (1983) Failure of an earth dam—a case-study. J Geotech Eng Asce 109(2): 244–259CrossRefGoogle Scholar
  36. Khoei AR, Barani OR, Mofid M (2011) Modeling of dynamic cohesive fracture propagation in porous saturated media. Int J Numer Anal Methods Geomech 35(10): 1160–1184CrossRefGoogle Scholar
  37. Lee OS, Kim DY (1999) Crack-arrest phenomenon of an aluminum alloy. Mech Res Commun 26(5): 575–581CrossRefGoogle Scholar
  38. Lee J, Fenves GL (1998) A plastic-damage concrete model for earthquake analysis of dams. Earthq Eng Struct Dyn 27(9): 937–956CrossRefGoogle Scholar
  39. Libersky LD, Petschek AG (1990) Smooth particle hydrodynamics with strength of materials. In: Trease HE, Crowley WP (eds) Advances in the Free-Lagrange Method. Springer, BerlinGoogle Scholar
  40. Liu ZS, Swaddiwudhipong S, Koh CG (2004) High velocity impact dynamic response of structures using SPH method. Int J Comput Eng Sci 5(2): 315–326CrossRefGoogle Scholar
  41. Martha LF, Llorca J, Ingraffea AR, Elices M (1991) Numerical simulation of crack initiation and propagation in an arch dam. Dam Eng 2(3): 193–211Google Scholar
  42. Martt DF, Shakoor A, Greene BH (2005) Austin Dam, Pennsylvania: the sliding failure of a concrete gravity dam. Environ Eng Geosci 11(1): 61–72CrossRefGoogle Scholar
  43. Melosh HJ, Ryan EV, Asphaug E (1992) Dynamic fragmentation in impacts: hydrocode simulation of laboratory impacts. J Geophys Res 97: 14735–14759CrossRefGoogle Scholar
  44. Monaghan JJ (1992) Smoothed particle hydrodynamics. Ann Rev Astron Astrophys 30: 543–574CrossRefGoogle Scholar
  45. Monaghan JJ (2005) Smoothed particle hydrodynamics. Rep Prog Phys 68: 1703–1759CrossRefGoogle Scholar
  46. Ozaki M, Hayashi S (1978) Earthquake resistant design of offshore building structures. IEEE J Ocean Eng 3(4): 152–162CrossRefGoogle Scholar
  47. Pekau OA, Batta V (1994) Seismic cracking behavior of concrete gravity dams. Dam Eng 5: 5–29Google Scholar
  48. Pekau OA, Yuzhu C (2004) Failure analysis of fractured dams during earthquakes by DEM. Eng Struct 26(10): 1483–1502CrossRefGoogle Scholar
  49. Pekau OA, Feng LM, Zheng CH (1995) Seismic fracture of Koyna dam—case-study. Earthq Eng Struct Dyn 24(1): 15–33CrossRefGoogle Scholar
  50. Ren Q, Dong Y, Yu T (2009) Numerical modeling of concrete hydraulic fracturing with extended finite element method. Sci China Ser E Technol Sci 52(3): 559–565CrossRefGoogle Scholar
  51. Shockey DA, Curran DR, Seaman L, Rosenberg JT, Petersen CF (1974) Fragmentation of rock under dynamic loads. Int J Rock Mech Min Sci 11: 303–317CrossRefGoogle Scholar
  52. Talwani P (1997) On the nature of reservoir-induced seismicity. Pure Appl Geophys 150(3): 473–492CrossRefGoogle Scholar
  53. Unger JF, Eckardt S, Könke C (2007) Modelling of cohesive crack growth in concrete structures with the extended finite element method. Comput Methods Appl Mech Eng 196(41–44): 4087–4100CrossRefGoogle Scholar
  54. Wingate CA, Fisher HN (1993) Strength modeling in SPHC. Los Alamos National Laboratory, Report no. LA-UR-93-3942Google Scholar
  55. Xu Y, Yuan H (2011) Applications of normal stress dominated cohesive zone models for mixed-mode crack simulation based on extended finite element methods. Eng Fract Mech 78(3): 544–558CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of AucklandAucklandNew Zealand
  2. 2.CSIRO Mathematics, Informatics and StatisticsClaytonAustralia

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