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Computational Mechanics

, Volume 61, Issue 3, pp 299–318 | Cite as

Phase-field modeling of fracture in variably saturated porous media

  • T. CajuhiEmail author
  • L. Sanavia
  • L. De Lorenzis
Original Paper

Abstract

We propose a mechanical and computational model to describe the coupled problem of poromechanics and cracking in variably saturated porous media. A classical poromechanical formulation is adopted and coupled with a phase-field formulation for the fracture problem. The latter has the advantage of being able to reproduce arbitrarily complex crack paths without introducing discontinuities on a fixed mesh. The obtained simulation results show good qualitative agreement with desiccation experiments on soils from the literature.

Keywords

Porous media mechanics Fracture Phase-field modeling Variably saturated conditions Desiccation 

Notes

Acknowledgements

We would like to acknowledge the funding provided by the German Research Foundation DFG GRK-2075.

References

  1. 1.
    Lakshmikantha MR (2009) Experimental and theoretical Analysis of cracking in drying soils. PhD thesis, Universitat Politecnica de CataluniaGoogle Scholar
  2. 2.
    Lakshmikantha MR, Prat PC, Ledesma A (2012) Experimental evidence of size effect in soil cracking. Can Geotech J 49(3):264–284CrossRefGoogle Scholar
  3. 3.
    Trabelsi H, Jamei M, Zenzri H, Olivella S (2012) Crack patterns in clayey soils: experiments and modeling. Int J Numer Anal Meth Geomech 36:1410–1433CrossRefGoogle Scholar
  4. 4.
    Péron H (2009) Desiccation cracking of soils. PhD thesis, École Polytechnique Fédérale de LausanneGoogle Scholar
  5. 5.
    Stirling RA (2014) Multiphase modelling of desiccation cracking in compacted soil. PhD thesis, Newcastle UniversityGoogle Scholar
  6. 6.
    Costa SM (2009) Study of desiccation cracking and fracture properties of clay soils. PhD thesis, Monash UniversityGoogle Scholar
  7. 7.
    Lecocq N, Vandewalle N (2002) Experimental study of cracking induced by desiccation in 1-dimensional systems. Eur Phys J E 8:445–452. doi: 10.1140/epje/i2002-10040-2
  8. 8.
    Musielak G, Śliwa T (2012) Fracturing of clay during drying: modelling and numerical simulation. Transp Porous Media 95(2):465–481CrossRefGoogle Scholar
  9. 9.
    Murray I, Tarantino A, Francescon F (2014) Crack formation in clayey geomaterials subjected to tensile (total) stress. Unsaturated Soils: Research & Applications, pp 823–828Google Scholar
  10. 10.
    Murray I, Tarantino A, Gérard P, Francescon F (2014) Desiccation cracking in clay forms subjected to non-uniform hydraulic and mechanical boundary conditions. In: Khalili N, Russell AR, Khoshghalb A (eds) Unsaturated Soils: Research & Applications. CRC Press, pp 829–834. doi: 10.1201/b17034-118
  11. 11.
    Péron H, Hueckel T, Laloui L, Hu L-B (2009) Fundamentals of desiccation cracking of fine-grained soils: experimental characterisation and mechanisms identification. Can Geotech J 46(10):1177–1201CrossRefGoogle Scholar
  12. 12.
    Simoni L, Schrefler BA (2014) Multi field simulation of fracture. Adv Appl Mech 47(C):367–519CrossRefGoogle Scholar
  13. 13.
    Ayada R, Konrad J-M, Soulié M (1997) Desiccation of a sensitive clay: application of the model CRACK. Can Geotech 34:943–951CrossRefGoogle Scholar
  14. 14.
    Prat PC, Ledesma A, Cabeza L (2002) Drying and cracking of soils: numerical modeling. In: Proceedings of the 8th international conference on numerical models in geomechanics, Rome, Italy, pp 10–12Google Scholar
  15. 15.
    Gerard P, Murray IW, Tarantino A, Francescon F (2015) On the mechanism for desiccation cracks initiation in clayey materials. In: Computer methods and recent advances in geomechanics-14th international conference of international association for computer methods and recent advances in geomechanics, IACMAG 2014, pp 1327–1331Google Scholar
  16. 16.
    Bui HH, Nguyen GD, Kodikara J, Sanchez M (2015) Soil cracking modelling using the mesh-free sph method. In: 12th Australia New Zealand conference on geomechanics (ANZ 2015)Google Scholar
  17. 17.
    Kodikara J, Costa S (2013) Desiccation cracking in clayey soils: mechanisms and modelling. In: Multiphysical testing of soils and shales. Springer, pp 21–32Google Scholar
  18. 18.
    Stirling RA, Davie CT, Glendinning S (2015) Multiphase modelling of desiccation cracking in the near-surface of compacted soils. In: Proceedings of the 16 th European conference on soil mechanics and geotechnical engineering. Edinburgh, pp 2311–2316Google Scholar
  19. 19.
    Peron H, Laloui L, Hu L-B, Hueckel T (2013) Formation of drying crack patterns in soils: a deterministic approach. Acta Geotech 8(2):215–221CrossRefGoogle Scholar
  20. 20.
    Hirobe S, Oguni K (2016) Coupling analysis of pattern formation in desiccation cracks. Comput Methods Appl Mech Eng 307:470–488MathSciNetCrossRefGoogle Scholar
  21. 21.
    Francfort GA, Marigo J-J (1998) Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids 46(8):1319–1342MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Bourdin B, Francfort GA, Marigo J-J (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48(4):797–826MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Ambati M, Gerasimov T, De Lorenzis L (2014) A review on phase-field models of brittle fracture and a new fast hybrid formulation. Comput Mech 55:383–405MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Mikelić A, Wheeler MF, Wick T (2014) A phase-field method for propagating fluid-filled fractures coupled to a surrounding porous medium. SIAM Multiscale Model Simul 13(1):367–398MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Mikelić A, Wheeler MF, Wick T (2015) Phase-field modeling of a fluid-driven fracture in a poroelastic medium. Comput Geosci 19:1–25MathSciNetCrossRefGoogle Scholar
  26. 26.
    Heider Y, Markert B (2016) A phase-field modeling approach of hydraulic fracture in saturated porous media. Mech Res Commun 80:38–46CrossRefGoogle Scholar
  27. 27.
    Zienkiewicz OC, Chan AHC, Pastor M, Schrefler BA, Shiomi T (1999) Computational geomechanics—with special reference to earthquake engineering. Wiley, ChichesterzbMATHGoogle Scholar
  28. 28.
    Lewis RW, Schrefler BA (1998) The finite element method in the static and dynamic deformation and consolidation of porous mediaGoogle Scholar
  29. 29.
    Schrefler BA, Sanavia L, Majorana CE (1996) A multiphase medium model for localisation and postlocalisation simulation in geomaterials. Mech Cohesive-frictional Mater 1(1):95–114CrossRefGoogle Scholar
  30. 30.
    Nuth M, Laloui L (2008) Effective stress concept in unsaturated soils: clarification and validation of a unified framework. Int J Numer Anal Meth Geomech 32(7):771–801CrossRefzbMATHGoogle Scholar
  31. 31.
    Schrefler BA (1984) The Finite Element Method in Soil Consolidation (with applications to Surface Subsidence). PhD thesis, University College of SwanseaGoogle Scholar
  32. 32.
    Gray WG, Hassanizadeh SM (1991) Unsaturated flow theory including interfacial phenomena. Water Resour Res 27(8):1855–1863CrossRefGoogle Scholar
  33. 33.
    van Genuchten MT (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44:892–898Google Scholar
  34. 34.
    Kuhn C, Noll T, Müller R (2016) On phase field modeling of ductile fracture. GAMM-Mitteilungen 39(1):35–54MathSciNetCrossRefGoogle Scholar
  35. 35.
    Wu T, De Lorenzis L (2016) A phase-field approach to fracture coupled with diffusion. Comput Methods Appl Mech Eng 312:196–223MathSciNetCrossRefGoogle Scholar
  36. 36.
    Miehe C, Hofacker M, Welschinger F (2010) A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng 199(45):2765–2778MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Freddi F, Royer-Carfagni G (2010) Regularized variational theories of fracture: a unified approach. J Mech Phys Solids 58(8):1154–1174MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Amor H, Marigo J-J, Maurini C (2009) Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments. J Mech Phys Solids 57(8):1209–1229Google Scholar
  39. 39.
    Miehe C, Welschinger F, Hofacker M (2010) Thermodynamically consistent phase-field models of fracture: variational principles and multi-field fe implementations. Int J Numer Meth Eng 83:1273–1311MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Stirling RA, Simpson DJ, Davie CT (2013) The application of digital image correlation to brazilian testing of sandstone. Int J Rock Mech Min Sci 60:1–11Google Scholar
  41. 41.
    Borden MJ, Verhoosel CV, Scott MA, Hughes TJR, Landis CM (2012) A phase-field description of dynamic brittle fracture. Comput Methods Appl Mech Eng 217:77–95MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Gerasimov T, De Lorenzis L (2016) A line search assisted monolithic approach for phase-field computing of brittle fracture. Phase field approaches to fracture. Comput Methods Appl Mech Eng 312:276–303CrossRefGoogle Scholar
  43. 43.
    Gross S, Reusken A (2011) Numerical methods for two-phase incompressible flows, vol 40. Springer Science & Business Media, New YorkzbMATHGoogle Scholar
  44. 44.
    Bangerth W, Davydov D, Heister T, Heltai L, Kanschat G, Kronbichler M, Maier M, Turcksin B, Wells D (2016) The deal.II library, version 8.4. J Numer Math 24:135–141MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Liakopoulos AC (1964) Transient flow through unsaturated porous media. PhD thesis, University of California, BerkeleyGoogle Scholar
  46. 46.
    Gawin D, Sanavia L (2009) A unified approach to numerical modeling of fully and partially saturated porous materials by considering air dissolved in water. Comput Model Eng Sci 53(3):255zbMATHGoogle Scholar
  47. 47.
    Gawin D, Schrefler BA (1996) Thermo-hydro-mechanical analysis of partially saturated porous materials. Eng Comput 13(7):113–143CrossRefzbMATHGoogle Scholar
  48. 48.
    Jommi C, Vaunat J, Gens A, Gawin D, Schrefler BA (1997) Multiphase flow in porous media: a numerical benchmark. Proc NAFEMS World Congr 97:1338–1349Google Scholar
  49. 49.
    Sanavia L, Pesavento F, Schrefler BA (2006) Finite element analysis of non-isothermal multiphase geomaterials with application to strain localization simulation. Comput Mech 37(4):331–348CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Institute of Applied MechanicsTechnische Universität BraunschweigBraunschweigGermany
  2. 2.Department of Civil, Architectural and Environmental EngineeringUniversity of PadovaPadovaItaly

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