Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Fracturing of Clay During Drying: Modelling and Numerical Simulation

  • 607 Accesses

  • 13 Citations

Abstract

Non-uniform distribution of moisture contents inside of the porous materials during drying results in compressional stresses inside of the material and tensional ones close to the surface. The tensional stresses together with brittleness of dry material are the reasons of fracturing of the material. The proposed model consists of two parts. The mass transfer is described by simple diffusion equation. The mechanical behaviour of the material is modelled with the network model in which the material is modelled as the set of small particles interconnected elastically via springs. The spring constants and strengths depend on Young modulus and the material tensional strength. The dependences of these material parameters on the moisture content are determined. Then two 2D initial-boundary problems are solved. The results show possible way of cracks initiation and generation by drying.

This is a preview of subscription content, log in to check access.

Abbreviations

A, B, C :

Constants in Eq. (21)

D :

Diffusion coefficient (m2 s−1)

E :

Young modulus (Pa)

F :

Force (N)

L :

Spring length (m)

X :

Moisture content dry basis (kg/kg)

a :

Moisture expansion coefficient (1)

h :

Plate thickness/bar height (m)

k :

Spring constant (N m−1)

l :

Plate length/bar width (m)

l :

Sample length

n :

Number of particles (–)

t :

Time (s)

x :

Length co-ordinate (m)

z :

Height co-ordinate (m)

α :

Moisture exchange coefficient (m s−1)

δ :

Size of particle (m)

θ :

Dimensionless moisture content (–)

ε :

Linear moisture expansion (–)

σ :

Material strength (Pa)

0:

Initial

cr :

Critical

d :

Dry state

e :

Equilibrium

f :

Free of force

j :

Spring number

x, y, z :

Direction x, y or z

References

  1. Andersen J.V., Brechet Y., Jensen H.J.: Fracturing described by a spring-block model. Europhys. Lett. 26, 13–18 (1994)

  2. Aoki, K., Dong N. H., Kaneko T., Kuriyama, S.: Physically based simulation of cracks on drying 3D solid. In: Proceedings of the 10th Pacific Conference on Computer Graphics and Applications, Beijing, China, 9–11 October, pp. 467–468 (2002)

  3. Aoki, K., Dong, N.H., Kaneko, T.: Representation method for cracks on drying 3D solid by physical model. Electron Commun Jpn Part 3, 90(5), 50–59 (2007) (translated from Denshi Joho Tsushin Gakkai Ronbunshi, J86-D-II (12), 1756–1764 (2003))

  4. Augier, F., Coumans, W.J., Hugget, A., Kaasschieter, E.F.: On the study of cracking in clay drying. In: Proceedings of the 12th International Drying Symposium, Noordwijkerhout, The Netherlands, 28–31 August, Paper No. 290 (2000)

  5. Banaszak J., Kowalski S.J.: Drying induced stresses estimated on the base of elastic and viscoelastic models. Chem. Eng. J 86, 139–143 (2002)

  6. Banaszak, J., Musielak, G.: Influence of moisture content on strength and yield stress limit of ceramic masses. In: Proceedings of the XII Polish Drying Symposium, Łódź, Poland, 14–16 September, pp. 141–146 (2009)

  7. Deng G., Shen Z.J.: Numerical simulation of crack formation process in clays during drying and wetting. Geomech. Geoeng. Int. J. 1(1), 27–41 (2006)

  8. Hammerle J.R.: Theoretical analysis of failure in viscoelastic slab subjected to temperature and moisture gradients. Trans. ASAE 15(5), 960–965 (1972)

  9. Itaya Y., Uchiyama S., Hatano S., Mori S.: Drying enhancement of clay slab by microwave heating. Dry. Technol. 23, 1243–1255 (2005)

  10. Katekawa M.E., Silva M.A.: A review of drying models including shrinkage effects. Dry. Technol. 24, 5–20 (2006)

  11. Ketelaars, A.A.J.: Drying Deformable Media. Kinetics, Shrinkage and Stresses, PhD Thesis, Technische Universiteit Eindhoven (1992)

  12. Kharaghani, A., Metzger, T., Tsotsas, E.: Mechanical effects during isothermal drying: a new discrete modelling approach. In: Proceedings of 16th International Drying Symposium, Hyderabad, India, 9–12 November, pp. 440–448 (2008)

  13. Kharaghani A., Metzger T., Tsotsas E.: A proposal for discrete modeling of mechanical effects during drying. Combining pore networks with DEM. AIChE J. 57(4), 872–885 (2011)

  14. Kowalski S., Rybicki A.: Cohesive strength of materials during drying processes. Dry. Technol. 27, 863–869 (2009)

  15. Kowalski S., Smoczkiewicz-Wojciechowska A.: Stresses in dried wood. Modelling and experimental identification. Transp. Porous Media 66, 145–158 (2007)

  16. Kowalski S., Musielak G., Rybicki A.: Distribution of drying induced stresses in samples with grooves. Stud. Geotech. Mech. 18(1–2), 3–17 (1996a)

  17. Kowalski S., Musielak G., Rybicki A.: Shrinkage stresses in dried materials with grooves of various shapes. Stud. Geotech. Mech. 18(3–4), 19–26 (1996b)

  18. Kowalski S.J., Moliński W., Musielak G.: The identification of fracture in dried wood based on theoretical modelling and acoustic emission. Wood Sci. Technol. 38, 35–52 (2004)

  19. Kowalski S., Rybicki A., Rajewska K.: Stress generated during convective and microwave drying. Dry. Technol. 23, 1875–1893 (2005)

  20. Kowalski S., Musielak G., Banaszak J.: Experimental validation of heat and mass transfer model for convective drying. Dry. Technol. 25(1), 107–121 (2007)

  21. Musielak G.: Possibility of clay damage during drying. Dry. Technol. 18(8), 1645–1659 (2001)

  22. Musielak G., Banaszak J.: Non-linear heat and mass transfer during convective drying of Kaolin cylinder under non-steady conditions. Trans. Porous Media 66, 121–134 (2007)

  23. Musielak G., Kieca A.: Temperature dependence of the moisture diffusion coefficient in a high moisture content material. Chem. Process. Eng. 30(2), 231–242 (2009)

  24. Musielak G., Mierzwa D.: Permanent strains in clay-like material during drying. Dry. Technol. 27, 894–902 (2009)

  25. Musielak, G., Bródka, A., Błaż, M.: Estimation of mechanical constants of clays using compression and Brazilian tests. In: Proceedings of the XII Polish Drying Symposium, Łódź, Poland, 14–16 September, pp. 289–297 (2009)

  26. Partyka, J., Wodnicka, K., Wójcik, Ł. Rheological parameters of kaolin koc water suspensions. Ceram. Mater. 62(2), 197–202 (in Polish) (2010)

  27. Peron H., Delenne J.Y., Laloui L., El Youssoufi M.S.: Discrete element modelling of drying shrinkage and cracking of soils. Comput. Geotech. 36, 61–69 (2009a)

  28. Peron H., Laloui L., Hueckel T., Hu L.B.: Desiccation cracking of soils. Eur. J. Civil Environ. Eng. 13(7–8), 869–888 (2009b)

  29. Pȩczalski R., Laurent P., Andrieu J., Boyer J.C., Boivin M.: Drying induced cracking of abrasive rings: risk prediction and process optimization by numerical simulation. Dry. Technol. 14, 333–348 (1996)

  30. Pourcel F., Jomaa W., Puiggali J.R., Rouleau L.: Criterion for crack initiation during drying: alumina porous ceramic strength improvement. Powder Technol. 172, 120–127 (2007a)

  31. Pourcel F., Jomaa W., Puiggali J.R., Rouleau L.: Crack appearance during drying of an alumina gel: thermo-hydro-mechanical properties. Dry. Technol. 25, 759–766 (2007b)

  32. Strumiłło, C.: Podstawy teorii i techniki suszenia, 2nd edn. WNT, Warsaw (1983) (in Polish)

Download references

Author information

Correspondence to G. Musielak.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Musielak, G., Śliwa, T. Fracturing of Clay During Drying: Modelling and Numerical Simulation. Transp Porous Med 95, 465–481 (2012). https://doi.org/10.1007/s11242-012-0055-4

Download citation

Keywords

  • Cracking by drying
  • Spring network model
  • Moisture distribution
  • Experimental data
  • Numerical solution