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Fracturing of Clay During Drying: Modelling and Numerical Simulation

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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.

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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)



cr :


d :

Dry state

e :


f :

Free of force

j :

Spring number

x, y, z :

Direction x, y or z


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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

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