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A model for regular desiccation cracks formation

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Abstract

A desiccation theory is developed providing a rational framework for a three-dimensional analysis of shrinkage and crack formation in a stiff clay surface layer. With the present model, we are estimating the shrinkage stress and the chemical potential variation in a morpheme produced after cracking, in a stiff clay surface layer, in terms of measurable quantities. In regular shrinkage morphemes, the shrinkage stresses are calculated from the shrinkage displacement and moisture content change. Other parameters such as the water mobility are introduced in order to express the chemical potential and the entropy changes in terms of the moisture content change and temperature at various instants of time.

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Abbreviations

A :

Elemental section of an area exposed by a new crack

a :

Coefficient

E :

Young’s modulus

e :

Linear strain

G :

Critical strain energy released rate

h :

Interstitial fluid pressure

h o :

Constant of integration

\({J_T^a}\) :

Desorbed flux of water

K(= P h /P v ):

Coefficient of lateral stress

L :

Major diameter of a soil column formed after cracking (assumed elliptical)

\({L_T^c}\) :

Wave length of maximum shrinkage

m w :

Mass of water

\({M_T^a}\) :

Water transportivity coefficient

N :

Normal on the external surface

P h , P v :

Lateral and vertical force driving shrinkage

P ij :

Direct shear forces driving shrinkage

r :

Internal radius of the morpheme

Q :

Heat absorbed during a given change

R :

Distance

s :

Critical strain energy released rate

S :

Entropy

T :

Temperature

ΔS i :

Entropy produced by the irreversible process

ΔS e :

Entropy flow to or from the environment

X ij :

Stress

X′:

Effective stress

X atm :

Atmospheric pressure

V :

Volume

U :

Internal energy

w :

Moisture content

W :

Work done

α :

Coefficient

β c :

Wave number of maximum shrinkage

γ :

Surface tension

λ :

Coefficient

μ w :

Chemical potential of the soil water

\({\xi^{p}}\) :

Iso-shrinkage width at the position p

ρ :

Bulk density

\({\varphi_{T}}\) :

Free energy at constant temperature per unit volume

\({\Phi_{T}}\) :

Free energy at constant temperature

\({\Phi_{P}=U+\Sigma x_{ij}P_{ij}}\) :

Total heat

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Authors and Affiliations

  1. Democritus University of Thrace, Xanthi, Greece

    T. K. Karalis

  2. National Technical University of Athens, Athens, Greece

    K. T. Karalis

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  1. T. K. Karalis
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Correspondence to T. K. Karalis.

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Karalis, T.K., Karalis, K.T. A model for regular desiccation cracks formation. Acta Mech 223, 1517–1536 (2012). https://doi.org/10.1007/s00707-012-0672-6

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