# Theoretical analysis of desiccation crack spacing of a thin, long soil layer

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## Abstract

Soil desiccation cracking is important for a range of engineering applications, but the theoretical advancement of this process is less than satisfactory. In particular, it is not well understood how the crack spacing-to-depth ratio depends on soil material behaviour. In the past, two approaches, namely stress relief and energy balance, have been used to predict the crack spacing-to-depth ratio. The current paper utilises these two approaches to predict the approximate spacing-to-depth ratio of parallel cracks that form in long desiccating soil layers subjected to uniform tensile stress (or suction profile) while resting on a hard base. The theoretical developments have examined the formation of simultaneous and sequential crack patterns and have identified an important relationship between the stress relief and energy approaches. In agreement with experimental observations, it was shown that the spacing-to-depth ratio decreases with layer depth, and crack spacing generally increases with layer depth. The influence of the stiffness at the base interface indicated that decreasing the basal interface stiffness makes the crack spacing to increase in sequential crack formation. The experimental observations also show a decrease in cracking water content with the decrease in layer thickness, and this behaviour was explained on the basis of a critical depth concept.

## Keywords

Cracking Desiccation Fracture toughness Moisture Soil Tensile strength## List of symbols

- \(d\)
Depth of the clay layer

*E*Elastic modulus of clay layer

- \(E_{\text{f}}\)
Energy consumed by crack formation (\(= G_{\text{c}} d\))

- \(E_{\text{f}}^{*}\)
Dimensionless form of \(E_{\text{f}}\)

*G*_{c}Crack energy release rate

*k*Shear stiffness of the interface between clay and hard base

- \(K_{\text{IC}}\)
Fracture toughness in Mode I (pure tensile) cracking

*s*Crack spacing

*u*_{b}Relative displacement at the basal interface

*x*Distance from the crack face

- \(w_{\text{cr}}\)
Water content at crack initiation

*α*Factor of tensile strength needed to from a sequential crack

- Δ
*σ*_{x} Change in normal stress in

*x*direction- \(\Delta \varepsilon_{x} ,\Delta \varepsilon_{y} ,\Delta \varepsilon_{xy}\)
Change in strain in x and y directions

- \(\Delta U,\Delta U^{*}\)
Change in strain energy and its dimensionless form

- \(\sigma_{x}^{\text{av}} ,\sigma_{y}^{\text{av}} ,\tau_{xy}^{\text{av}}\)
Average normal stresses and shear stresses in x and y directions

*υ*Poisson’s ratio

*τ*_{b}Shear stress at the base of the interface

*σ*_{o}Normal stress prior to cracking

*σ*_{t}Tensile strength of soil

*σ*_{xc}Horizontal stress due to an isolated crack subject to uniform compressive stress

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