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Drying, Shrinkage, and Cracking of Cementitious Materials

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Abstract

Concrete is a heterogeneous, reactive, viscoelastic material whose shrinkage during drying often results in cracking that compromises its durability. This paper reviews the principles of shrinkage and stress development during drying of cement paste and concrete, taking particular account of the changes in microstructure as the cement hydrates, which profoundly influence the transport and mechanical properties of the body.

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Notes

  1. Experimental observations and thermodynamic arguments (Flatt et al. 2011) indicate that hydration of cement is arrested below a relative humidity of about 80 %. However, during the time required to establish equilibrium following a desorption step below that value, the liquid may continue to react.

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    George W. Scherer

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Appendix

Appendix

To estimate the concentration of water in the vapor adjacent to the surface of the liquid, we consider a steady state in which there is a boundary layer with thickness \(\delta _\mathrm{V}\), at the outer edge of which (\(z = \delta _\mathrm{V}\)) the vapor concentration is set at the ambient value, \(c(\delta _\mathrm{V})=c_\mathrm{amb}\), and at the inner edge of which (\(z = 0\)) there is an evaporative flux, \(J_\mathrm{E}\), fixed at

$$\begin{aligned} -D_\mathrm{v} \left. {\frac{\text {d}c}{\text {d}z}} \right| _{z=0} = J_\mathrm{E} \end{aligned}$$
(22)

where \(D_\mathrm{v}\) is the diffusivity of the vapor. Solving \(D_\mathrm{v} \text {d}^{2}c/\text {d}z^{2} = 0\), the concentration profile in the boundary layer is found to be

$$\begin{aligned} c[z]= c_\mathrm{amb} + \frac{J_\mathrm{E} }{D_\mathrm{v} }\left( {\delta _\mathrm{V} -z} \right) \end{aligned}$$
(23)

If the rate of evaporation from the surface of the liquid is related to the vapor concentration by

$$\begin{aligned} J_\mathrm{E} =k_\mathrm{E} \left( {c_\mathrm{s} -c[0]} \right) \end{aligned}$$
(24)

where \(c_\mathrm{s}\) is the vapor concentration at saturation, then Eq. (23) requires that the concentration in the vapor phase adjacent to the liquid surface is

$$\begin{aligned} c\left[ 0 \right] = \frac{c_\mathrm{s} +c_\mathrm{amb} \left( {{D_\mathrm{v} }/{k_\mathrm{E} \delta _\mathrm{V} }} \right) }{1+{D_\mathrm{v} }/{k_\mathrm{E} \delta _\mathrm{V} }} \end{aligned}$$
(25)

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Scherer, G.W. Drying, Shrinkage, and Cracking of Cementitious Materials. Transp Porous Med 110, 311–331 (2015). https://doi.org/10.1007/s11242-015-0518-5

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