# Century-long expansion of hydrating cement counteracting concrete shrinkage due to humidity drop from selfdesiccation or external drying

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## Abstract

A physically based model for auotgenous shrinkage and swelling of portland cement paste is necessary for computation of long-time hydgrothermal effects in concrete structures. The goal is to propose such a model. As known since 1887, the volume of cement hydration products is slightly smaller than the original volume of cement and water (chemical shrinkage). Nevertheless, this does not imply that the hydration reaction results in contraction of the concrete and cement paste. According to the authors’ recently proposed paradigm, the opposite is true for the entire lifetime of porous cement paste as a whole. The hydration process causes *permanent volume expansion* of the porous cement paste as a whole, due to the growth of C–S–H shells around anhydrous cement grains which pushes the neighbors apart, while the volume reduction of hydration products contributes to porosity. Additional expansion can happen due to the growth of ettringite and portlandite crystals. On the material scale, the expansion always dominates over the contraction, i.e., the hydration per se is, in the bulk, always and permanently *expansive*, while the source of all of the observed shrinkage, both autogenous and drying, is the compressive elastic or viscoelastic strain in the solid skeleton caused by a decrease of chemical potential of pore water, along with the associated decrease in pore relative humidity. As a result, the selfdesiccation, shrinkage and swelling can all be predicted from one and the same unified model, in which, furthermore, the low-density and high-density C–S–H are distinguished. A new thermodynamic formulation of unsaturated poromechanics with capillarity and adsorption is presented. The recently formulated local continuum model for calculating the evolution of hydration degree and a new formulation of nonlinear desorption isotherm are important for realistic and efficient finite element analysis of shrinkage and swelling. Comparisons with the existing relevant experimental evidence validate the proposed model.

## Keywords

Autogenous shrinkage Swelling Hydration Swelling Drying Biot coefficient Pore water Thermodynamics Unsaturated poromechanics Capillarity and adsorption## Notes

### Acknowledgements

Partial financial support of poromechanics studies from DoE through Los Alamos National Lab grant to Northwestern University is gratefully acknowledged. Preliminary research was supported by the U.S. Department of Transportation through Grant 20778 from the Infrastructure Technology Institute of Northwestern University, and from the NSF under Grant CMMI-1129449.

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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