The equation of state of unsaturated cementitious composites – A new multiscale model

A new theoretical model for the equation of state (pressure–volumetric strain relationship, EOS) of cementitious composites is presented. The model employs a multi-scale approach and focuses on the loading branch of unsaturated cementitious composites like cement paste, mortar and concrete. The cementitious composite is a porous solid that combines the solid fractions of its constituents and capillary pores at different sizes filled in by air or partly by water. It is assumed that any contained water is fully drained during loading and it has no role in the compressibility process of the composite. Attention is given to the monotonic loading only, and unloading/reloading is not considered at this stage. The composite behavior under hydrostatic loading is described as a non-linear elastic-plastic material with hardening caused by the closure of the capillary pores. At the micro-scale level, a representative volume unit of an elastic-plastic spherical domain is considered to represent the solid material with a central single spherical cavity to represent the pore, while at the macro-scale level, it is assumed that every differential element has the properties of the above micro-level volume unit, where the interior and exterior boundaries radii are treated as random variables. The solid material is composed of cement particles and fine and coarse aggregates. The equations of state of the fine and coarse aggregates are assumed to be linear elastic. The phase mix rule is applied to account for the different mixture constituents and obtain the equation of state of the cementitious composite. The model is validated with available test results and good agreement is obtained. A parametric study of the model is performed to investigate the effect of mixture (cement paste and mortar) parameters on the shape of the equation of state.