Microstructural modelling of autogenous shrinkage in Portland cement paste at early age
Authors: Do Huy Quang , Bishnoi Shashank , Scrivener Karen Louise 
Published: May 2020

Purpose
This paper aims to develop a numerical, micromechanical model to predict the evolution of autogenous shrinkage of hydrating cement paste at early age (up to 7 days). Autogeneous shrinkage can be important in high-performance concrete characterized by low water to cement (w/c) ratios. The occurrence of this phenomenon during the first few days of hardening may result in early-age cracking in concrete structures. A good prediction of autogeneous shrinkage is necessary to achieve better understanding of the mechanisms and the deployment of effective measures to prevent early-age cracking.

Design/methodology/approach
Three-dimensional digital microstructures from the hydration modelling platform μic of cement paste were used to simulate macroscopic autogenous shrinkage based on the mechanism of capillary tension. Elastic and creep properties of the digital microstructures were calculated by means of finite element (FE) method homogenization. Autogenous shrinkage was then estimated as the average hydrostatic strain resulting from the capillary stress that was globally applied on the simulated digital microstructures. For this estimation, two approaches of homogenization technique, i.e. analytical poro-elasticity and numerical creep-superposition were used.

Findings
The comparisons of between the simulated and experimentally measured deformations indicate that the creep-superposition approach is more reasonable to estimate shrinkage at different water to cement ratios. It was found that better estimations could be obtained at low degrees of hydration, by assuming a loosely packed calcium silicate hydrates (C-S-H) growing in the microstructures. The simulation results show how numerical models can be used to upscale from microscopic characteristics of phases to macroscopic composite properties such as elasticity, creep and shrinkage.

Research limitations/implications
While the good predictions of some cement paste properties from the microstructure at early age were obtained, the current models have several limitations that are needed to overcome in the future. Firstly, the limitation of pore-structure representation is not only from lack understanding of C-S-H structure but also from the computational complexity. Secondly, the models do not consider early-age expansion that usually happens in practice and appears to be superimposed on an underlying shrinkage as observed in experiments. Thirdly, the simplified assumptions for mechanical simulation do not accurately reflect the solid–liquid interactions in the real partially saturated system, for example, the globally applying capillary stress on the boundary of the microstructure to find the effective deformation, neglecting water flow and the pore pressure. Last but not least, the models, due to the computational complexities, use many simplifications such as FE approximation, mechanical phase properties and creep statistical data.

Originality/value
This study holistically tackles the phenomenon of autogeneous shrinkage through microstructural modelling. In a first such attempt, the authors have used the same microstructural model to simulate the microstructural development, elastic properties, creep and autogeneous shrinkage. The task of putting these models together was not simple. The authors have successfully handled several problems at each step in an elegant manner. For example, although several earlier studies have pointed out that discrete models are unable to capture the late setting times of cements due to mesh effects, this study offers the most effective solution yet on the problem. It is also the first time that creep and shrinkage have been modelled on a young evolving microstructure that is subjected to a time variable load.