Influence of specimen size and measurements duration on the long-term extrapolation of drying shrinkage

The study presented in this paper aims at defining a procedure to study the efficiency of models used to extrapolate long-term shrinkage from experimental data. The approach allows estimating the minimum duration of measurements required to reach a given accuracy. The drying shrinkage of three Self-Consolidating Concretes (SCC) was monitored during 300 days for three cylinder sizes: ϕ78 mm, ϕ113 mm, and ϕ163 mm. Four mathematical forms of preexisting models have been studied: Model 1 (hyperbolic), Model 2 (square-root hyperbolic), Model 3 (square-root hyperbolic-tangent) and Model 4 (exponential). Two fitting parameters are provided by these models: ultimate shrinkage and characteristic time. Both parameters are overestimated for short experimental measurements duration. Their values cannot be considered as reliable unless a stabilization phase is reached vis-a-vis the measurements duration. Model 1 showed the fastest convergence and achieved this condition. The estimated ultimate shrinkage did not depend on specimen size. The stabilization phase was not reached for all models even after 300 days. The characteristic time was found to depend linearly on the square of the nominal cross section. Conclusions about the accuracy of the extrapolation cannot be drawn directly from these two parameters. Indeed, overestimations in the ultimate shrinkage and in the characteristic time result respectively in an increase and a decrease of the calculated shrinkage. To solve this problem, the coefficient of determination R2 is introduced and its evolution is computed according to the measurements duration for all cases. Thus, for given accuracy, model, and specimen size, minimum measurements duration can be determined.