# Numerical Design and Optimisation of Self-Compacting High Early-Strength Cement-Based Mortars
## 5 Conclusions  
The current study investigates the effect of SCHSM mixture design variables. It selects the best combination of powder materials (in a binary mixture of Portland cement + MTCK), water/binder ratio, superplasticiser dosage, and aggregates to reach optimum values of self-compactability and high early-age strength. As such, the DoE approach \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Response** & **Predicted Results** & **95\% CI Low** & **95\% CI High** \\ \hline D-flow & 259.15 & 237.78 & 280.51 \\ T-funnel & 9.87 & 9.1 & 10.79 \\ F,24 h & 10.31 & 9.93 & 10.7 \\ Rc,24 h & 50.00 & 46.86 & 53.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Estimated SCHSM properties of the optimised mixture. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Self-Compacting Ability** & **Self-Compacting Ability and High Early Strength** \\ \hline Constraints for optimisation & & \\ \hline Mixture parameters: & & \\ \hline Vw/Vc & In CCD range & In CCD range \\ Sp/p & In CCD range & In CCD range \\ Vw/Vp & In CCD range & In CCD range \\ Vs/Vm & In CCD range & In CCD range \\ Vfs/Vs & In CCD range & In CCD range \\ Vfs/Vs & In CCD range & In CCD range \\ \hline Response Variables: & & \\ \hline D-flow (mm) & Target 260 & In range [259; 261] \\ T-funnel (s) & Target 10 & In range [9.8, 10.2] \\ F,24 h (MPa) & None & None \\ Rc,24 h (MPa) & None & \(>\)50 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Optimisation criteria. was followed to obtain regression models that could describe and predict the relevant engineering properties. In addition, regression models were used for optimisation purposes. The following main conclusions were drawn:  
* Regression models were found to be adequate to describe SCHSCM properties over the experimental region, namely, slump-flow diameter, T-funnel time, and flexural and compressive strength at 24 h;
* The Vs/Vm factor exhibited the strongest (negative) effect on the slump-flow diameter and T-funnel time;
* The Vw/Vp factor was found to have the most significant effect on mechanical strength, corresponding to response variables F,24 h and Rc,24 h;
* Vw/Vc was the second most influencing factor, with a positive effect on the slump-flow diameter and T-funnel time and a negative effect on F,24 h and Rc,24 h;
* The variation of Sp/p used in the current CCD was small compared to the remaining factors. As such, Sp/p exhibited the lowest influence on SCHSCM properties when compared to other mixture parameters;
* The proposed optimal mixture represented the best compromise between self-compacting ability--a flow diameter of 250 mm and funnel time equal to 10 s--and a compressive strength higher than 50 MPa at 24 h without any special curing treatment and was found for Vc/Vp = 1.098; sp/p = 0.0243; Vw/Vp = 0.607; Vs/Vm = 0.478; and Vfs/vs = 0.047. Even though transposing the mortar study into SCC is out of the scope of the manuscript, SCC mixtures can be obtained by fixing the mortar mix proportions given in Section 4.2 and adding a coarse aggregate. However, tests on the concrete level are needed to optimise the aggregate skeleton. Moreover, based on regression models, contour plots or interaction diagrams can be computed and simplify the test protocol required to optimise a given SCC mixture, namely, to select the combination of powder materials with admixtures. In particular, they can help to compare the efficiency of different admixtures and alternative SCM. Optimised mortar mixtures can serve as reference mixtures in a quality control plan to detect variations in different deliveries of constituent materials, such as cement, filler, or superplasticiser. The derived models can also be useful to predict mortar properties when the material properties change, such as the cement source. The procedure presented in this work can easily be implemented in any concrete laboratory of a production centre since it involves mortar tests which are easy to carry out with simple tests and equipment. Conceptualisation, N.C., A.M.M., P.M.-O. and L.M. ; methodology, N.C.