###### Abstract
Moreover, real projects are challenging nowadays, and several performance requirements are targeted for engineering, architecture, and economic and ecological impacts. Generally, the SCC mixture design can be divided into four phases as follows [1; 6]:  
* Establishing the structural, constructive and environmental conditions of the application;
* The selection and characterisation of constituent raw materials;
* The preliminary SCC mixture design;
* Checking the performance requirements. The mixture design must be revised and tested if a requirement is not checked until the desired performance is achieved. In the literature, it is possible to find a wide range of compositions that satisfy the criteria of being able to self-compact. Therefore, no single original composition exists for a given application or performance requirements. An important and decisive factor for SCC mixture design is understanding the effect of each constituent material and its interaction on the final properties of the SCC [1]. Three main types of approaches can be distinguished for SCC mixture design. The first approach is based on laboratory experiments, using the trial-and-error method. The second is based on optimising concrete paste volume, and the third approach uses statistical analyses based on factorial plans, such as the design of experiments [6; 9; 10]. The factorial design approach refers to planning experiments so that good-quality data can be collected and analysed using statistical methods and empirical models can be constructed that enable valid and objective conclusions and involve a minimum number of experiments. The obtained numerical models can subsequently be mathematically manipulated for various purposes, particularly for the optimisation of mixtures. In general, after formulating the problem, the factorial design involves the following steps:  
1. The selection of factors (mixture parameters), levels to be considered and ranges of variation;
2. The selection of response variables;
3. The choice of the type of factorial plan;
4. Performing the experiments;
5. Performing the statistical data analysis (adjustments of a numerical model);Performing further calculations involving the fitted models (optimisation) and conclusions. Based on the method of [PERSON] et al. [3], the SCC mixture design can be defined by the following mixture parameters: the water-to-cement mass ratio (w/c), water-to-fines volume ratio (Vw/Vp), sand-to-mortar volume ratio (Vs/Vm), superplasticiser-to-fines mass ratio (Sp/p), the ratio between the volume of coarse aggregate and the maximum volume of coarse aggregate that can be included in 1 m\({}^{3}\) in the compacted state (Vg/Vg,lim) and the ratio between the sands in mass (s1/s2), if a mixture of two grains of sand is used as fine aggregate. The air content is generally fixed at 2%. Thus, all the variables except Vg/Vg,lim [1; 2; 7] are employed for the study of mortars. In turn, in the concrete study, only the variables related to the solid skeleton are adopted as independent variables (Vg/Vg,lim and Vs/Vm), because the paste composition remains fixed, as the result of a previous study performed at the mortar level [1; 2; 7].