# Numerical Design and Optimisation of Self-Compacting High Early-Strength Cement-Based Mortars
## 1 Introduction  
The building and construction industries have a heavy environmental impact. They account for 40% of natural resources, consume 70% of electrical power and 12% of potable water, and produce 45-65% of landfilled waste and 48% of GHG emissions [1]. In Europe, construction is the most significant economic sector, employing 18 million people directly and creating close to 10% of the European Union Gross Domestic Product. Thus, construction is an essential pillar in the context of the 2030 Agenda since it impacts the economic, environmental, and social spheres.  
Concrete is a massively used construction material and the second most-consumed material worldwide, just after water [2]. This is mainly because the basic constituents, cement, aggregates, and water, are widely available worldwide; thus, concrete can be produced locally and consequently, it is inexpensive. Moreover, it hardens quickly and in all habitable environments, including underwater.  
Over recent decades, efforts have been made to improve the behaviour of concrete materials. It took more than 150 years from the patenting of Portland cement (in 1824) until the discovery and development of self-compactable concrete (SCC) in the 1980 sin Japan [3,4]. The development of superplasticisers allowed the efficient dispersal of cementitious particles and the emergence of SCC. According to the European standard EN 206-1 (specification, performance, production, and conformity of concrete), the constituent raw materials of SCC are similar to ordinary vibrated concrete (OVC). The main differences between OVC and SCC are due to the constituents' proportions. Figure 1 presents the indicative volumetric proportions of SCC and OVC [5]. As can be seen, the main difference between SCC and OVC is a higher dosage of fine materials, i.e., cement and supplementary cementitious materials (SCM), and a smaller amount of coarse aggregate and smaller particle size distribution [6].  
As such, the design of more advanced cement-based materials such as SCC can be complex since several requirements must co-exist, such as (i) engineering properties, (ii) architecture, (iii) cost, and (iv) eco-efficiency, among others. Even though the selection of the material should try to improve robustness, making the mixture more tolerant to raw material variability, for economic reasons, depends significantly on local availability; hence, there is no fixed rule for the amount/type of aggregates, cement, additions, and admixtures [6]. Therefore, a decisive factor for designing advanced cementitious materials, such as self-compacting concrete (SCC), is a clear understanding of each constituent raw material's effect and interactions on the final product properties [7]. Additionally, the design and optimisation of such mixtures require intensive laboratory testing, particularly if new and unconventional supplementary cementitious materials or aggregates are incorporated [8], such as agricultural or industrial by-products [9]. Thus, a more scientific and multi-scale approach to mix-design is needed in which key mixture design variables can explain the composite properties [10].  
The Design of Experiments (DoE) is a systematic approach to understanding how process and product parameters affect response variables, such as processability, physical properties, or product performance. DoE uses statistical methodology to analyse data and predict product property performance under all possible conditions within limits selected for the experimental design [10]. From a literature survey, the DoE approach [11] has shown promise for aiding the understanding of the effect of mixture parameters on key fresh and hardened SCC properties. It can also facilitate the test protocol required to optimise SCC [12] or quantify SCC mixtures' robustness [6] to develop a more co-friendly SCC that incorporates different types of SCM and meets multiple performance requirements [3,13,14,15,16,17,18,19,20,21].