# Numerical Design and Optimisation of Self-Compacting High Early-Strength Cement-Based Mortars
## 1 Introduction
### Research Significance and Objectives  
Previous research shows that statistical models and numerical optimisation techniques allow for finding the best combination of self-compacting high-strength concrete (SCHPC)  
Figure 1: Mixture proportions of OVC and SCC (in % volume).  
constituents which (i) reduce the risk of cracking during the first days, ensuring a more impermeable concrete in the final structure [3]; (ii) study the influence of mixture parameters and their coupled effects on deformability, viscosity, compressive strength, resistivity and resistance to carbonation [15]; (iii) optimise chloride permeability and the strength of concrete containing metakaolin [22]; (iv) optimise the durability and service life of self-consolidating concrete containing metakaolin [19]; (v) optimise the mixture proportions and analyse the fresh and hardened properties [20]; and (vi) minimise the cost of the most unsustainable concrete components [21], including cost and sustainability indicators, in a reduced time [3,14,21,23]. These models and counterplot charts are beneficial for predicting and selecting the optimum mixture proportions for a given application simply and accurately.  
From a materials science point of view, self-compacting and high early-strength concrete mixes may be challenging because they contradict mixture design requirements and fresh-state properties. For example, a low water/binder ratio (w/b) is key to achieving high early strength [24]. However, it may also impact self-compacting ability, which is very sensitive to Vw/Vp.  
[PERSON] [25] carried out a full central composite design on self-compacting high early-strength cement-based mortars (SCHSCM) based on key mixture design parameters and described the target engineering properties, namely, self-compacting ability and high early-age strength. The key five SCHSM mixture parameters chosen were [25]: (i) Vw/Vc--water to cement volume ratio; (ii) Sp/p--superplasticiser to powder mass ratio; (iii) Vw/Vp--water to powder volume ratio; (iv) Vs/Vm--sand to mortar volume ratio; and (v) Vs/Vs--fine sand to total sand volume ratio to produce a total of 50 SCHSM mixtures. The current work aims at statistical analysis, model fitting, validation, and optimisation of the data experiments carried out by [PERSON] [25]. As such, combining the statistical design methods and regression analysis allowed for creating a model to mathematically describe the flow ability, viscosity, and flexural and compressive strength of SCHSCM. The models obtained were validated and used to optimise self-compacting mixtures with additional high early-age strength. The goal was to develop SCHSM with a minimum slump flow of 250 mm, flow time of 10 s, and compressive strength of at least 50 MPa at 24 h without any special curing treatment.  
The current work starts with a brief explanation of the data obtained by [PERSON] [25] in Section 2. The model's fitting and adequacy are detailed in Section 3, and Section 4 presents the optimisation of SCHSCM, considering the performance requirements established by the authors. Finally, Section 5 presents the main conclusions.